Observational Insights into White
Dwarf Planetary Systems
Laura Kathryn Rogers
Institute of Astronomy
University of Cambridge
This dissertation is submitted for the degree of
Doctor of Philosophy
Jesus College August 2022

To my astronomically amazing and supportive parents, Sue and Paul.

Declaration
I hereby declare that except where specific reference is made to the work of others, the
contents of this dissertation are original and have not been submitted in whole or in part for
consideration for any other degree or qualification in this, or any other university. I state
that except where specific reference is made in the text to the work of others, including
any collaborators, the contents of this dissertation are the result of my own work. This
dissertation contains fewer than 60,000 words including summary/abstract, tables, footnotes
and appendices.
Chapter 2 has been adapted from the publication: ‘Near-infrared variability in dusty
white dwarfs: tracing the accretion of planetary material’ L. K. Rogers, et al., MNRAS,
Volume 494, Issue 2, May 2020, Pages 2861–2874.
Chapter 4 has been adapted from work submitted to MNRAS: ‘Tracing the composition
of exoplanetary building blocks using seven polluted white dwarfs’ L. K. Rogers, et al. (2022,
submitted).
Laura Kathryn Rogers
August 2022

Abstract
Observational Insights into White Dwarf Planetary Systems
Laura Kathryn Rogers
In recent decades the number of known planets has escalated from the eight solar system
planets to over 5000 exoplanets; the focus has now shifted to their characterisation. Spec-
troscopic studies of white dwarfs ‘polluted’ by planetary material are a unique laboratory
allowing measurements of their bulk composition. This thesis focuses on these polluted
white dwarfs to observationally investigate how the material ultimately accretes onto the
white dwarfs, and the inferences made about the composition of exoplanetary bodies.
These white dwarfs become polluted due to the scattering of exoplanetary bodies on star
grazing orbits where they tidally disrupt, producing dusty debris detectable as excess infrared
emission, and then subsequently accrete onto the white dwarf. The scattering and accretion
are expected to be stochastic processes with variability predicted on human time-scales.
Chapter 2 reports near-infrared (JHK) monitoring campaigns of the dust emission with
the UKIRT/WFCAM and NTT/SOFI. Over timescales of hours, days, months, and years
no statistically significant variation is found. Chapter 3 reports spectroscopic monitoring
campaigns of the metal features in the white dwarfs using SALT/HRS and Magellan/MIKE.
Across more than 10 years and thousands of sinking timescales, no unambiguous statistically
significant variability in the amount of material in the photospheres of the white dwarfs is
found. Both results agree that the processes driving the accretion do so at a constant rate.
Polluted white dwarfs with infrared emission tend to be the most heavily polluted systems.
Chapter 4 presents the first composition studies from a novel programme which identifies
new heavily polluted white dwarfs discovered from their infrared excess. The planetary
material that polluted these seven white dwarfs are broadly consistent with rocky material, but
show some compositional and geological diversity. Some of the white dwarfs appear to have
accreted a fragment of a larger core-mantle differentiated body. Using oxygen budgeting,
two white dwarfs are discovered to have accreted oxygen-rich material which may imply
water-rich bodies. Also, evidence points towards one of the white dwarfs accreting material
from two distinct planetary bodies, this challenges the commonly used assumption that there
is one body in the white dwarf’s atmosphere at once.

Acknowledgements
I would firstly like to thank my wonderful supervisors, Amy Bonsor and Simon Hodgkin,
without which I would have never made it to the end of the PhD. Thank you for the endless
support and for always making time to help and encourage me during my PhD (and for
putting up with the endless silly questions). I will forever be grateful for Amy as my primary
advisor; she has been such a supportive, encouraging, and knowledgeable supervisor relating
to both research and life. I wish I could thank Amy a million times over, she has been such
an amazing role model and mentor and I will always look up to and aspire to be like her.
I am incredibly grateful for funding from the Science and Technology Facilities Coun-
cil which allowed me to pursue my dream of a PhD in astronomy. I would also like to
acknowledge funding from the University of Cambridge and Jesus College, Cambridge.
I am so grateful to my ‘unofficial’ supervisor, Siyi Xu; Siyi has supported me throughout
my PhD, her willingness to teach me and help me develop as a researcher has meant the
world to me and I am so grateful for her time, knowledge and patience, especially considering
the 11 hour time difference! I am so thankful to numerous members of the astronomical
community who have helped me throughout my PhD, but would especially like to thank:
Beth Klein, Ted von Hippel, and Patrick Dufour for their help and guidance.
I have loved learning about observing and have been very fortunate to gain lots of
observational experience during my PhD. I am incredibly grateful to Mike Shara and Ted
von Hippel for enabling me to obtain my very first data set using the HRS/SALT (reported in
Chapter 3). Thank you so much for your generosity, knowledge, and advice as I have learnt
infinite amounts from this project. I was also incredibly fortunate to go on an observing
trip to Chile with Anais Gonneau as part of my first accepted PI proposal, not only did I
learn lots from her, but we had such a wonderful time. I would also like to thank Claudia
Aguilera Gómez for teaching me all she knows about observations and for letting me watch
her remotely to observe.
I have thoroughly enjoyed my time as a PhD student at the IoA, and have especially
enjoyed the friendly and collaborative feel of the department. Thank you to everyone both
past and present for making the IoA such an amazing place to study for my PhD, even if
some of it was during a global pandemic! I have really appreciated the wealth of knowledge
xat the IoA and want to thank Mark Wyatt, Mike Irwin, and Matt Auger for always being
willing to answer my questions. I would distinctly like to thank Paul Hewett and Debbie
Peterson, I will be eternally grateful for their time, help and guidance. They both made it
possible and easy for me to continue and finish my PhD under difficult circumstances. My
PhD has been very unconventional, beginning full time and transitioning to part time after a
period of absence due to a head injury. However, the positive side of doing a PhD over 6
years meant that I got to overlap with 10 cohorts of amazing and inspiring PhD and Masters
students. It has been awesome sharing my time at the IoA with each and every one of them,
and I am so thankful for their support, friendships, and laughs. I would especially like to
thank all those who started their PhD at the same time as me, with special thanks to my
fellow polluted white dwarf enthusiast John, I learnt so much from John including the best
goalkeepers to pick for fantasy league. I would also like to thank the wonderful humans
from the years below who welcomed me into their years with open arms. I would especially
like to thank: Amy, Sophie, Anjali, Aoife, Chiara, Matthew, and Luis, your friendship and
support has been incredible. I also want to shout out to my numerous amazing office mates,
the white dwarf group, and the board games crews for always keeping me sane and happy.
I want to thank all my family and friends for their non-stop encouragement, care, and
love throughout this journey. I have chosen to dedicate my thesis to my amazing parents,
Paul and Sue, who have always shown me unconditional love and support. Thank you so
much for always being there for me, for encouraging me when I didn’t believe in myself,
and looking after me when I needed it most. To my amazing siblings Sarah, Matthew and
Sophie, thanks for always being there for me and I am so sorry for all the times you have had
to listen to me go on about astronomy! To my niece, Ella, thank you for always making me
smile, I love that you love the moon more than I do! To my friends outside of my PhD, thank
you so much for keeping me sane over these years and for the never ending love, laughs, and
support: Rosie, Kris, Thomas, Kitty, Georgia, and George, and to all my Jesus College and
Cambridge friends, thank you for making this such a memorable experience.
Finally, I want to thank my incredible partner, Dave. Life has been a roller coaster with
the PhD, head injury, and pandemic, but you have always been my calm constant that keeps
me grounded. You make me a better person and your love and support throughout the PhD is
something I am thankful for, far beyond words.
Table of contents
List of figures xv
List of tables xxv
1 Introduction 1
1.1 Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Rocky bodies in the solar system . . . . . . . . . . . . . . . . . . . 2
1.2 Exoplanets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 Discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.2 Characterisation . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 White dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.2 White dwarf properties . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.3 Spectral classification . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4 Polluted White Dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.1 How do the white dwarfs become polluted? . . . . . . . . . . . . . 17
1.4.2 Composition of polluting bodies . . . . . . . . . . . . . . . . . . . 18
1.4.3 Circumstellar Discs . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.4 The Link with the Main Sequence . . . . . . . . . . . . . . . . . . 33
1.5 This Thesis in Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2 Dust Variability 37
2.1 Dust variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.1 UKIRT Observations . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.2 Variability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.1.4 Conclusions from the UKIRT survey . . . . . . . . . . . . . . . . . 58
2.2 Dust variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
xii Table of contents
2.2.1 NTT Observations and data reduction . . . . . . . . . . . . . . . . 60
2.2.2 Variability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.2.4 Conclusions from the NTT/SOFI survey . . . . . . . . . . . . . . . 68
3 Metal line variability 71
3.1 Observations and Data Reduction . . . . . . . . . . . . . . . . . . . . . . . 72
3.1.1 Target Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.1.2 Spectroscopic observations . . . . . . . . . . . . . . . . . . . . . . 72
3.2 Variability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.3.1 WD 1929+011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.3.2 G29-38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.3.3 WD 0106−328 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.3.4 WD 0408−041 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.3.5 WD 1457−086 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4.1 Discussion of methods . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4.2 G29-38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.4.3 WD 0106−328 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.4.4 Accretion rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.4.5 White dwarf models . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.4.6 The link with circumstellar variability . . . . . . . . . . . . . . . . 99
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4 Tracing the composition of exoplanetary building blocks 103
4.1 Observations and Data Reduction . . . . . . . . . . . . . . . . . . . . . . . 104
4.1.1 Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.1.2 X-shooter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.1.3 HIRES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.1.4 MIKE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2 Modelling Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2.1 White Dwarf Parameters . . . . . . . . . . . . . . . . . . . . . . . 108
4.2.2 Line Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.2.3 Abundance of planetary material . . . . . . . . . . . . . . . . . . . 110
4.2.4 Interpreting the observed abundances . . . . . . . . . . . . . . . . 114
4.3 Results from individual systems . . . . . . . . . . . . . . . . . . . . . . . 118
Table of contents xiii
4.3.1 Gaia J0006+2858 . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.2 Gaia J0347+1624 . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.3 Gaia J0510+2315 . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.3.4 Gaia J0611−6931 . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3.5 Gaia J0644−0352 . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3.6 WD 1622+587 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.3.7 Gaia J2100+2122 . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.4 Comparing pollution in white dwarfs with and without detectable circumstel-
lar gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.4.1 Accretion rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.4.2 Metal abundances . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.5.1 Effects of uncertainties on elemental abundances . . . . . . . . . . 133
4.5.2 Volatiles in exoplanetary systems . . . . . . . . . . . . . . . . . . 134
4.5.3 Evidence for the accretion of multiple bodies? . . . . . . . . . . . . 135
4.5.4 Are high Ca/Mg ratios explained by the accretion of a high proportion
of refractory material? . . . . . . . . . . . . . . . . . . . . . . . . 136
4.5.5 Evidence for the formation of iron cores in exoplanetary systems . . 137
4.5.6 Magnetic field of WD 1622+587 . . . . . . . . . . . . . . . . . . . 138
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5 Conclusions and Future Work 141
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
References 147
6 Appendix 1: Additional tables and figures from Chapter 2 159
6.1 Observation Information . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.2 SEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7 Appendix 2: Additional tables and figures from Chapter 4 169
7.1 Spectral Energy Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.2 Spectral Lines and abundances . . . . . . . . . . . . . . . . . . . . . . . . 169
7.3 Equivalent Width Upper Limits . . . . . . . . . . . . . . . . . . . . . . . . 169
7.4 Model fits to spectral lines . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7.5 Bayesian output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

List of figures
1.1 Abundance ratio of element X to Mg, normalised to solar for compositions
of: CI Chondrites, bulk Earth, Earth’s mantle, and Earth’s core. Data are
from: McDonough (2003b); Grevesse et al. (2007). ∗ The core composition
is: 2/3 core and 1/3 mantle. . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 The relative abundance of X/Mg for bulk Earth (open circles) and classes of
carbonaceous chondrites (CM class is shown as filled circles, CV as filled
squares, and CO as open triangles), normalised to CI chondrites, plotted
against the log temperature at which 50% of the element would have con-
densed from a gas at 10−4 bar. The shaded regions defines the area covered
by the three carbonaceous chondrites classes. The volatility depletion trend
in bulk Earth and carbonaceous chondrites is clear. Figure from McDonough
(2003a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Orbital period versus planet mass for exoplanets with both measured/estimated
orbital period and mass. The colours highlight the different discovery meth-
ods. Figure using data from the NASA exoplanet archive1. . . . . . . . . . 8
1.4 A diagram highlighting the evolution of a solar mass star from the zero age
main sequence (ZAMS) to the white dwarf phase. Figure from Carroll &
Ostlie (2017). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5 Example spectra of white dwarf spectral types from LAMOST. Figure from
Gentile Fusillo et al. (2015). . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.6 A diagram to demonstrate the polluted white dwarf systems, taken from Jura
& Young (2014). The composition of the pollution in the atmosphere will
be discussed in Section 1.4.2 and the planetary debris will be discussed in
Section 1.4.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.7 Bar charts showing the pollutant mass fractions of: O, Mg, Si, Fe, C, for 19
polluted white dwarfs. The bulk compositions of the Earth and comet Halley
are shown on the left for comparison. Figure from Xu & Bonsor (2021). . . 22
xvi List of figures
1.8 The spectral energy distribution of G29-38. It shows the first infrared excess
discovered around a polluted white dwarf (Zuckerman & Becklin, 1987).
The data was taken using the NASA Infrared Telescope Facility. An excess
at near to mid-infrared wavelengths is clear. . . . . . . . . . . . . . . . . . 23
1.9 Spitzer/IRS spectrum of the dust around G29-38. The observed spectrum
was divided by a blackbody of temperature 930 K to give the black data
points. The best fitting linear combination of 12 minerals is plotted as the red
dashed line, to show the potential composition of the dust. The contribution
of each mineral is shown by the coloured lines (Reach et al., 2009). The
composition of this dusty material should match the composition of the
material polluting the star. Water ice, amorphous silicates and forsterites all
have distinguishable features in the mid-IR. . . . . . . . . . . . . . . . . . 24
1.10 The Ca II emission line profiles for WD 1226+110 from Gänsicke et al.
(2006). The double peaked profiles are clear, arising due to Keplerian
rotation. There are clear asymmetries in the red and blue Doppler shifted
lines, indicating the disc is eccentric. . . . . . . . . . . . . . . . . . . . . 26
1.11 Figure from Wyatt et al. (2014) showing model predictions for accretion
rate over time for 20 stars modelled to be similar to G29-38. Changes in the
accretion rate can be up to an order of magnitude over timescales of less than
a year. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.12 Figure from Swan et al. (2020) showing the mid-infrared variability observed
in a sample of ∼ 40 white dwarfs using the Spitzer space telescope. The
largest flux changes seem to occur over longer baselines with the largest
changes being those with circumstellar gaseous discs. . . . . . . . . . . . 29
1.13 A diagram from Rafikov (2011a) illustrating an interacting dust disc (black)
and gaseous disc (grey). The radial extent of the dust disc is defined on the
inner edge by the sublimation radius of solids and the outer edge by the
tidal disruption radius of the white dwarf. The gas disc has the same radial
extent as the dust, with a reservoir close to the white dwarf, feeding the
atmosphere with metallic gas. The movement of high metallicity materials is
demonstrated by the arrows. . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.14 This figure is taken from Bonsor et al. (2017). It demonstrates the accretion
rate plotted against the temperature of the white dwarfs. The plot has been
subdivided into four regions to explain the lack of observations of infrared
excesses around polluted white dwarfs. . . . . . . . . . . . . . . . . . . . . 33
List of figures xvii
2.1 A normalised histogram showing the distribution of photometrically cor-
rected magnitudes from the LIGHTCURVES software using all dithered
stacked frames for WD 1145+017. Each dithered stacked frame contains
5×10 second exposures. This white dwarf has 102 measurements in the K
band over 782 days. The Gaussian curve shows the median best-fitting Gaus-
sian, with a median magnitude of 17.467, and a median standard deviation
of 0.068 mags. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.2 The median observed magnitudes in the (a) J, (b) H and (c) K bands plotted
against the median standard deviation of this magnitude for all white dwarfs
and field stars. The two different observing modes, with 5 and 10 second
frame times, are analysed separately. The density plots on the left hand
side show the parameters for all field stellar objects in the field of view,
there are of the order 104 field stars in each plot. The blue points show the
white dwarfs, with the objects discussed in Section 2.1.2 labelled. The right
hand plots show the median magnitude and standard deviation with 16th
and 84th percentile confidence levels for field stars, in bins of width 0.5
mag. This forms a distribution about that median which should not comprise
contaminant variable stars. The white dwarfs are over-plotted in black with
the same values as in the left hand plots, but also including the 16th and
84th percentiles. This plot can be used to distinguish white dwarfs which are
variable from those that follow the field star distribution. . . . . . . . . . . 46
2.3 A lightcurve in the J, H and K bands for WD 1145+017. At each observation
date a number of observations were taken in the J, H and K bands, totalling 28
minutes. The dotted lines show the mean magnitude for each band calculated
from the first observation date, 02/05/15. This highlights how there was an
apparent dip on 09/05/17 in the flux in the J and H bands attributed to dust
transit features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4 A cumulative distribution showing the level of K band variability that can be
ruled out for the white dwarfs. The blue line shows the median cumulative
distribution, with the contours as the cumulative distribution on the upper
and lower limits (16th and 84th percentiles). For 90% of the sample, the K
band flux varied by less than 10%. . . . . . . . . . . . . . . . . . . . . . . 50
xviii List of figures
2.5 (a) The maximum K band median variability of each white dwarf that would
not have been detected over the time-scale of the survey. (b) The maximum
dust variability of each white dwarf that would not have been detected over
the time-scale of the survey. The variability constraint of the dust component
to the K band flux was calculated using equation 2.1. . . . . . . . . . . . . 53
2.6 Predictions for the maximum median variability at 4.5 µm that would have
escaped detection based on the maximum median K band variability not
detected with this UKIRT survey. The arrows represent that each axis is a
constraint on the level of variability. Most objects had Spitzer 4.5 µm data, but
for four objects WISE data was used as no Spitzer data was available. Swan
et al. (2019b, 2020) assessed the level of Spitzer and WISE mid infrared
variability at levels above these limits, future analyses that combine the
results from these studies are crucial for understanding these dusty white
dwarfs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.7 A lightcurve of WD 0408−041 showing the UKIRT K band data, and the
Spitzer/WISE data at which Farihi et al. (2018) observed a drop in the mid-
infrared flux. The grey regions represent the 1 and 3σ median variability
constraint for the K band, and then scaled up to Spitzer wavelengths using
equations 2.1 and 2.2 (assuming no colour change). The blue region shows
the period of time with UKIRT observations. Figure adapted from Farihi
et al. (2018). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.8 A histogram showing the characteristic survey sampling to search for vari-
ability. The plot shows the distribution of all time-scales between frames
of a given white dwarf, for all white dwarfs. This demonstrates that for all
white dwarfs the survey was sensitive to minute/hour time-scales and year
time-scales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.9 A toy model in which every white dwarf in the sample is considered to have
a K band flux that varies by ∆% every t days. The density plot indicates the
probability of detecting that combination of ∆ and t for white dwarfs in the
UKIRT survey. The smallest grid scale is 1 day and 0.1%. . . . . . . . . . 57
2.10 KS band measurements for the seven white dwarfs in the sample, all offset
by 0.2 mags. Observations were taken separated by hours and days. ∆K is
the output KS band magnitude subtracted from the median magnitude of the
lightcurve, such that > 0 is brighter than the median magnitude and < 0 is
fainter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
List of figures xix
2.11 The lightcurves of the four stars in the field of view of WD 1226+110 that
were used to perform differential photometry, each offset from one another.
∆K is the output KS band magnitude subtracted from the median magnitude
of the lightcurve, such that > 0 is brighter than the median magnitude and
< 0 is fainter. The median KS band magnitude of each comparison star is
labelled. The lightcurve labelled ‘offset’ is the calculated offset from the four
stars that was applied to the WD 1226+110 lightcurve to perform differential
photometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.12 K band lightcurve spanning ∼ 6 hours for WD 1226+110. ∆K is the output
KS band magnitude subtracted from the median magnitude of the lightcurve,
such that > 0 means WD 1226+110 is brighter than the median magnitude
and < 0 means it is fainter. The errors are large due to non-photometric
conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.13 Lomb-Scargle periodogram for WD 1226+110 using the lightcurve in Figure
2.12. The vertical dashed line shows the 123.4 minute period observed by
Manser et al. (2019) in the gaseous component of the disc for WD 1226+110.
The periodogram reveals two peaks at 0.011 days and 0.039 days but have
false alarm probabilities of 0.62 and 0.60 respectively and are unlikely to be
real. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.1 The Mg II 4481.125 Å spectral line from the MIKE/Magellan (blue) and
HRS/SALT (orange) spectra spanning more than a decade for WD 0106−328.
The spectra have been continuum normalised and are offset by 0.5. Spectra
with SNR < 10 are not plotted. . . . . . . . . . . . . . . . . . . . . . . . . 81
3.2 The Mg II 4481.125 Å spectral line from the MIKE/Magellan (blue) and
HRS/SALT (orange) spectra spanning more than a decade for WD 0408−041.
The spectra have been continuum normalised and are offset by 0.5. Spectra
with SNR < 10 are not plotted. . . . . . . . . . . . . . . . . . . . . . . . . 82
3.3 The Mg II 4481.125 Å spectral line from the MIKE/Magellan (blue) and
HRS/SALT (orange) spectra spanning more than a decade for WD 1457−086.
The spectra have been continuum normalised and are offset by 0.5. . . . . . 83
3.4 The Mg II 4481.125 Å spectral line from the MIKE/Magellan (blue) and
HRS/SALT (orange) spectra spanning more than a decade for WD 1929+011.
The spectra have been continuum normalised and are offset by 0.5. . . . . 84
xx List of figures
3.5 The Mg II 4481.125 Å spectral line from the MIKE/Magellan (blue) and
HRS/SALT (orange) spectra spanning more than a decade for G29-38. The
spectra have been continuum normalised and are offset by 0.15. Spectra with
SNR < 10 are not plotted. . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.6 The Ca II 3933 Å spectral line from the MIKE/Magellan (blue) for G29-38.
The spectra have been continuum normalised and are offset by 0.5. Spectra
with SNR < 10 are not plotted. . . . . . . . . . . . . . . . . . . . . . . . . 86
3.7 The Mg II (top), Ca II (middle), and Si II (bottom) equivalent width (EW)
measurements over time for WD 1929+011. Measurements from MIKE/Magellan
are reported as blue data points between 5000–6000 days, and measurements
from HRS/SALT are reported as orange data points after 7000 days. . . . . 87
3.8 Comparison of the equivalent width (EW) measurements from the MCMC
analysis on the MIKE/Magellan (M) and HRS/SALT (S) stacked spectra for
WD 1929+011. Markers represent different lines of Mg, Si, Fe and O with
their transition wavelength along the x axis. . . . . . . . . . . . . . . . . . 88
3.9 The Mg II doublet (top), Ca II K line (middle), and Mg I line, 5183.602 Å
(bottom) changes of equivalent width (EW) over time for G29-38. Mea-
surements from MIKE/Magellan are reported as blue data points between
5000–7000 days, and measurements from HRS/SALT are reported as orange
data points after 7000 days. . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.10 The stacked MIKE/Magellan and SALT/HRS data for the Mg II doublet
for WD 0106−328. The darker blue line is the MIKE/Magellan spectra
interpolated and convolved to the resolution of HRS/SALT. . . . . . . . . 92
3.11 The equivalent width of the Mg II doublet over time for WD 0106−328,
WD 0408−041, and WD 1457−086. . . . . . . . . . . . . . . . . . . . . . 94
3.12 (a) The best fitting model to the 2020-08-24 HRS/SALT spectrum of the Mg-
II doublet WD 1929+011. The best fitting Mg abundance is [Mg/H] = −4.25.
Models are plotted every 0.2 dex spreading to +/- 1 dex in [Mg/H]. Models
kindly provided by P. Dufour (Dufour et al., 2012). (b) The equivalent width
of the Mg II doublet over time for WD 1929+011. The equivalent width for
each model in (a) is plotted, showing the expected equivalent width values
for each [Mg/H] abundance. . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.13 The updated sinking timescales using 3D models including convection. The
1D sinking timescales reported in Table 3.2 are plotted for the three white
dwarfs in the temperature regime of interest. Figure adapted from Cunning-
ham et al. (2019) Figure 22. . . . . . . . . . . . . . . . . . . . . . . . . . . 99
List of figures xxi
3.14 The infrared fluxes of the white dwarfs with confirmed dust emission over
time. S1 and S2 are the Spitzer channels 1 and 2 with data from Swan et al.
(2020) (private communications). The K band data are from Rogers et al.
(2020), as reported in Chapter 2. The horizontal dashed lines are the median
values for each photometric band. . . . . . . . . . . . . . . . . . . . . . . 101
4.1 Model fits (red lines) to the Hydrogen Balmer line profiles from the X-shooter
spectra for Gaia J0006+2858, Gaia J0611−6931, and Gaia J2100+2122. The
best-fitting model parameters are labelled on each panel. Doubled peaked
emission lines from the circumstellar gas discs can be seen in the wings of
the hydrogen lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.2 Model fits (red lines) to the X-shooter Helium lines for Gaia J0644−0352.
The best-fitting white dwarf parameters and hydrogen abundance are labelled.
The green lines show the points used to re-normalise the spectrum to the
models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3 Model fits to the HIRES data using the average abundances for WD 1622+587.
Dashed orange line shows the model for a magnetic field of 0kG, and the
blue solid line shows the model for a magnetic field of 10kG. . . . . . . . 112
4.4 (a) [Mg/Ca] vs [Si/Ca] abundance ratios of the pollutant, normalised to
solar, derived from the spectroscopically determined white dwarf parameters.
The ellipses show a 1σ error ellipse on the abundance ratio. The Hypatia
catalogue (Hinkel et al., 2014) of nearby main sequence stars is plotted as
scatter points with a density histogram in the densest regions (around solar
values - dashed lines at 0, 0). The red arrows show how sinking in the
white dwarf atmosphere and heating affects the abundance ratios. Limits are
shown with arrows. (b) [O/Ca] vs [Fe/Ca] abundance ratios normalised to
solar, for reference the value of [O/Ca] normalised to solar for Bulk Earth is
-0.7. An additional red arrow describes how the [Fe/Ca] ratio changes as the
core-mass-fraction (CMF) of the planetary body is increased. . . . . . . . 115
4.5 The likely division of the observed oxygen abundance between metal oxides
(MgO, SiO2, Al2O3, CaO, and FeO) and water-ice (yellow), for Gaia J0611−6931
and Gaia 0644−0352. The approach is described in Section 4.2.4, using
abundances adjusted for sinking in steady-state. For Gaia J0611−6931 the
fraction of excess oxygen is 0.48, this excess oxygen is likely carried in
water-ice. For Gaia 0644−0352, the oxygen can all be accounted for in metal
oxides, and the pollutant was most likely dry and rocky. . . . . . . . . . . . 121
xxii List of figures
4.6 The number ratio of elemental abundances in the parent body relative to Mg,
normalised to solar (grey dash dot line). Abundances for the white dwarfs,
Gaia J0611−6931 and Gaia J2100+2122, are shown as green diamond and
black hexagon data points respectively, with 1σ errors, derived using the
spectroscopic temperature and log(g). Abundances have been adjusted for
sinking assuming steady state. The Fe/Mg for Gaia J0611−6931 lies 5.8σ
above solar, and for Gaia J2100+2122 the Fe/Mg value lies 3.2σ above solar;
both systems are enhanced in Fe compared to Mg. . . . . . . . . . . . . . . 123
4.7 The number ratio of elemental abundances in the pollutant material relative
to Mg, normalised to solar (dashed line). Observed abundances for the
white dwarf, Gaia J0644−0352, are shown as black points, with 1σ errors,
derived using the spectroscopic temperature and log(g). Sinking effects are
included in the model. The blue line represents the Bayesian model with
the maximum likelihood (max Z). The black line represents the maximum
likelihood median model with differentiation included and a 1σ error as the
shaded dark grey region. The body that was accreted by Gaia J0644−0352
may be mantle rich, but there is insufficient statistical evidence to include an
additional parameter in the model fit. The shaded light grey region indicates
the range of abundances seen in nearby stars using the catalogue from Brewer
& Fischer (2016). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.8 The accretion rates of polluted white dwarfs with and without detectable
gaseous discs in emission as a function of their effective temperatures. The
data for the accretion rates of polluted white dwarfs without circumstellar
gaseous discs are from Figure 3 in Xu et al. (2019), see reference for details.
The accretion rates for gaseous disc systems are from Table 4.4 including
the seven reported in this work. . . . . . . . . . . . . . . . . . . . . . . . 126
4.9 Single blackbody dust temperature for the dust emission from the literature
versus the [Ca/Mg] ratio, normalised to solar, of the pollutant body. Those in
this work are black squares, and those from the literature are grey. Horizon-
tal dashed grey lines show apparent condensation temperatures for Al, Ca,
Mg, Si and Fe (Lodders, 2003). The material polluting Gaia J0347+1624 is
depleted in moderate volatiles and has a composition most like Ca-Al–rich
inclusions, it is hypothesised that the material underwent incomplete conden-
sation during formation explaining the extreme [Ca/Mg]. Therefore the dust
surrounding Gaia J0347+1624 can survive to higher temperatures, and so the
dust emission has a hotter overall inferred blackbody temperature. . . . . . 127
List of figures xxiii
4.10 (a) Comparison of the [Si/Ca] against [Mg/Ca] composition of the material
that has polluted white dwarfs which have a detectable circumstellar gaseous
disc compared to those without. (b) Comparison of the [Fe/Ca] against
[O/Ca] composition. The grey ellipses show a 1σ , 2σ and 3σ error ellipse
based on solar abundances with Ca, Mg and Si errors of 0.1 dex. If a white
dwarf accreted material of solar abundance with typical errors of 0.1 dex, the
contours show the distribution of expected abundances. The arrows show
how the abundances are affected by: sinking in the white dwarfs atmosphere,
heating of the pollutant and increasing the core mass fraction (CMF). . . . 132
7.1 Spectral energy distributions for the seven white dwarfs. The X-shooter
spectra for the four white dwarfs observed are shown in grey, this is scaled
to fit the spectroscopic models as the spectra suffer from flux loss due to
non-ideal weather conditions and slit losses. There is a gap in the data
between 6360 Å– 6375 Å and telluric absorption features are present in the
reddest parts of the spectra. The photometric data points are given in black,
errors are plotted but are smaller than the data points. The photometric and
spectroscopic model fits are shown in orange (solid line) and blue (dashed
line) where available. Missing GALEX FUV or NUV fluxes implies either a
non-detection in that band, or the flux was flagged as it contained an artefact. 170
7.2 Model fits (red lines) to the HIRES data using the average abundances for
Gaia J0006+2858. There is additional non-photospheric absorption blue-
wards of the Ca II K line. . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7.3 Model fits (red lines) to the HIRES data using the average abundances for
Gaia J0347+1624. Silicon is shown for reference, the absorption is not
significant to 3σ and is therefore taken as an upper limit. . . . . . . . . . . 177
7.4 Model fits (red lines) to the HIRES data using the average abundances for
Gaia J0510+2315. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
7.5 Model fits (red lines) to the MIKE data using the average abundances for
Gaia J0611−6931. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.6 Model fits (red lines) to the HIRES data using the average abundances for
Gaia J0644−0352. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
7.7 Model fits (red lines) to the HIRES data using the average abundances
for Gaia J2100−2122. There is an additional non-photospheric absorption
bluewards of the Ca II K line. . . . . . . . . . . . . . . . . . . . . . . . . . 180

List of tables
2.1 The UKIRT sample of dusty polluted white dwarfs and their properties. H/He
column highlights the dominant element in the atmosphere. . . . . . . . . . 39
2.2 The resulting median magnitude and standard deviation found from the
Gaussian fits to the photometry from the UKIRT observations in the J, H
and K bands. The errors are quoted as the 16th and 84th percentiles from the
posterior distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3 The level of variability that can be detected at each magnitude in the K band,
calculated from the field stars. The objects which were observed with 5
and 10 second frames were analysed separately. The median percentage
variability is quoted for the field stars in bins with a width of one mag, along
with the 16th and 84th percentiles. . . . . . . . . . . . . . . . . . . . . . . 49
2.4 Observations of the white dwarfs listing the number of sets of JHK photome-
try obtained and the baseline for these observations. . . . . . . . . . . . . . 61
2.5 Table listing dates of observations for the white dwarfs in the sample, and
number of exposures. N comp is the number of comparison stellar objects in
the frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.1 The sample of polluted white dwarfs stating their effective temperature
and log(g) derived from a spectroscopic fit in previous works. The dust
column highlights whether they are confirmed to have an infrared excess
from circumstellar dust. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2 The pollution levels and sinking timescales for the sample of white dwarfs.
Sinking timescales interpolated from Koester et al. (2020). . . . . . . . . . 73
3.3 WD 0106−328 observation details. SNR determined from the continuum
around the Mg II line at 4481.125 Å as defined in Section 3.1.2. . . . . . . 75
3.4 WD 0408−041 observation details. SNR determined from the continuum
around the Mg II line at 4481.125 Å as defined in Section 3.1.2. . . . . . . 75
xxvi List of tables
3.5 WD 1457−086 observation details. SNR determined from the continuum
around the Mg II line at 4481.125 Å as defined in Section 3.1.2. . . . . . . 76
3.6 WD 1929+011 observation details. SNR determined from the continuum
around the Mg II line at 4481.125 Å as defined in Section 3.1.2. . . . . . . 76
3.7 G29-38 observation details. SNR determined from the continuum around the
Mg II line at 4481.125 Å as defined in Section 3.1.2. . . . . . . . . . . . . 77
3.8 The median equivalent width (mÅ) and error for the HRS/SALT (S) data and
the MIKE/Magellan (M) data obtained from the stacked spectra for the Mg
II doublet at 4481.125 Å. . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.9 The median equivalent width and error for the stacked HRS/SALT (S)
data and the MIKE/Magellan (M) data for weaker lines for WD 0106−328,
WD 1929+011, and G29-38. . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.10 The inferred accretion rates assuming a bulk Earth composition for the best
fitting [Mg/H] abundance for the 2020-08-24 data set (−4.25, in italics), and
for abundance +0.2, +0.4, −0.2, and −0.4 dex from the measure [Mg/H]
value. Macc, 10 yrs reports the mass of material that would accrete over a 10
year baseline. Assuming the abundance in the photosphere changed from
[Mg/H] = −4.25, ∆Macc, 10 yrs reports the change in mass between the new
[Mg/H] value and [Mg/H] = −4.25 that would accrue over 10 years, reported
as a fraction of the mass of Ceres, a dwarf planet in the asteroid belt, and the
fraction of the mass of Comet Halley. . . . . . . . . . . . . . . . . . . . . 96
3.11 Infrared variability from previous studies. The K band data is from Rogers
et al. (2020) where the variability measure is an upper limit that corresponds
to the measurement limit of the observations. The Spitzer data are from
Swan et al. (2020) showing the percentage change and significance of the data.100
4.1 Stellar parameters derived from the spectroscopic (spec) and photometric
(phot) fitting methods. Distances (D) are inferred from Gaia parallaxes. . . 104
4.2 Observations of the seven white dwarfs listing dates of observations, exposure
times in seconds, and SNR as defined in Section 4.1.2. The SNR for X-
shooter UVB, HIRESb and MIKE-blue were calculated from the continuum
around the Ca II K line (3933.7Å). The SNR for X-shooter VIS, HIRESr and
MIKE-red were calculated from the continuum around 6600Å. . . . . . . . 105
List of tables xxvii
4.3 Number abundances (log n(Z)/n(H(e)) of the pollutant material using the
photometric and spectroscopic white dwarf parameters separately. For the
derivation of the upper limits and the analysis of the abundances the spectro-
scopic solutions are used. Photometric abundances for Gaia J0510+2315 are
less reliable and are quoted in brackets. . . . . . . . . . . . . . . . . . . . 106
4.4 Total accretion rates based on Mg abundances for white dwarfs with an
observable gaseous disc with emission features. This is calculated us-
ing M˙ = (100/15.8)×MWD×10q×10[Mg/H(e)]×AMg/H(e)/τMg, where q=
log10(MCVZ/MWD), AMg/H(e) is the atomic mass of Mg divided by the atomic
mass of H or He, depending on the dominant atmospheric (atm) constituent,
and τMg is the sinking time of Mg. . . . . . . . . . . . . . . . . . . . . . . 130
6.1 All the polluted white dwarfs with an infrared excess observed with the
UKIRT and the dates they were observed. . . . . . . . . . . . . . . . . . . 160
6.2 All the polluted white dwarfs with an infrared excess observed with the
UKIRT survey and the total number of frames. Each frame consists of a
dithered stack of 5 exposures, each with the corresponding frame time of 5
or 10 seconds. FT = frame time for each individual exposure in the dithered
stack, FN = total number of dithered stacks over all observations. . . . . . . 167
7.1 The absorption lines in Gaia J0006+2858. If two lines lie within ∼ 10 Å,
equivalent widths and abundances were fitted simultaneously. . . . . . . . 171
7.2 The absorption lines measured in the HIRES spectrum of Gaia J0347+1624.
There are also Na D lines at both 5890 Angstrom and 5896 Angstrom.
However, in checking the ISM model, this line of sight intercepts LIC (RV of
22.36 km/s) and Hyades (RV of 14.16 km/s). This is close to the measured
RV of 15 km/s so it is deduced that these lines are not photospheric. . . . . 171
7.3 The absorption lines in the HIRES spectra of Gaia J0510+2315. If two lines
lie within ∼ 10 Å, equivalent widths and abundances were fitted simultane-
ously. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.4 The absorption lines in Gaia J0611−6931. If two lines lie within ∼ 10 Å,
equivalent widths and abundances were fitted simultaneously. . . . . . . . 173
7.5 The absorption lines in Gaia J0644−0352. If two lines lie within ∼ 10 Å,
equivalent widths and abundances were fitted simultaneously. . . . . . . . 174
7.6 The absorption lines measured in the WD 1622+587 HIRES spectra. If
two lines lie within ∼ 10 Å, equivalent widths and abundances were fitted
simultaneously. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
xxviii List of tables
7.7 The absorption lines measured in Gaia J2100+2122. If two lines lie within ∼
10 Å, equivalent widths and abundances were fitted simultaneously. . . . . 175
7.8 The upper limit equivalent widths in mÅ of the material polluting the seven
white dwarfs in this study. ∗ denotes when gaseous emission is present at
this wavelength. When calculating abundance upper limit, add 12 percent
onto the equivalent width quoted to be conservative. . . . . . . . . . . . . 176
7.9 The resulting median parameters from the Bayesian models, errors are given
as 16th and 84th percentiles. A description of the parameters is presented in
Section 4.2.4. The basic model uses a best-fitting initial stellar composition,
‘Stellar metallicity’; this is omitted from this table as most white dwarfs are
equally likely to have accreted material that started with a wide range of
initial compositions. The pollution fraction and the most likely accretion
phase: build up (BU), steady state (SS) or declining phase (DP) are output for
the basic primitive model. Italics represent optional complex parameters that
are only invoked when the Bayes factor is > 1. The fragment core fraction
(fcf) is quoted based on number fraction, and in brackets mass fraction, which
is calculated assuming the output core and mantle composition of the median
Bayesian model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Chapter 1
Introduction
Astronomy has entered the era of large observational surveys, providing us with unprece-
dented information about the Universe, and our place within in. Exoplanets are now known
to be ubiquitous with planets predicted to outnumber stars in the Milky Way (Cassan et al.,
2012). Over the last few decades the field of exoplanetary science has rapidly developed
with the focus shifting away from discovery and towards the characterisation of exoplanets
and exoplanetary populations. Key questions driving the field are: what are the compositions
of exoplanets? How similar are exoplanet compositions and system architectures to that
of the solar system? Do other planetary systems have the conditions to develop extrater-
restrial life? White dwarfs are unique laboratories that can contribute to studying these
questions. Between 25–50% of white dwarfs have accreted planetary material from their
remnant planetary systems (Zuckerman et al., 2003, 2010; Koester et al., 2014; Wilson et al.,
2019). Spectroscopic observations of these white dwarfs reveal the bulk composition of
the exoplanetary material accreted. This is the only observational method to directly infer
exoplanetary interior composition. These polluted white dwarf systems and what they reveal
about the composition of exoplanetary material is the focus of this thesis. This chapter will
first introduce the knowledge gained from studying planetary composition and architecture
of the solar system, then will discuss this in relation to exoplanets, and finally will combine
these topics to introduce white dwarfs and their remnant planetary systems.
1.1 Solar System
Before the 1990s, the solar system was the only planetary system known. Therefore, research
on planets concentrated on the solar system planets and small bodies consisting of the four
terrestrial bodies: Mercury, Venus, Earth and Mars, the four gas giants: Jupiter, Saturn,
Uranus and Neptune; and the small bodies: asteroid belt, Kuiper-belt, Oort cloud and their
2 Introduction
various constituents. The solar system formed from a collapsing cloud of dust and gas around
4.567 billion years ago forming the proto-Sun with an orbiting disc of gas and dust (Connelly
et al., 2012). The first solids condensed out of the protoplanetary nebula which constituted
the building blocks for the planets. The process of planetesimal formation is an extensive
field of scientific research, for further details refer to the review by Raymond & Morbidelli
(2022). Although the solar system is the only planetary system where planetary material can
be directly sampled, numerous open questions regarding the formation and evolution of the
solar system remain.
1.1.1 Rocky bodies in the solar system
Small bodies
Meteorites are debris from outer space that survive the journey through the Earth’s at-
mosphere to land on the surface. Laboratory measurements reveal their composition and
structure and thus gives insight into solar system formation, composition, and evolution. The
main classifications of meteorites are chondritic and achondritic. Chondritic meteorites are
primitive asteroids that contain the earliest solids and consequently define the age of the
solar system as 4.567 billion years (Connelly et al., 2012). They provide the abundances of
the material that condensed to form the solar system constituents, which provides powerful
information about the formation of planetary bodies. Achondritic meteorites have undergone
geological and collisional processing (melting and core–mantle differentiation, which are
discussed in more detail in the following section). These meteorites include those from the
asteroid belt, Mars, and the Moon, and can consequently reveal the formation and internal
structure of the terrestrial planets (Mittlefehldt et al., 1998; Weisberg et al., 2006).
Chondritic meteorites are composed of: chondrules, refractory inclusions (0.01—10 %
volume), metallic Fe and Ni (<0.1—70% volume), and are surrounded by a fine-grain matrix
(1—80% volume). Chondrules are millimeter sized particles that form by the melting of
material in the solar nebula, which are subsequently deposited onto the mid-plane of the
protoplanetary disc with other particles. Chondrules are mostly composed of olivine and
pyroxene minerals which have crystallised rapidly between temperatures of ∼ 1800 and
1300 K (Scott, 2007). Refractory inclusions are crystalline silicates and oxides which form at
high-temperatures (> 1300 K) from processes such as melting, evaporation and condensation.
The inclusions consist of calcium-aluminium rich inclusions (CAI’s) and amoeboid olivine
aggregates (AOA). Fe and Ni metallic grains can be present both within and outside of
chondrules. Similar to chondrules and inclusions they also form at the highest temperatures.
1.1 Solar System 3
The fine-grain matrix material contains volatile-rich minerals, which fills the space between
the other constituents of the chondritic meteorite (Alexander et al., 2018).
The three major classes of chondrites are: carbonaceous, ordinary, and enstatite. These
classes are sub-divided into 15 groups with variations that are categorised by chondrule sizes,
the quantity and composition of the refractory inclusions, the amount of metallic iron and
nickel, and the relative fraction of mineral matrix (Bizzarro et al., 2017). Carbonaceous
chondrites contain a significant fraction of volatiles, including carbon, and are thought to
originate furthest from the Sun, they account to 5% of known meteorites. The CI group of
carbonaceous chondrites have a composition most similar to the solar photosphere, as seen in
Figure 1.1, and chemically are the most primitive group of meteorites. Ordinary chondrites
are most common, consisting predominantly of chondrules, with small components of
refractory inclusions, Fe, Ni metals, and matrix. The rarest are enstatite which account to
2% of known meteorites, which contain a significant fraction of the mineral enstatite with
Fe taking the form of metallic-Fe rather than oxides. Enstatites likely formed in reduced
environments close to the proto-Sun.
Meteorites are thought to be the result of the fragmentation of asteroids that fall to
Earth. Understanding how the classes of meteorites link to classes of asteroids has been
subject to intensive study as their connection and properties can inform about the history
and evolution of the solar system. Asteroids have experienced significant dynamical and
collisional evolution which affects their composition, size, shape, rotation and location;
making it difficult to model the evolution of the small bodies. Asteroids are defined based
on their albedo and spectral features. C-class (carbonaceous) asteroids are thought to be the
precursors to carbonaceous chondrite meteorites and are typically associated with the outer
asteroid belt, they have low albedos and can contain up to 10% water by mass. Whereas, the
S-type (stony) asteroids have much higher albedos, have spectral signatures of silicates and
are dry with less than 0.1% water by mass, these asteroids are believed to be associated with
the ordinary chondrite class of meteorites. (Michel et al., 2015; Alexander et al., 2018). The
asteroid belt contains a mixture of both volatile-poor asteroids (S-type) in the inner regions
and volatile-rich asteroids (C-type) in the outer regions. Originally it was hypothesised that
this was due to the ice lines and formation conditions, but abundance and isotopic studies
revealed these asteroids formed in different reservoirs (Warren, 2011; Budde et al., 2016;
Kleine et al., 2020). Significant progress has been made modelling the solar system formation
and evolution, but no proposed model is able to explain all observations in the solar system,
including how the asteroid belt became a mix of two distinct reservoirs of small bodies (e.g.
Raymond & Morbidelli, 2022).
4 Introduction
Al Ti Ca Ni Fe Cr Si Na O
−1.0
−0.5
0.0
0.5
1.0
[X
/M
g]
-
[X
/M
g]
¯
Solar
Bulk Earth
CI Chondrites
Earth Mantle
Earth Core*
Fig. 1.1 Abundance ratio of element X to Mg, normalised to solar for compositions of:
CI Chondrites, bulk Earth, Earth’s mantle, and Earth’s core. Data are from: McDonough
(2003b); Grevesse et al. (2007). ∗ The core composition is: 2/3 core and 1/3 mantle.
1.1 Solar System 5
Core–mantle differentiation
The Earth has an iron rich core and is surrounded by an iron poor mantle. These layers are
key to the Earth being habitable and maintaining habitable conditions over time. The molten
Earth’s core generates a magnetic field which is crucial for shielding the Earth from harmful
solar winds. The mantle and crust result in tectonic activity which regulates the temperature
and atmospheric conditions of the planet, for example, by regulating the quantities of carbon
dioxide in the atmosphere via the carbon cycle, thus keeping the temperature stable.
Core–mantle differentiation is the process by which melting causes siderophilic (‘iron
loving’) elements to separate and sink towards the centre of the body, and lithophilic (‘rock
loving’) elements to go towards the surface of the body where they can combine readily with
oxygen. In order to melt the material such that core–mantle separation can occur, a heat
source is required. For larger bodies greater than ∼ 1500 km, the release of gravitational
potential energy during formation can result in large scale melting and differentiation into a
core and mantle. However, in the solar system the decay of 26Al is required to form cores in
asteroids as they are not massive enough to generate heat via gravitational potential energy.
Modelling indicates that for planetesimals greater than ∼ 20 km in diameter, 26Al heating
could cause melting and core formation (Hevey & Sanders, 2006; Elkins-Tanton, 2012).
Terrestrial planets
The terrestrial planets in the inner solar system are all composed of silicate material and
metals (e.g. iron). All four terrestrial planets are differentiated and have a core component
and a mantle/crust component. Differentiation into core and mantle is expected to have
occurred early in the formation of terrestrial bodies as the gravitational potential energy
released upon accretion was significant enough to melt their interior. The mass fraction of
the metallic core in Mercury, Venus, Earth, and Mars decreases as a function of distance
from the Sun from approximately 3/4, to 1/3 (Venus and Earth), to 1/5, respectively (Sohl &
Schubert, 2007).
The structure and composition of the Earth’s interior has been subject to extensive studies.
For example, measuring the velocities of seismic waves propagating through the Earth reveals
the density profile and therefore layered structure of the Earth; and studying rock samples
from the crust and upper mantle reveals the composition of the outer layers of the Earth. The
best estimate of the bulk constituents of the Earth by mass is: 32% iron, 29.7% oxygen, 16.1%
silicon, 15.4% magnesium, 1.82% nickel, 1.71% calcium, 1.59% aluminium, plus others in
smaller amounts (McDonough, 2003b). The core of the Earth is enhanced in siderophilic
elements, such as iron and nickel, and the mantle of the Earth is depleted in siderophilic
6 Introduction
Fig. 1.2 The relative abundance of X/Mg for bulk Earth (open circles) and classes of carbona-
ceous chondrites (CM class is shown as filled circles, CV as filled squares, and CO as open
triangles), normalised to CI chondrites, plotted against the log temperature at which 50% of
the element would have condensed from a gas at 10−4 bar. The shaded regions defines the
area covered by the three carbonaceous chondrites classes. The volatility depletion trend in
bulk Earth and carbonaceous chondrites is clear. Figure from McDonough (2003a).
1.2 Exoplanets 7
elements, as can be seen in Figure 1.1. The bulk composition of the Earth, disregarding
volatiles, matches that of the most primitive meteorites, CI chondrites, as seen in Figure 1.1.
These meteorites are assumed to be the building blocks of the Earth, although exactly which
is debated.
The volatiles, especially water, significantly contributed to the Earth becoming a habitable
planet. Figure 1.2 shows the volatility depletion trend in bulk Earth. The chemical composi-
tion of the Earth was largely inherited from the condensation and accretion of nearby material
in the protoplanetary disc. The standard model of the disc which the solar system formed
has the snow line at 2.7 au (Hayashi, 1981), the Earth formed within this line so appears to
have formed dry. However, water is present on the Earth with a mass fraction of ∼ 0.1%,
greater than would be expected based on its formation location (Van Dishoeck et al., 2014).
It is actively debated as to whether the volatiles were already present on Earth or whether
volatile-rich bodies were later accreted. If they were later accreted, it is thought that volatile
delivery from icy planetesimals is crucial for the present day levels of water on Earth (Wänke,
1981; McDonough, 2003a; Ballhaus et al., 2013; Yoshizaki & McDonough, 2021). The
ratio of deuterium, a stable isotope of hydrogen, to hydrogen ([D/H]) is a useful diagnostic
of where in the solar system objects formed as the [D/H] ratio changes depending on the
location in the protoplanetary disc the bodies originated from (Hallis, 2017). Therefore, the
[D/H] ratio can be used to investigate what bodies contributed to seeding the Earth with water
and where in the solar system they originated from. The [D/H] ratio of the outer asteroid
belt and the Kuiper belt have similar values to the Earth’s oceans and as they also have high
fractions of water, it is hypothesised that these reservoirs significantly contributed to water
delivery on Earth and the terrestrial planets (Van Dishoeck et al., 2014). Instabilities which
cause mixing of the different reservoirs are pivotal for understanding of the solar system
evolution and volatile delivery, for further discussions see (Raymond & Morbidelli, 2022).
1.2 Exoplanets
1.2.1 Discovery
It wasn’t until the 1990s that the first exoplanets were discovered (e.g. Wolszczan & Frail,
1992). The confirmation of exoplanets gauged much interest and excitement worldwide as
people began to wonder what these other worlds are like, could they potentially be habitable
and host life, and ultimately whether we are alone in the universe.
The advancement of modern technology has expanded our knowledge immensely; to date,
over 5,000 exoplanets have been discovered, Figure 1.3 shows the exoplanets discovered
8 Introduction
100 102 104 106 108
Period (days)
10 1
101
103
M
as
s (
Ea
rth
 M
as
se
s)
Transit
Radial Velocity
Imaging
Microlensing
Pulsar Timing
Pulsar Timing
Fig. 1.3 Orbital period versus planet mass for exoplanets with both measured/estimated
orbital period and mass. The colours highlight the different discovery methods. Figure using
data from the NASA exoplanet archive1.
1.2 Exoplanets 9
thus far1. Exoplanets appear to be ubiquitous and outnumber stars in the Milky Way (Cassan
et al., 2012). The first exoplanets discovered were around a millisecond pulsar, found using
precise timing measurements of the pulses (Wolszczan & Frail, 1992). Following this, the
first exoplanet discovered around a Sun-like star was 51 Pegasi b (Mayor & Queloz, 1995),
a Jupiter mass planet discovered with the radial velocity technique. The radial velocity
technique detects the presence of an orbiting companion from the Doppler shift in the stellar
spectral lines. The star and planet orbit the common centre of mass; if the stellar mass is
known, the minimum mass of the planet can be inferred (Fischer et al., 2015). Despite the
successes of these two detection methods delivering the first exoplanet discoveries, more
than three quarters of exoplanets were discovered with the transit technique.
The transit technique photometrically monitors a star; as a planet passes in front of the
stellar disc a flux drop proportional to the relative sizes of the star and the planet is observed.
This method provides information on the radius of the planet, assuming the radius of the star
is known, and constrains the inclination of the orbit. The first exoplanet transit detection
was around HD 209458, where radial velocity measurements had previously confirmed an
orbiting planet (Charbonneau et al., 1999). Other techniques have been employed to detect
exoplanets, such as, direct imaging, microlensing, and astrometry. The current detection
statistics are low, but with technology developments, current (e.g. Gaia, Collaboration et al.,
2016) and future space missions (e.g. LIFE, Quanz et al., 2021), as well as the upcoming
ground based extremely large telescopes, many more planets are expected to be discovered
with these methods.
Figure 1.3 shows the exoplanets discovered so far with the regions in parameter space
that these techniques are most sensitive to clearly standing out. The success of the Kepler
and TESS space missions significantly contributed to the discovery of transiting exoplanets
(e.g. Borucki et al., 2010; Guerrero et al., 2021), which has allowed the field of exoplanet
demographics to flourish (e.g. Batalha, 2014). The transit technique is sensitive to larger
planets, on close in orbits as this increases the transit depth and the probability of the transit
(as the star and planet must be aligned). The radial velocity technique is sensitive to more
massive planets on shorter orbits, as these produce larger amplitude signals and multiple
orbital periods can be measured. With current and future generations of higher-resolution
and higher-stability instruments, radial velocity surveys can push to discover Earth mass
planets around Sun like stars. However, stellar activity signals now dominate the noise so in
order to discover planets that are increasingly lower in mass and on longer orbital periods,
stellar variability needs to be better understood and quantified (e.g. Rajpaul et al., 2015;
Vanderburg et al., 2016; Nava et al., 2019). Direct imaging is most sensitive to planets on
1Data from: https://exoplanets.nasa.gov/discovery/discoveries-dashboard/ on 26/07/2022
10 Introduction
wide (> 5 au) orbits, the best targets tend to be those that are young and massive as these
are self-luminous due to heat from formation. The photons from the planet are directly
measured demonstrating the power of this technique as these planets can be studied both
photometrically and spectroscopically. Exoplanets detected via microlensing events happen
when a background object becomes aligned with an intermediate star with an orbiting planet.
The star and planet act as a lens and cause brightening of the background source. This
technique does not depend as strongly on planetary mass so has a wide discovery space
which includes free-floating planets (Gaudi, 2012).
1.2.2 Characterisation
With the number of exoplanet discoveries increasing everyday, the research focus has shifted
towards their characterisation. The field of characterisation is focused on the composition of
their interior and atmosphere, and the potential of these worlds to be habitable.
To constrain a planet’s bulk composition, measurements of its mass and radius are
required. The first exoplanet characterised in this way was HD 209458, radial velocity
measurements provided a minimum planetary mass (M sin i), and transit photometry provided
the inclination (i), resulting in the determination of the true planetary mass. The combined
mass estimate from the radial velocity technique with the radius estimate from the transit
technique provides an estimate for the average density of the exoplanet, the average density
was low and due to its size it was designated a gas giant (Charbonneau et al., 1999), therefore
beginning the era of exoplanet characterisation.
Theoretical mass-radius relationships derived from interior models can be compared to
derived mass and radii of exoplanets to infer the interior structure of the exoplanets. Various
compositions and interior structures can be invoked in the models, for example, the models
can be in the form of a single composition, e.g. 100% Fe, or 100% H/He; or multi-layered
composition with combinations of: Fe core, MgSiO3 mantle, H2O layer; or more exotic
compositions (e.g. Seager et al., 2007; Dorn et al., 2015). However, degeneracies arise as
different compositions can produce similar mass-radius curves, thus introducing uncertainties
in the determination of bulk compositions. In order to more accurately determine the
bulk composition of these bodies, additional input information or alternate measurement
techniques are required.
The study of exoplanet atmospheres reveals information about the outer layers of an
exoplanet (e.g. Crossfield, 2015; Madhusudhan, 2019). Over the coming decades the study
of exoplanetary atmospheres will be a key focus of the field. For transiting planets, the
opacity of the atmosphere varies with wavelength due to its composition, and measuring the
transit depth as a function of wavelength, the ‘transmission spectrum’, can reveal information
1.3 White dwarfs 11
about its atmospheric composition. Transiting planets are also eclipsed by their host star,
subtracting the spectrum of the star alone from the combined star and planet spectrum, reveals
the thermal ‘emission spectrum’ of the planet. Current space missions such as Hubble and
JWST have been revealing the spectrum of increasingly smaller planets. Directly imaged
planets allow direct spectroscopy without contamination from the stellar spectrum to reveal
their thermal emission spectra. With plans for future large telescopes e.g. LUVOIR, LIFE
missions, this technique will enable characterisation of non-transiting planets, not possible
via other methods and on longer period orbits.
With increasing amounts of data and computing power, the field of exoplanet characteri-
sation is moving towards a combined approach, where models and results from sub-fields are
combined to gain a global understanding of individual exoplanets, for example, interior and
atmospheric coupling (e.g. Madhusudhan et al., 2020). The study of exoplanet atmospheres
reveals the bulk properties of exoplanets (e.g. planetary mass, radius, atmospheric proper-
ties), these can be input into exoplanet interior models to constrain the internal structure and
thermodynamic conditions. Continued efforts to combine observations and computational
techniques from sub-fields will help to piece together what these other worlds are like.
1.3 White dwarfs
1.3.1 Formation
White dwarfs are the final product of stellar evolution for stars with an initial main sequence
mass in the range 0.07 to 8 M⊙. It is predicted that as the Milky Way ages more than 97%
of the stars will eventually evolve to white dwarfs (Fontaine et al., 2001). Figure 1.4 shows
how a solar mass star evolves from the zero age main sequence (ZAMS) to the white dwarf
phase. On the main sequence, stars burn hydrogen to helium via the proton-proton chain,
building up helium in their core. Stars spend ∼ 90% of their lifetimes on the main sequence.
Once hydrogen fusion in the core ceases, the central temperatures are not sufficient to ignite
helium fusion, however, the hydrogen shell surrounding the core reaches the temperature and
pressure required for proton-proton chain fusion, and hydrogen shell burning commences.
The stellar envelope expands, cooling the star and increasing the luminosity, positioning the
star on the sub giant branch (SGB). As the shell burns hydrogen to helium, helium is dumped
onto the core, increasing its mass and eventually the helium core becomes degenerate. The
stellar envelope continues expanding causing a rapid increase in luminosity and it travels
up the red giant branch (RGB). Due to the larger temperature gradients, energy transport
is via convection rather than radiation. This causes large convection zones which dredges
12 Introduction
Fig. 1.4 A diagram highlighting the evolution of a solar mass star from the zero age main
sequence (ZAMS) to the white dwarf phase. Figure from Carroll & Ostlie (2017).
1.3 White dwarfs 13
up material that has been modified by nuclear processes - the first convective dredge up.
Helium continues to be produced and dumped onto the core, and as the core is degenerate, the
increased mass causes core contraction. Eventually the conditions in the core are sufficient
for helium to fuse via the triple alpha process; this causes the helium flash. The core expands
and is no longer degenerate, so helium core burning and hydrogen shell burning occurs as the
star settles onto the horizontal branch (HB). The HB is the equivalent of the hydrogen burning
main sequence for helium burning, except the lifetime is much shorter due to the higher
luminosity. Once the star has exhausted helium in the core, the core contraction results in a
degenerate core consisting of C and O. The temperature is not sufficient for C and O to burn
in the core, but the core contraction generates sufficient energy that helium and hydrogen
shell burning can occur. The outer layers of the star expands and luminosity increases moving
it up the asymptotic giant branch (AGB) to transition to a red super-giant. Instabilities in
the burning shells result in thermal runaways driving thermal pulses which cause the outer
layers of the star to be ejected producing a planetary nebula. The remnant stellar core has
insufficient gravity to fuse so becomes a carbon-oxygen white dwarf supported entirely by
electron degeneracy pressure. The average mass of a white dwarf is ∼ 0.6 M⊙ with radii
similar to that of the Earth. They form extremely hot (>100,000 K) and radiate as they fade
over long cooling times, τcool:
τcool ∝ L−5/7, (1.1)
where L is their luminosity (Mestel, 1952; Van Horn, 1971). This demonstrates the connection
between a white dwarfs age and its temperature, with the coolest systems being the oldest.
Consequently, white dwarfs can be used to constrain the ages of stellar populations in the
Milky Way (e.g. Fontaine et al., 2001). It is expected that white dwarfs will eventually cool
and fade into a black dwarf (Adams & Laughlin, 1997).
1.3.2 White dwarf properties
White dwarfs are powerful laboratories to study numerous aspects of physics and astrophysics,
including: degenerate states of matter, age history of stellar populations in the Milky Way, and
the bulk composition of exoplanets. However, without knowledge of the stellar properties,
this work is not possible. The following discussion focuses on the determination of the
effective temperature and log(g). There are two main methods to observationally determine
these parameters: the spectroscopic method and the photometric method.
The spectroscopic method fits white dwarf models to the H/He lines in their spectrum. The
cores of white dwarfs are made of degenerate matter due to the high pressures (∼ 106 g cm−3),
this electron degeneracy pressure prevents the further collapse of the core. These degenerate
14 Introduction
C-O cores are surrounded by a layer of non-degenerate gas, most often He, with a thin H
layer on top. Therefore, the spectra of most white dwarfs exhibit only absorption lines from
hydrogen and/or helium, and these absorption lines are pressure broadened by a variety of
mechanisms. For example, the Stark Broadening Effect; due to the extreme temperatures,
the envelopes of the white dwarfs are often ionised, these moving charges give rise to local
electric fields. As a consequence of the extreme densities, the neutral emitters feel the
presence of the electric field which results in the shifting of energy levels via the Stark
Broadening Effect (Stark, 1913), one of the main causes of the broadening of the spectral
lines in the temperature range of interest in this thesis (> 15,000 K). The profiles of the
Balmer lines, and optical helium lines are very sensitive to temperature, therefore, comparing
the observed H/He absorption profiles with those predicted from theoretical models, the
white dwarf parameters can be determined, this is the spectroscopic method (e.g. Holberg
et al., 1985; Bergeron et al., 1992, 2011).
The photometric method fits white dwarf models to broad band photometry. For this
method, the white dwarf models are convolved with the band-passes of the photometric
filters and are fitted to the broad band photometry. Combining the parallax to give the
distance, theoretical mass-radius relations, and the synthetic photometry gives the best-fitting
effective temperature and surface gravity, (log(g) = log(M)−2log(R)+4.437 in solar units).
Reddening becomes important for objects > 100 pc, and so it is crucial to de-redden the
photometry before fitting for accurate parameter determination. Genest-Beaulieu & Bergeron
(2019) highlights the importance of including the Sloan Digital Sky Survey (SDSS) ‘u’ band
for accurate and consistent parameter determination as often the optical photometry lies on
the Rayleigh Jeans slope, but the ‘u’ band samples the peak of the white dwarf’s spectral
energy distribution (SED), therefore, including ‘u’ band photometry allows for improved
estimates of the effective temperature.
1.3.3 Spectral classification
White dwarfs tend to be classified based on their spectra. Spectral classifications begin with
the letter ‘D’ which highlights that it is a degenerate object. The main spectral classifications
of white dwarfs are: DA, DB, DC, DO, DQ, and DZ, Figure 1.5 shows an example spectrum
from each sub-class. Most white dwarfs are DAs, where strong hydrogen absorption lines are
present in their atmospheric spectra due to an outer hydrogen envelope on top of a helium
layer. DBs, however, show strong helium absorption lines (McCook & Sion, 1999), it is
hypothesised that they fused their outer hydrogen envelope during the post main sequence and
are left with a pure helium envelope. The pressure broadening of the spectral lines (discussed
above), makes the hydrogen and helium lines strong and observable. The strength of the DA
1.4 Polluted White Dwarfs 15
and DB spectral features change by significant amounts between stars due to the white dwarf
parameters and differing histories, for example, due to accretion events, convective mixing
or rotation (Fontaine & Michaud, 1979; Chayer et al., 1995a,b). DC white dwarfs contain no
hydrogen or helium lines, this most often occurs when DA white dwarfs cool below 6,000 K,
or when DB white dwarfs cool below 11,000 K. Therefore, below 6,000 K it is not possible
to differentiate between hydrogen or helium dominated white dwarf atmospheres. DO white
dwarfs contain absorption lines of ionised helium (He II), it is thought that around 45,000 K
these DO white dwarfs transition to DB white dwarfs. DQ white dwarfs have spectra that
show strong carbon absorption features. Cool DQs are thought to have deep convection zones
which can result in carbon dredge up from the core to the atmosphere. Hot DQs are thought
to arise due to binary mergers. DZs are white dwarfs which contain absorption lines from
metals. They are cool DC white dwarfs which have accreted metals into their atmosphere.
It is possible for a white dwarf to have multiple classifications and for those the letters are
listed in order of which absorption features dominate, for example, DAZ and DBZ are DA
and DB white dwarfs which also show strong metal absorption features.
The combination of strong gravitational and electric fields in the outer stellar layers
causes elements to become separated by diffusion. This leaves only the lightest elements,
hydrogen or helium, in the observable atmosphere. The separation of the elements is expected
to occur quickly as diffusion time scales are much shorter than white dwarf cooling times (∼
1 Gyr for an effective temperature of 10,000 K). This picture is complicated by stellar winds,
convection, accretion and radiative levitation (Vauclair et al., 1979; Koester & Chanmugam,
1990) which can disrupt the layers.
1.4 Polluted White Dwarfs
In recent years evidence for planetary systems around white dwarf stars has grown, from the
discovery of planets orbiting white dwarfs (e.g. Vanderburg et al., 2020; Blackman et al.,
2021), to approximately 25–50% of white dwarfs being observed with planetary material
polluting their atmospheres (e.g. Zuckerman et al., 2003, 2010; Koester et al., 2014; Hollands
et al., 2017). The latter are titled polluted white dwarfs. The rapid gravitational settling times
in comparison to the white dwarf’s cooling age implies that for metals to remain in the white
dwarfs’ atmosphere ongoing accretion from an external reservoir is required (Koester, 2009).
Figure 1.6 shows a schematic of these polluted white dwarf systems including the settling of
the metals.
vMa2 was the first single white dwarf discovered, but spectroscopic follow up revealed
it had strong metal lines and was therefore designated as a ‘F type’ star (Van Maanen,
16 Introduction
Fig. 1.5 Example spectra of white dwarf spectral types from LAMOST. Figure from Gen-
tile Fusillo et al. (2015).
1.4 Polluted White Dwarfs 17
Fig. 1.6 A diagram to demonstrate the polluted white dwarf systems, taken from Jura &
Young (2014). The composition of the pollution in the atmosphere will be discussed in
Section 1.4.2 and the planetary debris will be discussed in Section 1.4.3.
1917). Almost a century later it was determined that this was a white dwarf which had been
polluted with planetary material. Therefore, exoplanetary material has been observed for
over a century. The first unambiguous detection of metal pollution that was attributed to a
white dwarf was G74−7, this was hypothesised to be accretion from the interstellar medium
(ISM) (Lacombe et al., 1983; Dupuis et al., 1993). This hypothesis involves a white dwarf
transitioning a dense region of the ISM; dust and gas become gravitationally attracted to the
star and therefore polluting its atmosphere. Much evidence invalidated this claim with the
main argument being that the abundances of the accreted material did not correlate with the
position and kinematics of the white dwarf in comparison to the ISM (Hansen & Liebert,
2003; Farihi et al., 2010a). It is now unambiguously known that these polluted white dwarfs
are accreting material from their remnant planetary systems.
1.4.1 How do the white dwarfs become polluted?
The favoured theory regarding the pollution source is that it originates from planetesimals
scattered on eccentric orbits towards the white dwarf where they tidally disrupt, migrate
inwards, sublimate, and finally accrete onto the atmosphere of the white dwarf (as seen in
Figure 1.6). These planetesimals have masses comparable to solar system asteroids (Debes
18 Introduction
& Sigurdsson, 2002; Jura, 2003; Farihi et al., 2010a; Jura & Young, 2014; Veras et al., 2014).
Additional support for the asteroid tidal disruption model is the discovery of disintegrating
planetesimals transiting the polluted and dusty white dwarf WD 1145+017 (Vanderburg et al.,
2015). The deepest transit of this star has a period of 4.5 hours and blocks 60% of the
flux from the star in the optical (Rappaport et al., 2016; Gary et al., 2017). Following this
discovery, transiting debris was found around ZTF J032833.52−121945.27 with periods of
9.9 and 11.2 hrs (Vanderbosch et al., 2021).
For the asteroid tidal disruption model, planetary bodies need to be scattered inwards
from the surviving outer planetary system of the white dwarf. There are many dynamical
mechanisms which can perturb planetesimals onto star-grazing orbits, the favoured theories
cite planets as the source. Stellar mass loss can induce instabilities whereby a planet or
planets perturb planetesimals onto star-grazing orbits (Debes & Sigurdsson, 2002; Bonsor
et al., 2011; Veras et al., 2011; Debes et al., 2012a; Mustill et al., 2018). There is now
evidence that planets can survive to the white dwarf phase (Gänsicke et al., 2019; Vanderburg
et al., 2020), supporting these models. Alternative mechanisms to scatter planetesimals
include: perturbations due to wide binary companions (Hamers & Portegies Zwart, 2016;
Veras et al., 2016; Petrovich & Muñoz, 2017; Stephan et al., 2017; Smallwood et al., 2018),
and the liberation of exo-moons (Payne et al., 2016; Trierweiler et al., 2022).
1.4.2 Composition of polluting bodies
When assessing the composition of pollutant bodies, it must be acknowledged that certain
phenomena occurring inside white dwarfs can contribute to metals polluting their atmo-
spheres. For white dwarfs with an effective temperature greater than ∼ 25,000 K, radiative
levitation can lead to an observable amount of heavy elements in the atmosphere (Vauclair
et al., 1979; Chayer et al., 1995a,b). Convection zones that extend deep into the white
dwarf interior can also cause the dredge up of heavy elements such that they appear in the
outer layers of the convective zone of white dwarfs (Pelletier et al., 1986). This causes
difficulty in determining the origin of polluting heavy elements for these temperature ranges.
However, for white dwarfs with effective temperatures between 10,000 K and 25,000 K, the
pollutant must be external, and therefore, the bulk composition of the pollutant can be directly
measured using spectroscopic techniques.
Spectroscopic studies of polluted white dwarfs combined with white dwarf atmospheric
models allow the measurement of the bulk composition of extrasolar planetesimals making
them unique laboratories. So far, 23 heavy elements have been discovered across all polluted
white dwarfs (see references in Table 1. of Klein et al., 2021). The polluted white dwarf
GD 362 has absorption features from 19 elements, the most elements detected for a given
1.4 Polluted White Dwarfs 19
white dwarf (e.g. Zuckerman et al., 2007; Xu et al., 2013; Melis & Dufour, 2016; Xu et al.,
2017). For the majority of systems, the polluting materials’ abundance resembles rocky
material similar to asteroids and the terrestrial planets in the inner solar system as seen in
Figure 1.7 (Jura & Young, 2014). The inferred accreted mass is consistent with the masses
of solar system asteroids (∼ 1020 g). The polluted white dwarf SDSS J073842.56+183509.06
has the most mass inferred in its photosphere, 7×1023 g, similar to the mass of the dwarf
planet Ceres in the solar system (Dufour et al., 2012).
Accretion phase:
In order to reconstruct the abundances of the parent body that was accreted by the white
dwarf, it is crucial to consider the differential sinking of elements and the affects this can
have on the observed abundances. There are three accretion and diffusion scenarios that
could occur. Build up stage - when accretion has just started so the observed abundances
correspond closely to the actual abundances of the parent body,
nX(A) par
nX(B) par
=
nX(A)WD
nX(B)WD
, (1.2)
where nX(A) par and nX(B) par are the abundances for element A and B respectively of the
parent body before being accreted by the white dwarf, and nX(A)WD and nX(B)WD are the
derived number abundances for element A and B from the observations of the photosphere
of the white dwarf (Koester, 2009; Harrison et al., 2018). Steady state – when accretion and
diffusion processes have reached an equilibrium. For this phase the abundances derived for
the accreted material need to be modified to consider gravitational settling for the elements
in the white dwarf photosphere,
nX(A) par
nX(B) par
=
τB
τA
X(A)WD
X(B)WD
, (1.3)
where τA and τB are the diffusion time-scales of element A and B respectively through the
white dwarfs photosphere. Declining phase – after the parent body has been fully accreted
by the white dwarf, the abundances decrease exponentially with the decay factors depending
on the time since accretion ceased, t,
nX(A) par
nX(B) par
=
nX(A)WD
nX(B)WD
e−t/τB
e−t/τA
. (1.4)
20 Introduction
The sinking timescales of the heavy metals in the photospheres of white dwarfs varies
depending both on the element sinking and the white dwarf properties. Warm DAZ white
dwarfs have sinking timescales on the order of days–years, whereas DBZ white dwarfs have
much longer sinking timescales on the order of 102 to 106 years. The sinking timescales
are most often based on 1D models (e.g. Koester, 2009). However, recent works have
been incorporating various mixing mechanisms (e.g. convective instability, thermohaline
instability2) at the surfaces of white dwarfs in 3D atmosphere models, this has the effect of
increasing the sinking timescale of metals in white dwarfs (e.g. Cunningham et al., 2019).
As inferences about the pollutants relies on accurate knowledge of the sinking timescales,
further work is required to confirm the sinking timescales.
Differentiation:
Fragments of core-mantle differentiated bodies have been observed in the atmospheres of
polluted white dwarfs, where observations show enhancement or depletion in siderophilic
elements (core-rich or mantle-rich respectively) (e.g. Zuckerman et al., 2011; Hollands
et al., 2018; Harrison et al., 2018). Figure 1.7 shows that some white dwarfs are en-
hanced in elements commonly found in the mantle (Mg, Si) compared to core (Fe), e.g.
SDSS J1043+08556 (S1043), and others are enhanced in core elements, e.g. PG 0843+516
(PG0843). If the white dwarfs are accreting the collisional fragments of parent bodies that
formed an iron core, a large (as much as two thirds) fraction of white dwarfs may have
accreted fragments of larger core-mantle differentiated bodies (Bonsor et al., 2020). This
implies that the process of (iron) core formation in exo-asteroids is likely ubiquitous across
exoplanetary systems.
Water:
Water is widely recognised as one of the key components required for life, and therefore,
there is much astrophysical interest in its detection. Water-rich exoplanetary material which
pollutes white dwarfs cannot be directly detected in the white dwarf photospheres as it
dissociates into oxygen and hydrogen. However, by calculating how much oxygen would be
expected to be in the form of metal oxides (MgO, SiO2, Al2O3, CaO, and FeO), the oxygen
remainder can be attributed to water (Klein et al., 2010). A handful of objects have accreted
bodies rich in water-ice (Farihi et al., 2011, 2013; Raddi et al., 2015; Hoskin et al., 2020;
2The thermohaline instability arises due to unstable gradients in composition which become stabilised by a
temperature gradient. Therefore, in polluted white dwarfs the thermohaline instability could lead to additional
mixing as the significant mean molecular weight of the material that has accreted compared to the atmosphere
of hydrogen below can lead to this instability arising.
1.4 Polluted White Dwarfs 21
Klein et al., 2021), Figure 1.7 shows WD 1425+540 (WD 1425), WD 1232+563 (WD 1232),
SDSS 1242+5226 (S 1242), WD 0738 (WD J0738+1835), and GD 61 have excess oxygen and
are inferred to be ice-rich objects. WD 1425+540 has accreted a fragment of a Kuiper-belt
like icy body rich in both water and nitrogen ices (Xu et al., 2017). Trace hydrogen is
detected in up to 75% of DB white dwarfs (Koester & Kepler, 2015). Gentile Fusillo et al.
(2017) found a link between trace hydrogen and metal polluted white dwarfs, demonstrating
another way to infer the accretion of water-rich planetesimals onto white dwarfs.
Carbon:
Carbon is a key species for the understanding of life. It can be in the form of graphite,
organics or ices and is a volatile element, hence the amount of carbon in solid species in the
solar system is depleted in comparison to the solar photosphere. There is only one report
of carbon rich material, in Ton 345; however, the abundance is debated. Ground based
spectroscopy revealed that it was carbon rich with a composition similar to Kuiper Belt
objects with small amounts of ice due to the low oxygen abundance (Jura et al., 2015), whilst
space based UV observations revealed a much lower abundance of carbon (Wilson et al.,
2015). Therefore, there is no definitive evidence for any white dwarf accreting carbon-rich
exoplanetary bodies, and all but one demonstrate a carbon depletion (Jura, 2006; Wilson
et al., 2016). The body that does not show a carbon depletion is that polluting WD 1425+540,
discovered by Xu et al. (2017), as mentioned in the previous section. This body was also the
first exo-planetary debris to be detected with Nitrogen; this insinuates that this body formed
in a Kuiper belt-like region. UV spectroscopy is most sensitive to detecting carbon, therefore
with more UV spectra of polluted white dwarfs providing detections and stringent limits
on the carbon abundance, further understanding about the form of carbon in exo-planetary
worlds will be revealed.
1.4.3 Circumstellar Discs
Observations of dust discs:
Dust debris from tidally disrupted planetesimals has been discovered via excess infrared
emission above that expected from the white dwarf around 1.5–4% of white dwarfs (e.g.
Becklin et al., 2005; Kilic et al., 2006; Jura et al., 2007b; Rebassa-Mansergas et al., 2019;
Wilson et al., 2019; Xu et al., 2020). G29-38, one of the brightest and most heavily polluted
white dwarfs, was the first polluted white dwarf to be discovered with excess emission at
infrared wavelengths, as seen in Figure 1.8. It was initially hypothesised that the excess was
caused by a brown dwarf companion (Zuckerman & Becklin, 1987). However, pulsation
22 Introduction
Fig. 1.7 Bar charts showing the pollutant mass fractions of: O, Mg, Si, Fe, C, for 19 polluted
white dwarfs. The bulk compositions of the Earth and comet Halley are shown on the left for
comparison. Figure from Xu & Bonsor (2021).
timing in the optical and infrared found echoing signals which were difficult to explain with
the presence of a brown dwarf companion. Also, infrared spectra demonstrated an excess
emission at 10 µm, triple the intensity expected from a brown dwarf (Graham et al., 1990).
These arguments favour the infrared excess resulted from a dust disc close to the white dwarf.
The number of infrared excess detections remained at one for nearly two decades. Ground
based observations discovered GD 362 as the second white dwarf with an infrared excess
associated with a dust disc, with GD 40 closely following this (Becklin et al., 2005; Kilic et al.,
2005, 2006). The launch of the Spitzer Space Telescope in 2003 exponentially increased the
number of detected discs. To date, tens of white dwarfs have been found with an infrared
excess associated with a dust disc, and all are found to also be polluted, implying that the
circumstellar material is accreting onto the atmosphere (e.g. Jura et al., 2007b).
Infrared spectra of the dust can inform about the composition of the dust grains. Low
signal-to-noise Spitzer spectra from the infrared spectrograph (IRS) of a number of polluted
white dwarfs demonstrates strong 10 µm silicate emission features, originating from the
orbiting dust disc (Jura et al., 2007a, 2009a). All spectra show the 10 µm feature, with
the red wing extending to 12 µm. This feature is characteristic of micron-sized olivine
glasses, associated with a tidally disrupted asteroid. G29-38 is the only dusty white dwarf
bright enough to have a sufficiently high signal-to-noise infrared spectrum that an in depth
mineralogy study could be conducted. Reach et al. (2009) reported a 1–35 µm spectrum,
1.4 Polluted White Dwarfs 23
Fig. 1.8 The spectral energy distribution of G29-38. It shows the first infrared excess
discovered around a polluted white dwarf (Zuckerman & Becklin, 1987). The data was taken
using the NASA Infrared Telescope Facility. An excess at near to mid-infrared wavelengths
is clear.
as shown in Figure 1.9, and determined the possible mineral compositions of the dust disc.
Disc modelling found it likely that the disc is formed of amorphous carbon, amorphous
and crystalline silicates, water ice and metal sulphides. Xu et al. (2014) compared the disc
abundances with those in the white dwarf atmosphere and found that the overall agreement is
consistent, except for a few elements. JWST will provide high quality mid-infrared (mid-IR)
spectra that covers strong features from different minerals for discs fainter than G29-38.
This will allow further investigation into the correlation between the atmospheric pollution
and the disc material, and reveal both the chemical and mineral compositions of extrasolar
planetesimals.
It has been suggested that there may be observable signatures of dust beyond the tidal
radius, in the form of an asteroid belt or Kuiper belt analogue. This could supply the
planetesimals that eventually accrete onto the white dwarfs. Xu et al. (2013) used the
Herschel Space Observatory to search for a parent population of dusty bodies around GD 362,
the data resulted in null detections and stringent upper limits were placed. Farihi et al. (2014)
used the Herschel Space Observatory and the Atacama Large Millimetre/submillimetre Array
(ALMA) to search for this parent population around the closest and brightest dusty white
dwarf, G29-38. Both Herschel Space Observatory and ALMA data resulted in null detections,
24 Introduction
Em
iss
iv
ity
 =
 O
bs
er
ve
d 
/ B
ν(
93
0 
K)
Wavelength (μm)
am. carbon
carbonates
PAHwater vap.
water ice
sulfides
phyllosilicates
cryst. pyr.
am. silicates
cryst. forsterite
5 10 30 3515 20 25
0.0
0.5
1.0
Fig. 1.9 Spitzer/IRS spectrum of the dust around G29-38. The observed spectrum was
divided by a blackbody of temperature 930 K to give the black data points. The best fitting
linear combination of 12 minerals is plotted as the red dashed line, to show the potential
composition of the dust. The contribution of each mineral is shown by the coloured lines
(Reach et al., 2009). The composition of this dusty material should match the composition
of the material polluting the star. Water ice, amorphous silicates and forsterites all have
distinguishable features in the mid-IR.
1.4 Polluted White Dwarfs 25
putting strong upper limits on the amount of cold dust in the systems. Further observations
of dusty white dwarfs using the full capabilities of ALMA could be beneficial.
Contrary to this, there are detections of cold dust, however, they are discovered around
hot white dwarfs ∼ 100,000 K. These hot systems are different to the cool metal rich white
dwarfs. Su et al. (2007) discovered excess infrared emission from the central region of
the Helix nebula. The central star is a hot white dwarf, WD 2226-210, with an effective
temperature of ∼ 110,000 K. Spitzer detected excess emission at 8, 24 and 70 µm, which was
hypothesised to be from a dust disc, with a blackbody temperature in the range 90–130 K. It
is thought the dust originates from Kuiper belt-like objects, which have survived the violent
evolution of the host star and collided to form a disc. This demonstrates it is possible for
cold dust to survive and exist around white dwarf systems. Motivated by this work, Chu et al.
(2011) used the Spitzer Multi-band Imaging Photometer to investigate a sample of 71 hot
white dwarfs, or pre-white dwarfs to search for excess emission at 24 µm. Excess emission
was discovered for a number of the sources so it can be hypothesised that dust at ∼ 100 K
should be found around ≳ 15 % of white dwarfs and pre-white dwarfs. However, these cool
infrared excesses are widely debated as a number of these objects have been discovered to
host companions.
Observations of gas discs:
21 of the white dwarfs with dust debris also show evidence of circumstellar gas in emission
near the same radius as the dust (Gänsicke et al., 2006, 2007, 2008; Melis et al., 2010;
Farihi et al., 2012a; Melis et al., 2012; Brinkworth et al., 2012; Debes et al., 2012b; Dennihy
et al., 2020; Melis et al., 2020; Gentile Fusillo et al., 2020). These systems are identified by
their double peaked emission features, usually strongest at the Ca II infrared triplet (8498 Å,
8542 Å, and 8662 Å). WD 1226+110 was the first of such detections, where Ca II emission
lines in the optical and near infrared (NIR) were observed. The Ca II emission line profiles for
WD 1226+110 are shown in Figure 1.10. The double peaked spectral lines are characteristic
of Doppler broadening due to a Keplerian rotating gaseous disc. This has a rotational velocity
law of ΣKαr−3/2 where the inner disc rotates faster than the outer disc. Gaia J0611−6931
has the most elements detected in emission, with observations of Ca, O, Si, Mg, Na and Fe
(Dennihy et al., 2020; Melis et al., 2020). As there are a lack of hydrogen and helium spectral
features in the gaseous discs, this implies the gas discs are metallic. The only gas disc found
to consist of predominantly volatiles (H, O, S) is that around WD J091405.30+191412.25 as
reported in Gänsicke et al. (2019), where the chemical composition matches that found deep
in the atmospheric layers of icy giant planets.
26 Introduction
Fig. 1.10 The Ca II emission line profiles for WD 1226+110 from Gänsicke et al. (2006).
The double peaked profiles are clear, arising due to Keplerian rotation. There are clear
asymmetries in the red and blue Doppler shifted lines, indicating the disc is eccentric.
Disc Variability:
The scattering of planetary bodies that lead to pollution is expected to be a stochastic process,
with the potential for variability on human time scales as seen in Figure 1.11 by the predicted
order of magnitude changes in the accretion rate over timescales of less than a year (Wyatt
et al., 2014). Such dust variability has previously been identified. The first infrared variability
associated with the dust was for white dwarf WD J0959-0200. The fluxes in both Spitzer
(Infrared Array Camera) channels, 3.6 µm and 4.5 µm, dropped by approximately 35 % within
a year baseline. The NIR K band flux also dropped by 20 %, emphasising the dust is close
to the star and dissipating on short time scales (Xu & Jura, 2014). Several scenarios could
explain the large drop in flux for WD J0959-0200. One scenario involves planetesimals being
scattered inward by a large outer planet and impacting a pre-existing disc. Scattering from a
size distribution of small bodies can be approximated as continuous accretion, but infrequent
scattering of larger bodies can affect the disc and accretion signatures, with the frequency
of impact being be as often as once every 30 years or less (Jura, 2008; Wyatt et al., 2014).
Mutual collisions between fragments can cause the inner disc to evaporate. If this hypothesis
is supported, Xu & Jura (2014) suggested that WD J0959-0200 lost approximately 3 % of
the disc mass within 300 days, implying that white dwarf accretion is intrinsically variable.
1.4 Polluted White Dwarfs 27
Fig. 1.11 Figure from Wyatt et al. (2014) showing model predictions for accretion rate over
time for 20 stars modelled to be similar to G29-38. Changes in the accretion rate can be up
to an order of magnitude over timescales of less than a year.
28 Introduction
Investigations into whether the accretion rate of white dwarfs varies as a function of time
have been conducted previously for one white dwarf, G29-38 (von Hippel & Thompson,
2007; Debes & López-Morales, 2008). Further observations of accretion rate over time
will allow insight to be gained into whether this model is correct. Another scenario could
explain the variability if the white dwarfs are observed with both circumstellar gas and dust.
The dust and gas may interact and cause the inner disc to evaporate, resulting in non-steady
state accretion. WD J0959-0200 has both gas and dust discs, emphasising this assumption is
reasonable. However, variability has now been observed to be ubiquitous in the mid-infrared
even for those systems without observable gas discs, with no preference for increases or
decreases in dust flux as shown in Figure 1.12 (Swan et al., 2019a, 2020).
Variability in the circumstellar gas has also been observed for white dwarfs with cir-
cumstellar gaseous discs (Wilson et al., 2014, 2015; Manser et al., 2015, 2016b; Dennihy
et al., 2018). Variability tends to be morphological variations in the line profile shape, or
increases/decreases in the equivalent widths of the spectral features. The variability is mostly
attributed to the precession of eccentric rings, collisions, or planetesimals orbiting within the
debris discs (Manser et al., 2019).
Jura (2003) Flat and Opaque Disc Model:
In 2003 it was well known that metals polluted the atmospheres of some white dwarfs,
however, the only known infrared excess was that of G29-38. Jura (2003) developed a model
to explain both the atmospheric pollutants and the infrared excess for G29-38. Scattered
planetesimals perturbed onto highly eccentric orbits can fall within the Roche radius of the
white dwarf. This causes them to become tidally disrupted, and over time the system relaxes
into a flat orbiting dust disc. It is assumed that the white dwarf illuminates the thin, flat,
optically thick disc and the incident flux is re-radiated in the infrared. The thermal emission
of the discs are of the order 103 K, demonstrating these discs lie close to their host star. The
closest solar system analogue are the rings of Saturn; the physics of these rings can mostly
be applied to white dwarfs (Brahic, 1977; Dones, 1991). The temperature of the white dwarf
disc, Tdisc, as a function of distance from the star, R, which has a stellar radius of R∗ and a
temperature of T∗, is given by:
Tdisc ≈
(
2
3π
)1/4 (R∗
R
)3/4
T∗. (1.5)
1.4 Polluted White Dwarfs 29
Fig. 1.12 Figure from Swan et al. (2020) showing the mid-infrared variability observed in
a sample of ∼ 40 white dwarfs using the Spitzer space telescope. The largest flux changes
seem to occur over longer baselines with the largest changes being those with circumstellar
gaseous discs.
30 Introduction
The flux from the disc, is predicted to be:
Fdisc =
2π cos i
D2∗
∫ Rout
Rin
Bν (Tdisc)RdR, (1.6)
where D∗ is the distance to the white dwarf, i is the inclination angle of the disc, Rin and Rout
are the inner and outer radii of the dust disc respectively and Bν is the Planck function. In
this model, the inner radius is defined by the sublimation radius of solids. The sublimation
radius, RS, is given by:
RS =
√
ε R∗
2
(
T∗
TS
)2
, (1.7)
where ε is the ratio of the emissivity of the particle for the white dwarf radiation and for its
own thermal radiation, and TS is the sublimation temperature for the particles in the disc
(Rafikov, 2011a). The dust ring is expected to form from the tidal disruption of an asteroid,
therefore the outer radius is defined by the tidal radius of the white dwarf. This radius, Rtide,
is given by:
Rtide =Ctide
(
ρ∗
ρa
)1/3
R∗, (1.8)
where ρ∗ is the density of the white dwarf, ρa is the density of the asteroid and Ctide is a
constant, O(1), dependent on the composition, rotation and orbit of the asteroid (Davidsson,
1999).
The process of accretion from the disc onto the stellar atmosphere is complicated and
refuted. After the asteroid is tidally disrupted, collisions result in the dissipation of energy,
such that the dust settles onto a flat plane. Veras et al. (2015) established that the radiation
from the white dwarf can circularise and compress the orbiting dust. The radiation from
the white dwarf drives matter towards the sublimation radius via Poynting-Robertson (PR)
drag (Robertson, 1937; Burns et al., 1979) shown in Figure 1.13. This delivers material
to a reservoir of metallic gas close to the white dwarf. Viscous torques provide the means
for metals to accrete onto the white dwarf surface (Rafikov, 2011a). Rafikov (2011b)
demonstrated that PR drag is sufficient to achieve metal accretion rates of at least 108 g s−1.
But this is not sufficient to explain the accretion rates of the highest accretors (∼1011 g s−1).
Paradigm Shift:
The model of the flat opaque disc as developed in Jura (2003) was revolutionary as it provided
a framework to understand these enigmatic polluted white dwarf systems. However, there
is increasing evidence for the requirement of an optically thin component, moving the field
away from the flat opaque disc model. The 10 µm silicate emission features detected for
1.4 Polluted White Dwarfs 31
a number of white dwarfs with infrared excesses must result from an optically thin region
(Jura et al., 2009a). In order to fit the strong 10 µm features and the shape of the infrared
excesses, GD 362 (Jura et al., 2007a) and G29-38 (Reach et al., 2009) were fitted with models
which invoked warped/flared discs. Large infrared variability is observed in a number of
systems with both increases and decreases observed. In order to explain this collisional
models are proposed where collisions cause infrared brightening as dust is produced, and
then dimming occurs as the cascade grinds the material down such that it no longer emits at
micron wavelengths (Farihi et al., 2018; Swan et al., 2020, 2021).
The tidal disruption model implies that observable dust discs should be more frequent
than is detected. Bonsor et al. (2017) found that no more than 3.3% of white dwarfs can have
a wide, flat, opaque dust disc and suggest four reasons to explain the lack of discs observed.
These reasons are extracted from Figure 1.14 where the accretion rate is plotted against the
white dwarf temperature. The green region (A) may represent white dwarfs which have
already accreted their disc. This is possible if a white dwarf has a long sinking time scale
such that pollutants exist in the atmosphere after the full dissipation of the disc. The blue
region (B) may represent white dwarfs which are surrounded by undetectable optically thin
dust. The brown region (C) may explain the lack of infrared excess for hot white dwarfs
where the sublimation radius of solids lies outside of the tidal disruption radius. This means
that gas is accreted onto the stellar photosphere without a disc forming (Steckloff et al., 2021).
The red region (D) represents an area of phase space where there is enhanced accretion,
although it is difficult to explain the lack of infrared detections here. Although further work
is required to confirm these hypotheses, this work emphasises the need for a paradigm shift
away from the optically thick, razor thin model.
As previously stated, 21 systems have been observed with both circumstellar dust and
gas discs. These gas discs extend to a similar radii as the dust discs (e.g. Melis et al.,
2012). This is surprising as gas is observed at radii larger than the sublimation radius for
refractory elements. The vertical extent of the gas disc appears to be much greater than
the flat, opaque dust disc. Different theories have been proposed to explain the production
of the gas - sublimation of solids, and collisions. Metallic gas inwards of the sublimation
radius feeds the stellar atmosphere via viscous torques. To conserve angular momentum a
proportion of the gas produced at the sublimation radius viscously spreads outwards causing
an overlap in the location of the dust and gas (Rafikov, 2011a; Metzger et al., 2012). This
gas disc has a higher temperature than the dust disc enabling the gas disc to exist outside of
the sublimation radius. This outwardly spreading gas causes drag on the dust particles and
thus accelerates their accretion onto the white dwarf creating a runaway effect; this might
explain the highest accretion rates observed in polluted white dwarfs (Rafikov, 2011a). To
32 Introduction
Fig. 1.13 A diagram from Rafikov (2011a) illustrating an interacting dust disc (black) and
gaseous disc (grey). The radial extent of the dust disc is defined on the inner edge by the
sublimation radius of solids and the outer edge by the tidal disruption radius of the white
dwarf. The gas disc has the same radial extent as the dust, with a reservoir close to the white
dwarf, feeding the atmosphere with metallic gas. The movement of high metallicity materials
is demonstrated by the arrows.
investigate this, the accretion rates of white dwarfs with circumstellar gas needs to be studied
in comparison to the population. A schematic of this theory is shown in Figure 1.13. An
alternative explanation for the gas emission is collisional cascades of planetesimals within
the Roche radius of the white dwarf, these collisions produce gaseous material (Kenyon &
Bromley, 2017a,b). Observations of infrared variability in WD 0145+234 appear consistent
with simple collisional cascade models (Swan et al., 2021). It is likely numerous routes of
planetesimals arriving in the white dwarf atmosphere are active to explain the diversity in
the architecture of the systems and accretion rates, a more thorough discussion appears in
Brouwers et al. (2022).
Dust provides information regarding how planetary material arrives into the atmosphere
of these polluted white dwarfs. No theoretical models can encompass all dust observations,
including the shapes of the SEDs, the silicate emission features, and the dust variability.
Dust variability studies are crucial as they can reveal information about the optical depth
and geometry of the circumstellar dust. However, as of 2016 (when this thesis work begun),
studies of dust variability only focused on individual systems rather than the population, so
creating theoretical models that can explain the population was impossible. Therefore, it is
crucial to determine how frequent variability is within the population and at what wavelengths
this variability is dominant.
1.4 Polluted White Dwarfs 33
Fig. 1.14 This figure is taken from Bonsor et al. (2017). It demonstrates the accretion rate
plotted against the temperature of the white dwarfs. The plot has been subdivided into four
regions to explain the lack of observations of infrared excesses around polluted white dwarfs.
1.4.4 The Link with the Main Sequence
The asteroid destruction model relies on the survival of at least one large planet as well
as planetesimals from the main sequence to the white dwarf phase. As nearly all stars are
expected to end their lives as white dwarfs, looking at the planetary systems around main
sequence stars can reveal what could survive. There are over 5,000 exoplanets confirmed
to date, with a large range of radius, mass, semi-major axis and orbital period. Due to this
diversity, it is likely that some exoplanets have the necessary location and properties to
survive to the white dwarf phase.
The post main sequence evolution of a star is a violent process, however dynamicists
have hypothesised that certain planets can survive. Mustill & Villaver (2012) argued that
terrestrial planets need an initial semi-major axis of at least 2.8 AU and gas giants need an
initial semi-major axis of 5 AU to avoid being engulfed by the expanding envelope of the
giant star. During the asymptotic giant branch phase, the star loses a large fraction of its
initial mass. This mass loss occurs over such long time scales that it is possible for objects
to have stable expanding orbits (Debes & Sigurdsson, 2002). Therefore, if planets have a
sufficiently large semi-major axis, they could survive to the white dwarf phase and perturb
asteroids into highly eccentric orbits. The fate of this asteroid could be: a collision with
another surviving body, to be ejected from the planetary system, to directly hit the white
dwarf, or to fall within the tidal disruption radius of the white dwarf (Villaver & Livio, 2007;
34 Introduction
Veras et al., 2011, 2013; McDonald & Veras, 2021). A fraction of main sequence planets
have been observed with these large semi-major axis, so the idea that they could survive to
the white dwarf phase is reasonable.
Bonsor & Wyatt (2010) found that debris belts with sufficiently massive planetesimals
that lie beyond a few AU can survive to the white dwarf phase. However, the masses of the
discs are reduced significantly; this is mainly due to the loss of small planetesimals. The
small planetesimals are subsequently replenished via collisions once the system has settled
into the white dwarf phase. It has been shown that 25–50% of white dwarfs are polluted (e.g.
Zuckerman et al., 2003). Therefore, the study of these objects could provide information
about main sequence exo-planetary systems, if we assume that this observed pollution is due
to scattered planetesimals. This implies that at least 25–50% of low mass main sequence
systems must have a massive planetesimal belt with enough debris to survive to the white
dwarf phase and pollute the atmosphere of the white dwarf. Cold outer belts around main
sequence stars have detection rates of 30% around A stars and about 20% for FGK stars
(Marino, 2022). This is broadly consistent with the fraction of white dwarfs found to be
polluted.
Sub-stellar bodies have been discovered around white dwarfs. Numerous brown dwarf
companions to white dwarfs have been discovered (Longstaff et al., 2019; van Roestel et al.,
2021), but a limited number of planets have been found. Most notably, the giant transiting
planet candidate, WD 1856+534b (Vanderburg et al., 2020). Although it is expected that
planets around white dwarfs should be commonplace in order for 25–50% of white dwarfs
to be polluted, few other planet candidates have been observed (Xu et al., 2015a; Belardi
et al., 2016). This is unsurprising as the probability of observing a transiting planet is
low due to small radii of white dwarfs and surviving planets are predicted to be far from
the star (Debes & Sigurdsson, 2002). Gaia will enable planets to be discovered around
white dwarfs astrometrically. Gaia eDR3 resulted in a candidate super-Jupiter around
WD 0141−675, if confirmed this would be the first polluted white dwarf with an exoplanet
detected (Collaboration et al., 2022). With the release of Gaia DR5 it is expected that Gaia
will astrometrically discover 6±1 planets between 1.6–3.91 au with masses between 0.03 –
13 MJ (Sanderson et al., 2022) allowing investigations into the evolution of planetary systems
from the main sequence to white dwarf phase.
1.5 This Thesis in Context
Polluted white dwarfs are unique laboratories that can be used to directly sample the bulk
composition of exoplanets; this is not possible via any other method. We are transitioning
1.5 This Thesis in Context 35
into the era of big data. For white dwarfs, Gaia has aided the discovery of > 350,000 white
dwarfs (Gentile Fusillo et al., 2021), and with large spectroscopic surveys upcoming such
as 4MOST, DESI, WEAVE, and SDSS-V, thousands of new polluted white dwarfs will be
discovered. Each white dwarf tells its own unique story about the exoplanetary material
surrounding it, therefore, it will be crucial to follow up with high resolution instruments
across large wavelength ranges to ensure a thorough characterisation and understanding of
this exoplanetary material. These individual studies have led to ground-breaking discoveries
regarding the composition and geology of planetary material around other stars, such as
the discovery of water-rich exoplanetary bodies (e.g. Farihi et al., 2011), which in turn has
prompted further investigations into the possibility of life in exoplanetary systems.
For exoplanets, over the next decades a myriad of rocky planets will be discovered and
characterised with current missions such as TESS, CHEOPS, and JWST; and future missions,
such as: PLATO, LUVOIR, and LIFE. With this wealth of new data, collaboration will be
crucial, information about exoplanetary material from polluted white dwarf systems can
help to answer big questions about the solar system, exoplanetary systems, and galactic
populations, and similarly these subjects can help inform inferences from white dwarf
planetary systems. In order to fully understand and characterise exoplanetary rocky worlds,
as well as determine whether they could be habitable, it is crucial to understand what they are
made of. Current models of the interiors of exoplanets suffer from degeneracies; however,
the population of the bulk composition of exoplanetary material, as inferred from polluted
white dwarfs, can be used as inputs into planetary interior modelling to help to break these
degeneracies. With the wealth of data coming it is crucial for sub-fields to collaborate such
that a new era of Earth 2.0 discovery can begin. Our place in the solar system and galaxy
appears to be key to life developing on Earth, but it is unknown whether the solar system
is common, or how planet formation is affected by our place in the galaxy. Polluted white
dwarfs can reveal the population of exoplanetary material which can be used to answer
these questions. Combining the inferred exoplanetary composition with Gaia astrometric
information reveals whether different galactic populations have different planet compositions
and the affects this has on the resultant planetary systems.
This thesis focuses on white dwarf planetary systems, with an emphasis on using obser-
vations to inform models of the disruption and accretion processes, and using large ground
based spectrographs to make inferences about exoplanetary composition of individual sys-
tems. Chapter 2 reports large ground-based near-infrared photometric monitoring campaigns
of the circumstellar dust around ∼ 40 white dwarfs. There is increasing evidence for a
paradigm shift away from the model where a planetesimal tidally disrupts and forms an
opaque flat disc (Jura, 2003). Dust variability sheds light on the dynamics of the planetary
36 Introduction
bodies, the distribution of the dust, and the optical depth and properties of the dust. Chapter
3 reports an optical spectroscopic monitoring campaign of 5 DAZ white dwarfs over decade
long timescales. Stochastic models of the accretion of planetesimals predicts variability
in the accretion rate, and therefore the amount of material in the atmosphere. Warm DAZ
white dwarfs have accretion rates on the order of days, therefore enabling the search for
variability in the accretion rate using spectroscopic monitoring. Constraining accretion rates
provides valuable information to inform models of accretion and disc lifetimes. Chapter
4 reports the abundances for the material accreting onto seven white dwarf stars and the
composition and geological history of these exoplanetary bodies. These findings can be used
to aid interior structure models of exoplanets, investigate whether the composition of solar
system bodies are unique, and study volatiles and their delivery in exoplanetary systems.
Finally, Chapter 5 presents the conclusions from this thesis and provides suggestions for
future work to contribute to questions raised.
Chapter 2
Dust Variability
The favoured theory regarding the source of white dwarf pollution is that it originates from
planetesimals scattered onto eccentric orbits towards the white dwarf where they tidally
disrupt, producing dusty debris detectable as excess infrared emission, and subsequently
accrete onto the atmosphere of the white dwarf. This inwards scattering of planetary bodies
that leads to pollution is expected to be a stochastic process (Wyatt et al., 2014), with
variability predicted on human time-scales. Variations could come in the form of gaseous
emission, dusty emission, or total flux caused by transiting debris. Studying the circumstellar
dust via time series photometry of the infrared emission can reveal how this planetary material
arrives in their atmospheres.
The first white dwarf discovered to show dust emission variability was WD J0959−0200.
The 3–5 µm flux dropped by 35% between observations separated by a year and appeared
to be stable afterwards, and the near-infrared K band flux dropped by 18.5% between
observations separated by 8 years (Xu & Jura, 2014). The large K band excess for this white
dwarf implies that the dust is hot and close-in. These findings imply that the variability event
was large and became stable quickly. Motivated by the large variability in WD J0959−0200,
ground based near-infrared monitoring campaigns were conducted to search for variability in
the dust for white dwarfs with infrared excesses. This chapter focuses on these monitoring
campaigns and characterising how white dwarfs vary in the near-infrared in order to better
understand how dusty material arrives in the atmospheres of the white dwarfs. Section 2.1
presents a near-infrared monitoring campaign of 34 white dwarfs with circumstellar dust
emission using the UKIRT/WFCAM to search for variability on timescales of months –
years. Section 2.2 presents a near-infrared monitoring campaign of 8 white dwarfs with dust
emission using the NTT/SOFI to search for variability over timescales of hours – days.
38 Dust Variability
2.1 The UKIRT/WFCAM near-infrared monitoring
A near-infrared monitoring campaign of 34 white dwarfs with infrared excesses was con-
ducted with the aim to search for variability in the dust emission. Time series photometry
of these white dwarfs from the United Kingdom Infrared Telescope (Wide Field Camera)
in the J, H and K bands were obtained over baselines of up to three years. No statistically
significant variation is found in the dust emission in all three near-infrared bands. Specifically,
variability at ∼ 1.3% can be ruled out for the 13 white dwarfs brighter than 16th mag in
K band, and at ∼ 10% for the 32 white dwarfs brighter than 18th mag over time-scales of
three years. Although to date two white dwarfs, SDSS J095904.69−020047.6 (Xu & Jura,
2014) and WD 1226+110 (Xu et al., 2018b), have shown K band variability, in the sample no
evidence of new K band variability at these levels is seen. One interpretation is that the tidal
disruption events which lead to large variabilities are rare, occur on short time-scales, and
after a few years the white dwarfs return to being stable in the near-infrared.
2.1.1 UKIRT Observations
An infrared monitoring campaign was completed using the Wide Field Camera (WFCAM) on
the UKIRT on Maunakea, Hawaii (PI: Xu). WFCAM operates in the near-infrared between
0.83 and 2.37 µm ; this includes the J, H and K filters (Hewett et al., 2006). WFCAM has
four detectors composed of 2048 by 2048 18 micron pixels, with a pixel scale of 0.4′′.
The sample consists of 34 white dwarfs with infrared excesses. Table 2.1 shows the
sample, giving the white dwarf parameters and the nature of the infrared excess. In the
sample, 30 white dwarfs have dust emission confirmed with Spitzer observations, the 4
remaining objects are identified by WISE and are labelled as dust candidates. JHK broadband
photometry was obtained for the 34 targets with the UKIRT. 48 hours of UKIRT WFCAM
time between semesters 2014B and 2017A were used to study long-term variability in the
near-infrared. The dates of the observations for the 34 white dwarfs are shown in Table 6.1.
Each white dwarf was observed up to 6 times across the 3 year campaign. The UKIRT
observations probed short time-scales (minutes) between individual frames taken on a given
night, and long time-scales (years) between observation dates. Further discussions about
time-scales are given in Section 2.1.3. The observations were designed such that a signal-
to-noise ratio (SNR) of 30 was obtained for the J and H bands, and 40 for the K band. To
achieve the required SNR, the brightest white dwarfs in the sample required 25 s of exposure
time for the J and H band, and 75 s for the K band. For the faintest white dwarfs, this required
150 s for the J band, 450 s for the H band, and 1250 s for the K band. As the infrared sky
is bright, each frame consisted of a dithered stack of five 5 s or 10 s exposures. Table 6.2
2.1 Dust variability 39
Table 2.1 The UKIRT sample of dusty polluted white dwarfs and their properties. H/He
column highlights the dominant element in the atmosphere.
WD Name Other Name H/He Te f f ⋆ log(g)⋆ Nature of Excess †
WD 0010+280 PG 0010+281 H 23700 7.731 Dustα
WD 0106−328 HE 0106−3253 H 16200 8.031 Dustβ
WD 0146+187 GD 16 He 11500 8.002 Dustγ
WD 0300−013 GD 40 He 13600 8.023 Dustδ
WD 0307+077 HS 0307+0746 H 10100 7.991 Dustβ
WD 0408−041 GD 56 H 14200 7.961 Dustδ
WD 0435+410 GD 61 He 15700 8.043 Dustε
WD J0738+1835∗ SDSS J073842.57+183509.6 He 14000 8.404 Dustζ
WD J0959−0200∗ SDSS J095904.69−020047.6 H 13300 8.065 Dustη
WD 1015+161 PG 1015+161 H 19200 8.031 Dustδ
WD 1018+410 PG 1018+411 H 21700 8.051 Dustθ
WD 1041+092 Gaia DR2 3869060540584643328 H 17600 8.121 Dustζ
WD 1116+026 GD 133 H 12600 8.046 Dustδ
WD 1145+017 HE 1145+0145 He 15900 8.007 Dust ι
WD 1145+288 Gaia DR2 4019789359821201536 H 12400 7.961 Candκ
WD 1150−153 EC 11507−1519 H 11400 7.981 Dustλ
WD J1221+1245∗ SDSS J122150.81+124513.3 H 12300 8.205 Dustη
WD 1225−079 PG 1225−079 He 10800 8.008 Dustβ
WD 1226+110 Gaia DR2 3904415787947492096 H 20900 8.111 Dustµ
WD 1232+563 Gaia DR2 1571584539980588544 He 11800 8.303 Candκ
WD 1349−230 HE 1349−2305 He 18200 8.139 Dustν
WD 1456+298 G166-58 H 7390 8.001 Dustξ
WD 1504+329 Gaia DR2 1288812212565231232 H 7180 8.0610 Candκ
WD 1536+520 Gaia DR2 1595298501827000960 H 16700 7.706 Candκ
WD 1551+175 Gaia DR2 1196531988354226560 He 15600 7.9611 Dustπ
WD 1554+094 KUV 15519+1730 H 21800 7.6312 BD+Dustρ
WD J1617+1620∗ SDSS J161717.04+162022.4 H 13200 8.041 Dustζ
WD 1729+371 GD 362 H 10300 8.136 Dustξ
WD 1929+011 Gaia DR2 4287654959563143168 H 25400 8.171 Dustθ
WD 2132+096 HS 2132+0941 H 13100 7.9613 Dustπ
WD 2207+121 Gaia DR2 2727904257071365760 He 14800 7.973 Dustσ
WD 2221−165 HE 2221−1630 H 9900 8.121 Dustβ
WD 2326+049 G29-38 H 11200 8.001 Dustτ
WD 2328+107 PG 2328+108 H 17900 7.741 Dustθ
Notes:
⋆ Temperature and log(g): Temperature and log(g) come from photometric fits, where possible, otherwise
a new fit considering the Gaia distances was performed (see Section 2.1.3). (1) This work, (2) Koester et al.
(2005), (3) Coutu et al. (2019), (4) Dufour et al. (2012), (5) Farihi et al. (2012a), (6) Dufour et al. (2017),
(7) Vanderburg et al. (2015), (8) Klein et al. (2011), (9) Voss et al. (2007), (10) Barber et al. (2014), (11)
Bergeron et al. (2011), (12) Farihi et al. (2017), (13) Gentile Fusillo et al. (2018).
† Nature of infrared excess references: ‘dust’ refers to white dwarfs with confirmed dust detection with
Spitzer observations and the reference is that of the Spitzer observations, otherwise it is labelled ‘cand’
(candidate), and the reference is the paper that first refers to dust emission. WD 1554+094 has a brown
dwarf companion and dust. (α) Xu et al. (2015b), (β ) Farihi et al. (2010b), (γ) Farihi et al. (2009), (δ ) Jura
et al. (2007b), (ε) Farihi et al. (2011), (ζ ) Brinkworth et al. (2012), (η) Farihi et al. (2012a), (θ ) Rocchetto
et al. (2015), (ι) Xu et al. (2018a), (κ) Debes et al. (2011), (λ ) Jura et al. (2009a), (µ) Brinkworth et al.
(2009), (ν) Girven et al. (2012), (ξ ) Farihi et al. (2008), (π) Bergfors et al. (2014), (ρ) Farihi et al. (2017),
(σ ) Xu & Jura (2012), (τ) Reach et al. (2005).
40 Dust Variability
(Appendix 1: Chapter 6) shows the exposure time for each of the five individual exposures
making up the dithered stack. All data obtained with WFCAM were pipeline-processed by
the Cambridge Astronomical Survey Unit using standard infrared photometry data reduction
steps (CASU, Irwin et al., 2004; Dye et al., 2006).
Further processing using the LIGHTCURVES software1 was executed to improve the
precision of the photometry (Irwin et al., 2007). List driven photometry was performed using
a master frame to force the centroid positions for the objects. Here, the master frame is
the stacked image of all frames; this increases the SNR of the master frame and reduces
errors associated with inaccurately placed centroids. Each frame used in the construction of
the lightcurves was re-aligned to the same set of astrometric calibrators (from 2MASS) as
the master frame, which gives significantly improved precision in aperture location when
compared to centroiding for faint sources (see Irwin et al., 2007). For a particular object,
all frames had an aperture between 3–5 pixels (1.2–2′′), depending on which aperture gave
the lowest root mean square (RMS) value. Using a large number of non-variable stars,
the zero-point shift for each frame was calculated to reduce atmospheric effects, and a 2D
polynomial was fitted to the magnitude residuals to minimise the error associated with the
position on the detector. LIGHTCURVES outputs a robustly calibrated lightcurve for each
filter and for each object in the catalogue list. For variability searches this is essential as it
allows us to probe changes down to the percent level.
2.1.2 Variability Analysis
Analysis Method
This work aimed to obtain high precision JHK photometry of a sample of dusty white dwarfs
and to search for and constrain the level of variability in the photometry over the length
of the survey. Throughout the analysis the Vega magnitude system was adopted. In order
to robustly study the statistics of the photometry, the same analysis method was applied
to all white dwarf observations regardless of the magnitude of the white dwarf and the
number of measurements in the J, H and K bands. Gaussians were fitted to the distribution
of photometrically corrected magnitudes from the LIGHTCURVES software using all dithered
stacked frames, as demonstrated in Fig. 2.1. The total number of dithered stacked frames for
each filter is shown in Table 6.2 (Appendix 1: Chapter 6), this ranges from 3 to 125, with
the median number of frames for the J, H and K bands being 9, 12 and 20 respectively. A
Markov Chain Monte Carlo (MCMC) approach was implemented to model the magnitude
distribution of each star with a Gaussian profile, yielding posterior distributions for the
1https://github.com/mdwarfgeek/lightcurves
2.1 Dust variability 41
mean and standard deviation thereof. In the analysis, the median values from the posteriors
are adopted. Uniform priors were used for the magnitude between 0 and 20, and standard
deviation between 0 and 2. Larger upper values for the assumed prior range are used to test
the sensitivity on the parameters. The results remained consistent independent of the size
of the prior. A python package, PYMC2 (Patil et al., 2010), was used for MCMC parameter
estimation. Five walkers were used, each resulting in 100,000 posterior samples, with the first
40% of the chain being discarded in the burn-in phase. The Gelman-Rubin statistic (Gelman
et al., 1992) was implemented to check for chain convergence. For the two parameters
(magnitude and standard deviation), all white dwarfs had values 1.000<GR< 1.037 for
the J band, 0.999<GR< 1.002 for the H band, and 1.000<GR< 1.005 for the K band,
demonstrating good convergence. The median value of the posterior distribution of the
standard deviation was used for the variability measurement. The errors are quoted using the
16th and 84th percentiles of the posterior distribution. This median variability measurement
is a robust and reliable way of measuring variability.
To ensure that any variability detected was real, stellar objects in the field of view were
analysed using the same approach for comparison. For all field stars the median value of
the standard deviation of the Gaussian as a function of magnitude was used to represent the
sensitivity of the survey as a function of magnitude. Using the median ensures no variable
field stars are contaminating the function. The white dwarfs were then compared to the
median MCMC standard deviation of the non-variable field stars at the same magnitude as
the white dwarf. If the standard deviation of the white dwarf was significantly higher than
that of the field stars, then they were identified as variable. The field objects selected for
the comparison were those classified by LIGHTCURVES as stellar and those observed in the
same detector as the white dwarf. The number of field stars used in the comparison for each
white dwarf ranged from 110 for white dwarfs in sparse fields of view up to 6700 for white
dwarfs in densely populated regions. The median number of field stellar objects used in the
comparison for each white dwarf was 210.
Variability Results
Table 2.2 shows the results of the MCMC runs, and lists the median magnitude and median
standard deviation on this magnitude for all white dwarfs in the survey. Fig. 2.2 plots these
median magnitudes and standard deviations for the white dwarfs and field stars in the J, H
and K bands. Most white dwarfs have standard deviations which are consistent with that of
the field stellar objects. This implies that most of the white dwarfs have J, H and K fluxes
2https://www.pymc.io
42 Dust Variability
Fig. 2.1 A normalised histogram showing the distribution of photometrically corrected magni-
tudes from the LIGHTCURVES software using all dithered stacked frames for WD 1145+017.
Each dithered stacked frame contains 5×10 second exposures. This white dwarf has 102
measurements in the K band over 782 days. The Gaussian curve shows the median best-fitting
Gaussian, with a median magnitude of 17.467, and a median standard deviation of 0.068
mags.
2.1 Dust variability 43
which are no more variable than the field stars, which are taken to be a proxy of the sensitivity
of the survey as a function of magnitude.
A typical SED for a white dwarf that is representative of the sample peaks in the optical,
whereas the dust emission peaks in the infrared. Of the near-infrared bands, the K band is
more sensitive to the dust emission. Consistent fluxes in the K band imply there was little
change in the K band dust emission for the white dwarfs. A few objects stand out from the
plots, these objects are discussed further in the following section. Objects from the literature
that previously showed variability are also discussed.
Discussion of Individual Sources
WD 1145+017:
Vanderburg et al. (2015) discovered that WD 1145+017 is transited by multiple disinte-
grating planetesimals. The transit periods were approximately 4.5 hours and lasted various
lengths from minutes to hours, with varying transit depths; the deepest blocks 60% of the
flux from the star in the optical. The transits were not always present, and the transit activity
level was variable (Gary et al., 2017).
The pink inverted triangle in Figs. 2.2a, 2.2b, and 2.2c show WD 1145+017 was variable
at 4.1σ in the J band, 2.1σ in the H band, and was not significantly variable in the K band.
From the UKIRT lightcurves of this white dwarf, shown in Fig. 2.3, it appears that the J
band and possibly H band magnitudes were fainter on 09/05/2017. The J, H and K band
observations were taken consecutively, the length of the observations were 3.5, 7.5 and 17
minutes respectively. Therefore, as the median dip duration is 9 minutes (Gary et al., 2017),
it is possible that the transit occurred during the J band observations, with an overlap into the
H band observations. Alternatively, as the variability was strongest in the J band and weakest
in the K band it is consistent with the transit depth measurements found in Xu et al. (2018a),
and could also explain the differences in the observed variability. Near contemporaneous
optical observations indeed show transits in the lightcurve (B. Gary, private communications3
Rappaport et al., 2017). The decrease in the J and H band flux is very likely to be caused by
transits, rather than dust variability.
3http://www.brucegary.net/zombie6/
44 Dust Variability
Table 2.2 The resulting median magnitude and standard deviation found from the Gaussian
fits to the photometry from the UKIRT observations in the J, H and K bands. The errors are
quoted as the 16th and 84th percentiles from the posterior distributions.
WD Name J Mag J Std H Mag H Std K Mag K Std
WD 0010+280 16.304+0.014−0.014 0.016
+0.019
−0.011 16.375
+0.011
−0.011 0.014
+0.016
−0.010 16.345
+0.019
−0.018 0.043
+0.023
−0.019
WD 0106−328 15.616+0.009−0.009 0.008+0.011−0.006 15.831+0.020−0.020 0.041+0.026−0.017 15.836+0.035−0.034 0.038+0.049−0.027
WD 0146+187 15.679+0.007−0.007 0.006
+0.008
−0.004 15.650
+0.010
−0.010 0.013
+0.014
−0.009 15.472
+0.029
−0.029 0.060
+0.039
−0.025
WD 0300−013 15.888+0.006−0.006 0.006+0.007−0.004 15.873+0.013−0.013 0.017+0.017−0.012 15.861+0.014−0.014 0.022+0.020−0.015
WD 0307+077 16.274+0.013−0.013 0.012
+0.016
−0.008 16.159
+0.012
−0.011 0.016
+0.017
−0.011 16.217
+0.018
−0.018 0.046
+0.020
−0.015
WD 0408−041 16.005+0.006−0.006 0.007+0.008−0.005 15.909+0.012−0.012 0.010+0.012−0.007 14.968+0.011−0.011 0.012+0.014−0.008
WD 0435+410 15.305+0.017−0.018 0.022
+0.055
−0.015 15.318
+0.043
−0.037 0.055
+0.138
−0.035 15.271
+0.011
−0.011 0.010
+0.012
−0.007
WD J0738+1835 18.080+0.015−0.016 0.026
+0.022
−0.017 17.857
+0.012
−0.012 0.028
+0.019
−0.018 17.329
+0.011
−0.011 0.065
+0.012
−0.012
WD J0959−0200 18.388+0.027−0.025 0.044+0.037−0.029 18.221+0.022−0.021 0.090+0.024−0.021 17.809+0.015−0.015 0.085+0.019−0.019
WD 1015+161 16.044+0.013−0.012 0.016
+0.020
−0.011 16.114
+0.016
−0.015 0.019
+0.023
−0.013 16.016
+0.018
−0.018 0.018
+0.022
−0.012
WD 1018+410 16.954+0.024−0.022 0.029
+0.039
−0.021 16.964
+0.025
−0.024 0.045
+0.037
−0.024 16.835
+0.019
−0.019 0.026
+0.026
−0.018
WD 1041+092 17.701+0.014−0.014 0.014
+0.016
−0.010 17.690
+0.015
−0.015 0.020
+0.021
−0.014 17.761
+0.018
−0.018 0.037
+0.028
−0.024
WD 1116+026 14.852+0.008−0.008 0.008
+0.013
−0.006 14.825
+0.013
−0.013 0.013
+0.023
−0.009 14.795
+0.006
−0.007 0.005
+0.006
−0.004
WD 1145+017 17.671+0.031−0.031 0.118
+0.030
−0.024 17.680
+0.015
−0.015 0.075
+0.016
−0.014 17.467
+0.012
−0.012 0.068
+0.015
−0.015
WD 1145+288 17.671+0.016−0.016 0.015
+0.017
−0.011 17.664
+0.015
−0.015 0.040
+0.020
−0.022 17.281
+0.012
−0.012 0.056
+0.016
−0.017
WD 1150−153 16.236+0.007−0.007 0.008+0.009−0.006 16.189+0.010−0.010 0.011+0.012−0.008 15.847+0.011−0.011 0.014+0.014−0.010
WD J1221+1245 18.413+0.029−0.029 0.039
+0.037
−0.027 18.264
+0.026
−0.024 0.103
+0.029
−0.027 17.841
+0.013
−0.013 0.039
+0.026
−0.025
WD 1225−079 14.963+0.009−0.008 0.010+0.014−0.007 14.960+0.015−0.015 0.013+0.023−0.010 14.957+0.007−0.007 0.012+0.010−0.008
WD 1226+110 16.965+0.012−0.012 0.011
+0.013
−0.008 16.944
+0.011
−0.011 0.012
+0.013
−0.008 16.623
+0.015
−0.015 0.029
+0.022
−0.019
WD J1234+5606 18.279+0.023−0.023 0.035
+0.032
−0.023 18.240
+0.023
−0.022 0.056
+0.032
−0.033 17.797
+0.021
−0.020 0.122
+0.022
−0.020
WD 1349−230 17.018+0.011−0.011 0.016+0.015−0.011 17.056+0.013−0.013 0.022+0.019−0.015 16.982+0.018−0.017 0.031+0.027−0.021
WD 1456+298 14.995+0.013−0.012 0.020
+0.025
−0.012 15.062
+0.012
−0.012 0.012
+0.021
−0.009 14.830
+0.009
−0.009 0.014
+0.013
−0.010
WD 1504+329 18.234+0.038−0.036 0.061
+0.055
−0.041 18.056
+0.018
−0.017 0.052
+0.026
−0.028 18.029
+0.022
−0.021 0.142
+0.023
−0.022
WD 1536+520 17.749+0.011−0.011 0.011
+0.012
−0.008 17.546
+0.011
−0.011 0.019
+0.016
−0.013 16.830
+0.009
−0.008 0.042
+0.010
−0.010
WD 1551+175 17.642+0.015−0.015 0.028
+0.021
−0.017 17.736
+0.014
−0.013 0.031
+0.019
−0.019 17.708
+0.018
−0.017 0.086
+0.021
−0.021
WD 1554+094 19.019+0.033−0.033 0.039
+0.042
−0.027 18.973
+0.045
−0.042 0.193
+0.047
−0.042 18.662
+0.035
−0.034 0.194
+0.037
−0.036
WD J1617+1620 17.337+0.011−0.011 0.018
+0.016
−0.012 17.202
+0.013
−0.013 0.049
+0.015
−0.013 16.865
+0.012
−0.012 0.026
+0.020
−0.017
WD 1729+371 16.130+0.005−0.005 0.008
+0.007
−0.005 16.068
+0.007
−0.007 0.012
+0.011
−0.008 15.853
+0.006
−0.006 0.008
+0.008
−0.005
WD 1929+011 14.820+0.006−0.006 0.006
+0.008
−0.004 14.843
+0.007
−0.007 0.011
+0.009
−0.007 14.656
+0.007
−0.007 0.007
+0.008
−0.005
WD 2132+096 16.238+0.005−0.005 0.006
+0.006
−0.004 16.283
+0.009
−0.009 0.015
+0.013
−0.010 16.282
+0.008
−0.008 0.017
+0.012
−0.011
WD 2207+121 17.600+0.011−0.011 0.030
+0.014
−0.013 17.452
+0.011
−0.010 0.037
+0.013
−0.014 17.245
+0.012
−0.011 0.062
+0.013
−0.013
WD 2221−165 15.978+0.009−0.010 0.011+0.012−0.008 15.902+0.009−0.009 0.010+0.011−0.007 15.858+0.020−0.021 0.033+0.029−0.022
WD 2326+049 13.143+0.080−0.078 0.113
+0.229
−0.058 13.038
+0.053
−0.049 0.071
+0.178
−0.037 12.652
+0.006
−0.006 0.011
+0.009
−0.007
WD 2328+107 15.999+0.004−0.004 0.007
+0.006
−0.005 16.004
+0.006
−0.006 0.006
+0.007
−0.004 16.071
+0.011
−0.011 0.024
+0.015
−0.015
2.1 Dust variability 45
(a) J Band Observations
(b) H Band Observations
Fig. 2.2
46 Dust Variability
(c) K Band Observations
Fig. 2.2 The median observed magnitudes in the (a) J, (b) H and (c) K bands plotted against
the median standard deviation of this magnitude for all white dwarfs and field stars. The two
different observing modes, with 5 and 10 second frame times, are analysed separately. The
density plots on the left hand side show the parameters for all field stellar objects in the field
of view, there are of the order 104 field stars in each plot. The blue points show the white
dwarfs, with the objects discussed in Section 2.1.2 labelled. The right hand plots show the
median magnitude and standard deviation with 16th and 84th percentile confidence levels
for field stars, in bins of width 0.5 mag. This forms a distribution about that median which
should not comprise contaminant variable stars. The white dwarfs are over-plotted in black
with the same values as in the left hand plots, but also including the 16th and 84th percentiles.
This plot can be used to distinguish white dwarfs which are variable from those that follow
the field star distribution.
2.1 Dust variability 47
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48 Dust Variability
WD 0146+187:
The object with the most significant deviation in the K band was WD 0146+187. In Fig.
2.2c the red triangle, which represents this object, shows a 2σ variability in the K band.
There was a flux brightening of 0.14 mag from the 1st to the 2nd stacked frames on 03/10/14.
There were no significant variations between the subsequent frames. Further investigations
revealed there was nothing anomalous in the pixel map, and objects in the field of view
within 100′′ do not show the same brightening trend. This could be a real change, but as there
is only one data point, and the variation is not statistically significant, it is difficult to make
any substantial conclusions. Swan et al. (2020) did not find variation in the Spitzer 3.6 µm
band for this white dwarf but observed variability at the 7 percent level in the 4.5 µm band.
Therefore, as no variability is seen at the 3.6 µm band it is likely that the K band variability is
not real.
WD J0959−0200:
WD J0959−0200 was previously observed to display a 35% flux drop in 2010 in both
Spitzer 3.6 and 4.5 µm Infrared Array Camera (IRAC) channels. The K band flux also
dropped by 18.5% between 2005 and 2014 (Xu & Jura, 2014). This variability measurement
uses the peak-to-peak method, where the maximum flux change between two frames is
quoted. After the Xu & Jura (2014) UKIRT data taken on the 27/03/14, the K band data were
consistent between multiple observations spanning 1153 days (Nov 2014, Feb 2015, Mar
2016, May 2016, May 2017). The K band flux was stable within 7.5+1.6−1.6 % (σ = 0.085
+0.019
−0.019)
over these observations, seen in Fig. 2.2c as the yellow pentagon.
WD 1226+110:
The peak-to-peak drop in flux of WD 1226+110 was 20% in the Spitzer 3.6 and 4.5 µm
bands, and 13% in the K band, when comparing the 2007 UKIRT Infrared Deep Sky Survey
K band flux with the 2015 UKIRT observation in this work (Xu et al., 2018b). Since 2015,
this UKIRT survey has shown no significant changes in flux for WD 1226+110 with multiple
observations separated by 738 days (May 2015, Feb 2016, May 2016, May 2017). The K
band flux was stable within 2.7+1.9−1.7 % (σ = 0.029
+0.022
−0.019) for these observations, seen in Fig.
2.2c as the gold square.
WD 0408−041:
Previously observed dust emission variations for WD 0408−041 (GD56) were seen at
3–5 µm showing brightening and dimming with peak-to-peak changes of 20% over 11.2 yrs
(Farihi et al., 2018). This was attributed to dust production and consequentially depletion. In
2.1 Dust variability 49
Table 2.3 The level of variability that can be detected at each magnitude in the K band,
calculated from the field stars. The objects which were observed with 5 and 10 second frames
were analysed separately. The median percentage variability is quoted for the field stars in
bins with a width of one mag, along with the 16th and 84th percentiles.
Magnitude 5 s variability (%) 10 s variability (%)
11.0-12.0 0.41+0.08−0.02 0.20
+0.27
−0.08
12.0-13.0 0.41+0.07−0.02 0.15
+0.14
−0.04
13.0-14.0 0.43+0.10−0.04 0.14
+0.12
−0.04
14.0-15.0 0.57+0.29−0.11 0.20
+0.18
−0.07
15.0-16.0 1.27+1.31−0.51 0.52
+0.58
−0.27
16.0-17.0 3.91+3.47−1.75 2.32
+1.65
−1.17
17.0-18.0 9.43+6.23−3.89 6.34
+3.33
−2.52
18.0-19.0 16.14+7.67−6.48 13.16
+5.38
−4.62
this work, the fluxes were found to be consistent between multiple observations separated by
851 days (Oct 2014, Oct 2016, Jan 2017). The K band dust emission appears to be stable
within 1.1+1.2−0.8 % (σ = 0.012
+0.014
−0.008) for these observations, seen in Fig. 2.2c as the orange
diamond. WD 0408−041 will be discussed again in Section 2.1.3 in reference to the Spitzer
variability.
Expected Variability
From the UKIRT survey the level at which variability could be detected and ruled out is
determined. Table 2.3 shows the level of variability that can be detected at each K band
magnitude. For each non-variable star in the fields of views of the white dwarfs, the median
standard deviation of the magnitude measurements from the MCMC model is output. The
level of variability is the median value of the non-variable stars’ standard deviations, found in
magnitude bins with a width of one mag. This median standard deviation was then converted
to a percentage in flux space. This rules out K band flux variability at 1.3+1.3−0.5 % for objects
brighter than 16th mag in the K band, and at 9.4+6.2−3.4 % for objects brighter than 18th mag.
Fig. 2.4 shows a cumulative distribution of the level of variability ruled out for all white
dwarfs. In other words, the percentage of white dwarfs where the K band flux was seen to
vary by no more than the plotted value. This was calculated as the median standard deviation
converted to a percentage in flux space. This was also calculated for the 16th and 84th
percentile errors, which is shown as the shaded region in the figure. The K band flux of each
50 Dust Variability
Fig. 2.4 A cumulative distribution showing the level of K band variability that can be ruled
out for the white dwarfs. The blue line shows the median cumulative distribution, with
the contours as the cumulative distribution on the upper and lower limits (16th and 84th
percentiles). For 90% of the sample, the K band flux varied by less than 10%.
white dwarf cannot have varied more than its equivalent standard deviation. Therefore, the K
band flux has varied at less than 16.4± 2.8% for the entire sample, and less than 2.88+2.5−1.9%
for the median case. For greater than 90% of the sample variability is ruled out at the 10%
level, and for the 10 most constrained cases, variability is ruled out at the percent level,
1.57+1.1−1.0%.
Fig. 2.5a shows the percentage variability ruled out for each white dwarf plotted against
the maximum time-scale over which that white dwarf was monitored in this survey. For
example, for the white dwarf monitored over the longest period, WD 1929+011, variability
is ruled out at the 0.7+0.7−0.5 % level over a time-scale of 1013 days.
There are a handful of objects in the literature with previous detections of a change in
their dusty emission, as discussed in Section 2.1.2. For WD J0959−0200, Xu & Jura (2014)
found a drop in K band flux from 57µJy to 46µJy which is equivalent to a peak-to-peak
drop of 18.5%, and Xu et al. (2018b) found a K band peak-to-peak drop of 13% for WD
1226+110. It is noted that there is difficulty in comparing the peak-to-peak variability quoted
for these objects with the median variability quoted in this work. With two measurements it
is not possible to constrain the distribution of fluxes that an object could be demonstrating,
so the quoted variability is peak-to-peak. As there are more K band measurements, a median
2.1 Dust variability 51
variability is used for all white dwarfs, which is compared to the distribution of the field
objects to constrain the level of variability. Typically, peak-to-peak variability is larger than
the medium variability adopted here. The peak-to-peak variability was also calculated for the
sample using the maximum difference between the mean flux at each observation date, and
the conclusions are consistent. In this sample equivalent peak-to-peak and median variability
are ruled out for all white dwarfs across the time-scales observed. The observations of both
WD J0959−0200 and WD 1226+110 suggest that the campaign is capable of detecting the
same level of variability as observed previously, and yet no such variability is detected during
the survey time span for all white dwarfs.
2.1.3 Discussion
K Band Excess
For all objects in the sample, a white dwarf atmospheric model was fitted to find the expected
contribution from the white dwarf photosphere to the K band flux. The white dwarf model
atmospheres were kindly provided by P. Dufour using models from the Montreal white dwarf
group (Bergeron et al., 2011; Coutu et al., 2019). The temperature, and log(g) used for the
models are shown in Table 2.1; where possible, these parameters were taken from a previous
photometric fit. For a number of white dwarfs where no photometric fit was available, a new
fit was performed including data from the Gaia Data Release 2 (Prusti et al., 2016; Brown
et al., 2018). The white dwarf radii (R) were determined from the photometric fit and the
distances (D) were from the Gaia parallax (except for WD J0959−0200 which was from
Farihi et al. (2012a)). The SED fits are shown in Appendix 1: 6.2; the photometric fit works
well in most cases. Sometimes, additional adjustments were needed in R/D to improve the
fits to the Sloan Digital Sky Survey (SDSS) and Pan-STARRS photometry. Those systems
often had a large uncertainty in the parallax.
The white dwarf models were convolved with the bandpass of the UKIRT WFCAM K
band filter (Hewett et al., 2006) to find the expected flux contribution from the white dwarf
photosphere. From this, the excess flux associated with the dust was determined.
White dwarfs are usually photometrically stable and are often used as flux standards. A
few white dwarfs in the sample are variable pulsators, however the optical variability is small,
typically < 1%. Assuming the white dwarf photosphere displays no flux variations, the K
band variability limit can be converted to the dust variability limit,
σdust = σK
FK
FK−FWD , (2.1)
52 Dust Variability
where σdust is the variability constraint for the dust, σK is the variability constraint for the K
band (dust and photosphere), FK is the UKIRT K band flux measurement, and FWD is the
convolved model flux in the K band for the white dwarf photosphere. This puts a constraint
on how much the dust could have changed without being detected in this survey assuming
the star remains constant.
The maximum variability not detected in the K band is used and converted to a maximum
variability not detected in the dusty emission using equation 2.1. Fig. 2.5b is a similar plot to
Fig. 2.5a, but instead showing the level of variability ruled out for the dust emission after the
white dwarf photosphere is subtracted. A K band excess is seen for 23/34 of the white dwarfs,
as seen in the SEDs in Appendix 1: 6.2. The 11 white dwarfs without a significant K band
excess are: WD 0106−328, WD 0300−013, WD 0307+077, WD 1041+092, WD 1225−079,
WD 1456+298, WD 2132+096, WD 2221−165, WD 2328+107, WD 1504+329, and WD
1551+175. For the 23 objects with significant K band excesses, limits are constructed on
how much dust variation could be hidden from detection. For 11 white dwarfs (∼ 50% of the
sample with significant K band excesses) dust changes were constrained to be less than 10%,
demonstrating the dust emission was stable over the course of the monitoring period. For
the 11 systems where the K band excess was negligible, the dust variability constraint would
have been 100%. For these objects it was only possible to be sensitive to an increase in dust
emission, not a decrease. Therefore, the dust could have completely disappeared, and it could
not be distinguished from the dust displaying no variability. For those with no significant K
band excess, it is imperative to go to the mid-infrared for dust variability searches.
Expected Variability at 4.5 µm
Using the variability constraint derived from the UKIRT survey, the expected variability at
4.5 µm can be predicted by assuming the dust emission has a constant colour temperature (i.e.,
the change is due to the amount of dust, not the location). So the shape of the dusty emission
is assumed to remain constant, such that the percentage change of the dusty emission at K
wavelengths can be equalled to the percentage change at 4.5 µm . Paralleling the K band
analysis and equation 2.1, the expected variability at Spitzer 4.5 µm wavelengths is calculated,
σ[4.5] = σdust
F[4.5]−FWD
F[4.5]
, (2.2)
where σ[4.5] is the predicted variability constraint for the 4.5 µm Spitzer waveband, σdust is
calculated from the K band using equation 2.1, F[4.5] is the 4.5 µm Spitzer flux, and FWD is
the convolved model flux in the 4.5 µm band for the white dwarf photosphere.
2.1 Dust variability 53
(a) K band variability
(b) Dust variability
Fig. 2.5 (a) The maximum K band median variability of each white dwarf that would not
have been detected over the time-scale of the survey. (b) The maximum dust variability of
each white dwarf that would not have been detected over the time-scale of the survey. The
variability constraint of the dust component to the K band flux was calculated using equation
2.1.
54 Dust Variability
Fig. 2.6 Predictions for the maximum median variability at 4.5 µm that would have escaped
detection based on the maximum median K band variability not detected with this UKIRT
survey. The arrows represent that each axis is a constraint on the level of variability. Most
objects had Spitzer 4.5 µm data, but for four objects WISE data was used as no Spitzer data
was available. Swan et al. (2019b, 2020) assessed the level of Spitzer and WISE mid infrared
variability at levels above these limits, future analyses that combine the results from these
studies are crucial for understanding these dusty white dwarfs.
Fig. 2.6 shows the K band variability constraint, converted into a Spitzer 4.5 µm band
variability constraint using equation 2.2. The Spitzer data was taken from the references
listed in Table 2.1. If there was no Spitzer 4.5 µm data available then WISE 4.6 µm data
was used instead. The dust excess at 4.5 µm is larger than that at the K band, therefore, the
variability constraint in flux units will be larger for 4.5 µm, as seen in the figure. Those
white dwarfs with negligible K band excess are excluded from this study. For those 23 white
dwarfs with significant K band excess, at Spitzer wavelengths it is predicted that variability
can be ruled out above 10% for ∼60% of the sample, above 20% for ∼ 85% of the sample,
and above 36% for all the sample.
A particular application using the UKIRT survey can be applied to the WD 0408−041
system. Farihi et al. (2018) found the dust emission of WD 0408−041 to increase and
decrease with a peak-to-peak variability of 20% over ∼ 11 years. As can be seen from
Appendix 1: 6.2, the SED of WD 0408−041 demonstrates a large K band excess. Therefore,
any variability observed at mid-infrared wavelengths should be mimicked at a lower level in
the K band, unless there is a colour change associated with the flux change. Fig. 2.7 shows
2.1 Dust variability 55
Fig. 2.7 A lightcurve of WD 0408−041 showing the UKIRT K band data, and the
Spitzer/WISE data at which Farihi et al. (2018) observed a drop in the mid-infrared flux. The
grey regions represent the 1 and 3σ median variability constraint for the K band, and then
scaled up to Spitzer wavelengths using equations 2.1 and 2.2 (assuming no colour change).
The blue region shows the period of time with UKIRT observations. Figure adapted from
Farihi et al. (2018).
the lightcurve for WD 0408−041 over approximately four years showing Spitzer, WISE
and UKIRT K band data. The drop in mid-infrared flux is evident. There are not UKIRT K
band observations which cover the full mid-infrared time-scale, as shown by the blue shaded
region. Using equations 2.1 and 2.2, the K band variability ruled out using the UKIRT survey
is scaled up to mid-infrared wavelengths. The change in the Spitzer 4.5 µm flux is consistent
with the variability constraint derived from the K band data, implying that the variability
could be consistent with the same colour temperature of the dust emission during the three
year UKIRT survey. However, looking across the four year baseline, even at 3σ , the Spitzer
flux values lie outside of the shaded region, i.e. prior to 56880 MJD and after 58100 MJD.
The most significant drop in Spitzer flux was around 58100 days. There are not simultaneous
K band observations, with the closest K band measurement being over a year previous to
this. There is previous evidence that large scale flux changes can occur on time-scales of
less than a year (Xu & Jura, 2014). A further K band measurement is needed in order to
understand whether the K band flux also dropped around MJD58100, or if there is a colour
change associated with this variability.
56 Dust Variability
Variability Time-scales
Fig. 2.8 shows the characteristic sampling for all the white dwarfs in the sample. This survey
was sensitive to short time-scales on the order of minutes to hours and long time-scales on the
order of years. Previous examples of gas variability show changes on both these time-scales
(e.g. Manser et al., 2019), and previous example of dust variability show changes on year
long time-scales (e.g. Xu & Jura, 2014).
A toy model is considered where the K band flux of every white dwarf varies as a step
function by ∆%, every t days. The probability of detecting this variability in this UKIRT
survey is calculated. Each white dwarf has a minimum detectable variability which is 3σ
above the median variability of the field stars at the same magnitude as the white dwarf, where
σ is the standard deviation on this median variability. If ∆ was smaller than the minimum
detectable variability for that white dwarf, the probability of detection was 0. For every
combination of ∆ and t, the lightcurve was randomly sampled 1000 times for each white
dwarf using the UKIRT sampling times to calculate the probability that if it were varying
in this manner, it would have been detected in this survey. By averaging over all 34 white
dwarfs at each ∆ and t, the overall probability of detection was deduced, as shown in Fig. 2.9.
The colour scheme represents the probability that the UKIRT survey would have detected
that combination of ∆ and t if all white dwarfs varied in this way. The highest probability
time-scales show that the survey was sensitive to variability over days, and years. Models
where all white dwarfs vary on time-scales of ∼ 1–2 years with large amplitudes are ruled
out. However, it isn’t possible to rule out models where white dwarfs vary on time-scales
much longer than this, or with smaller amplitudes (< 10%). This may explain why some
objects from the literature which have been previously found to vary are consistent with little
or no variability in this survey. For example, using seven years of WISE data, Swan et al.
(2019a) found variability in a number of dusty white dwarfs. Using this model it can be seen
that for these longer time-scales, there is less than a 30% chance of detecting variability.
Implications
The leading explanation for white dwarf pollution cites asteroids as the source which are
scattered inwards stochastically. How frequently these asteroids are scattered inwards remains
an open question, with debate in the literature between whether pollution is caused by a
single large body, or many small bodies (e.g. Jura, 2008; Jura et al., 2009b; Wyatt et al.,
2014).
Wyatt et al. (2014) presented a model whereby white dwarf pollution is explained by
a continuous stream of many small asteroids, with the stochastic scattering of the largest
2.1 Dust variability 57
Fig. 2.8 A histogram showing the characteristic survey sampling to search for variability.
The plot shows the distribution of all time-scales between frames of a given white dwarf,
for all white dwarfs. This demonstrates that for all white dwarfs the survey was sensitive to
minute/hour time-scales and year time-scales.
Fig. 2.9 A toy model in which every white dwarf in the sample is considered to have a K band
flux that varies by ∆% every t days. The density plot indicates the probability of detecting
that combination of ∆ and t for white dwarfs in the UKIRT survey. The smallest grid scale is
1 day and 0.1%.
58 Dust Variability
bodies dominating the accretion rates. In this model, the lifetime of the dusty material is
a free parameter, with a best-fitting value of 20 years. The survey would be unlikely to
detect variations on such long time-scales. However, if the disc lifetime was instead an
order of magnitude smaller (∼ 2 years), large amplitude variations in the infrared flux on
these time-scales would be expected. In this survey, large variability is ruled out over these
time-scales. Therefore, the results of this survey provide further evidence in support of long
(> 3 year) lifetimes for the dusty material around white dwarfs. It also demonstrates that
disruption events large enough to be detectable in the infrared do not regularly occur on short
time-scales such as years. This is crucial, as for many highly polluted DA white dwarfs,
material can sink out of the atmospheres on time-scales of days to years. This work provides
observational evidence that dusty material has a lifetime of at least 2–3 years. Therefore, it
is highlighted that further monitoring in the infrared is needed to discover the frequency of
scattering events.
2.1.4 Conclusions from the UKIRT survey
Infrared studies are crucial for understanding the accretion processes associated with polluted
white dwarfs. This work reports a near-infrared J, H, and K band monitoring campaign with
the UKIRT, completed over three years which studied 34 polluted white dwarfs with infrared
excesses. High precision J, H, and K band photometry was reported for the white dwarfs in
the sample, for many of these objects high precision photometry is not previously reported.
The main results are summarised as follows.
1. The K band flux was stable within the error of the survey for all observations of the
white dwarfs, where the observation sampling rates were on the order of minutes and
years. Of the near-infrared bands, the K band is the most sensitive to the dust. It was
possible to rule out median K band variability greater than 16.4+2.8−2.8% for the faintest
white dwarf in the sample and greater than than 2.88+2.5−1.9% for half of the sample.
For > 90% of the sample variability at the 10% level was ruled out, and for the 10
most constrained white dwarfs, K band variability was ruled out at the percent level,
< 1.57+1.1−1.0%.
2. WD J0959−0200 and WD 1226+110 have previously exhibited variability in their
dusty emission as seen at the K band (18.5% for WD J0959−0200 and 13% for
WD 1226+110) and Spitzer 3.6 and 4.5 µm bands. These objects did not display any
significant variability in the study. For most of the sample (except the faintest object,
WD 1554+094) similar K band variability to these white dwarfs was ruled out. This
highlights that these large K band variability events are rare.
2.2 Dust variability 59
3. Assuming there is no colour change associated with the dust emission, the variability
at 4.5 µm was predicted based on the K band variability. The white dwarfs should
not vary at 4.5 µm above 10% for ∼ 60% of the sample, above 20% for ∼ 85% of the
sample, and above 36% for all the sample.
4. It was demonstrated that any white dwarf with large amplitude (> 20%) near-infrared
variability on short (< 3 year) time-scales should have been found with this survey.
This implies that major tidal disruption events that lead to white dwarf pollution occur
less frequently than every three years, and are consequently rare. Infrared variability
around white dwarfs with infrared excesses does exist as revealed by other observations.
The constraints provided from the K band survey imply that such events, if they occur,
do so on short time-scales, and quickly become stable within a few years.
5. Ground based near-infrared searches for white dwarf dust variability are fruitful, and
as demonstrated in this survey can search for variability down to the percent level
for the brightest sources. This survey was not sensitive to long time-scale (> 3 year)
variability and, therefore, it is crucial to highlight the need for long-term monitoring of
white dwarfs with infrared excesses. Also, with recent advances finding variability in
the gas discs over periods of hours (Manser et al., 2019), it is also crucial to search
for variability over hours–days timescales in the dust to fully understand these highly
enigmatic and dynamic systems.
2.2 NIR dust variability with SOFI/NTT
Variability in the near infrared was ruled out over timescales of months–years using the
UKIRT/WFCAM. However, there are previous examples of white dwarfs with remnant
planetary systems demonstrating variability on shorter timescales such as hours. Manser et al.
(2019) discovered rapid variability in the gaseous disc of WD 1226+110. A 123.4 minute
stable period was observed in the spectral shape of the gaseous emission features and was
attributed to a planetesimal orbiting within the disc on a short period. Furthermore, time
series lightcurves of a number of white dwarfs reveal they are being transited by material and
have periods as short as a few hours (e.g. Vanderburg et al., 2015). The material orbiting the
white dwarfs on timescales of hours are on close-in orbits, and studying this material can
shed light on exactly how this material ultimately disrupts, migrates towards the white dwarf,
and accretes. No studies have searched for variability in the dust emission at short timescales
of hours – days, this is the focus of the following section.
60 Dust Variability
2.2.1 NTT Observations and data reduction
A near-infrared monitoring campaign was conducted using the SOFI near-infrared imaging
instrument on the New Technology Telescope in La Silla, Chile between April 17th 2019 –
April 24th 2019 (PI: Rogers). Table 2.4 lists the white dwarfs observed. The targets consist
of eight white dwarfs that: have atmospheric pollution, have infrared emission associated
with a dust disc, are brighter than 17th magnitude in the K band, and were observable from
the southern hemisphere during the observing run.
The observing run had two main goals: to search for dust emission changes through KS
band observations over timescales of hours–days for a sample of white dwarfs with dust
discs, and to obtain a continuous KS band lightcurve of WD 1226+110 over a number of
hours. For the first goal, the observing strategy was to obtain sets of J, H and KS band
photometry separated by hours, and then days, but due to extreme weather conditions it was
difficult to plan cadences. G166-58 is missing the set of observations separated by hours, but
is still included in the analysis. The aim was to achieve a SNR of 30 for each frame for the
J and H band, and 40 for the KS band, mirroring the UKIRT/WFCAM observing strategy.
Dithering enables the removal of instrument signatures, such as bad pixels, and allows the
removal of the sky background, therefore, a five point dither pattern was used with each
pattern producing one frame. For the second goal, the aim was to obtain a continuous KS
band lightcurve of WD 1226+110 whilst it was above an altitude of 30 degrees in the sky.
In total 340 frames of 10 second KS band exposures were taken which spanned across ∼
6 hours. Exposure times of 10 seconds per frame were used to avoid detector saturation.
Sets of five frames were stacked together to produce a single KS band frame providing one
stacked frame every ∼ 6 minutes.
Standard infrared imaging data reduction techniques were used to process the images
using ESO SOFI pipeline (v1.5.10), including dark subtraction, flat fielding and sky subtrac-
tion. WCS information was updated using the WCSFIT package as part of CASUTOOLS to
obtain more accurate positional information using 2MASS catalogue sources. Photometric
calibration was performed using 2MASS sources in the field of view. LIGHTCURVES was
used to obtain improved precision of the photometry as described in Section 2.1.1 for the
UKIRT/WFCAM data.
2.2.2 Variability Analysis
JHKS photometry for seven white dwarfs
This work aimed to obtain high precision JHKS photometry of seven dusty white dwarfs
to investigate whether variability is observed over timescales of hours–days. Of the near-
2.2 Dust variability 61
Table 2.4 Observations of the white dwarfs listing the number of sets of JHK photometry
obtained and the baseline for these observations.
WD Name Other Name N sets Min Baseline Max Baseline
WD 0959−57 WG 14 8 0.3 hrs 7 days
EC 05365−4749 - 3 0.4 hrs 7 days
WD 1929+011 - 4 2 hrs 3 days
WD 2115−560 - 3 2 hrs 2 days
WD 2221−165 HE 2221−165 3 1.1 hrs 2 days
WD J1617+1620 SDSS J161717.04+162022.4 3 2 hrs 2 days
G166-58 - 2 2 days† 2 days†
WD 1226+110 SDSS J122859.93+104032.9 340∗ 6 mins 6 hours
Notes:
∗ WD 1226+110 has 340 KS band frames taken over 6 hours.
† G166-58 has only 2 sets of JHK observations so minimum and maximum baseline is the same.
infrared bands, the KS band is the most sensitive to the dust, as discussed previously, therefore
it will be investigated whether there is variability in the KS band that is not present in the J or
H bands. Throughout the analysis the Vega magnitude system was adopted.
LIGHTCURVES was used to perform differential photometry and fit 2D polynomials to
the magnitude residuals to minimise the error associated with the position on the detector,
allowing improved precision lightcurves for the white dwarfs. It is crucial to have enough
comparison stars in the field of view for LIGHTCURVES. Table 2.5 lists the number of
comparison stars used in LIGHTCURVES, the number varies from 15–1155. G166-58 has the
smallest number of comparison stars, further investigations varying the parameters used in
LIGHTCURVES revealed no significant changes to the final results.
Figure 2.10 shows the output KS band magnitude over time from LIGHTCURVES for the
seven white dwarfs. As can be seen, no statistically significant variability is observed in these
lightcurves. This rules out variability in the KS band dust emission over timescales of hours
and days for these white dwarfs.
The median KS band magnitude is measured for each white dwarf and compared with
historic KS band data from 2MASS, KS band data Dennihy et al. (2016), and the UKIRT K
band magnitudes in Section 2.1 for those where there is overlap (see Table 2.5). The only
white dwarf displaying discrepant K band measurements are for WD 1929+011. The 2MASS
KS band is ∼ 0.2 mags brighter than the measurement here. Other K band measurements
from the literature, 14.62±0.05 (Melis et al., 2011) and 14.66±0.01 (Rogers et al., 2020) are
consistent with the KS band measurement from SOFI, when correcting for the differences in
the magnitudes from the KS and K filters (Carpenter, 2001). Melis et al. (2011) discusses
the discrepancy between 2MASS and their K band measurement and find that it is likely
62 Dust Variability
Table 2.5 Table listing dates of observations for the white dwarfs in the sample, and number
of exposures. N comp is the number of comparison stellar objects in the frame.
WD Name 2MASS J 2MASS H 2MASS KS N comp Kobs
WD 0959−57 15.18±0.07 15.03±0.09 15.16±0.18 1155 15.17±0.10
EC 05365−4749 16.10±0.01 † 15.92±0.18 16.11±0.04 † 53 16.05±0.08
WD 1929+011 14.66±0.05 14.54±0.09 14.45±0.10 513 14.63±0.06
WD 2115−560 14.11±0.0 13.99±0.06 14.02±0.06 31 14.02±0.03
WD 2221−165 15.80±0.06 15.79±0.14 15.86±0.03 ∗ 30 15.74±0.10
WD J1617+1620 17.34±0.02 ∗ 17.20±0.05 ∗ 16.87±0.03 ∗ 58 16.77±0.11
G166-58 14.97±0.05 14.61±0.08 14.74±0.13 15 14.72±0.03
Notes:
∗ Magnitude from the UKIRT survey in Section 2.1. Note: UKIRT is K band whereas SOFI is KS, so
the magnitudes are not directly comparable.
† EC 05365−4749 J and KS band magnitudes from Dennihy et al. (2016).
WD 1929+011 suffers from contamination from background sources in 2MASS, which due to
the large pixel sizes for 2MASS can cause discrepant photometry. Therefore, no statistically
significant variability is observed for these white dwarfs which reinforces the conclusions
from the UKIRT survey.
WD 1226+110
LIGHTCURVES was used to output KS band aperture photometry lightcurves for WD 1226+110
and four comparison stars. The field of view of WD 1226+110 is sparse, therefore, insuffi-
cient numbers of comparison stars were in the field of view for LIGHTCURVES to perform
differential photometry or to fit 2D polynomials to the magnitude residuals to minimise the
error associated with the position on the detector. Instead four stars were selected from the
LIGHTCURVES output for manual differential photometry, these were selected as they were:
less than one magnitude brighter than WD 1226+110, more than 100 pixels from the edge
of the detector, and classified as non-variable stars. The KS band lightcurves for the four
comparison stars are shown in Figure 2.11. The offset required to correct the lightcurve of
WD 1226+110 for photometric variation induced by external factors (e.g. atmospheric/cloud
variations) was constructed by calculating the weighted mean ∆ K of the four stars for each
frame, weighted by the measurement error for each magnitude in the lightcurve. For each
object, LIGHTCURVES flags frames where the aperture contained bad or saturated pixels, so
the associated measurements from these frames were excluded from the calculation and are
not plotted in Figure 2.11. The magnitude ‘offset’ lightcurve is plotted in black along the
top of Figure 2.11, and this is subtracted from the KS band lightcurve for WD 1226+110 to
2.2 Dust variability 63
1 2 3 4 5 6 7
BJD - 58590 (d)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
∆
K
(m
ag
)
ECO5365-4749
G166-58
WD1931+0117
WD0959-572
WD2115-560
WDJ1617+1620
WD2221-165
Fig. 2.10 KS band measurements for the seven white dwarfs in the sample, all offset by 0.2
mags. Observations were taken separated by hours and days. ∆K is the output KS band
magnitude subtracted from the median magnitude of the lightcurve, such that > 0 is brighter
than the median magnitude and < 0 is fainter.
64 Dust Variability
obtain the corrected lightcurve shown in Figure 2.12 with measurement errors output from
the aperture photometry of LIGHTCURVES added in quadrature with the errors from the offset
lightcurve.
By eye, the lightcurve of WD 1226+110 reveals no significant variations. However, it
should be noted that the errors are large due to poor weather conditions, with SNR per frame
<10. The median offset in ∆K, as shown in Figure 2.11, is 0.31 mags, and the maximum
offset is 1.5 mags. In order to search for hidden periodicities, a Lomb-Scargle periodogram
was constructed using ASTROPY4 tools, Figure 2.13 (Lomb, 1976; Scargle, 1982; VanderPlas,
2018). Lomb-Scargle periodograms are a powerful tool that can detect periodic signals when
observations are unevenly spaced in time. Frames that were flagged by LIGHTCURVES are
excluded from this study. Periods between 7 minutes and 300 minutes were sampled, the
periodogram reveals two peaks at: 0.011 days and 0.039 days. In order to assess whether
these periods are significant, false alarm probabilities are calculated. This finds the probability
that a peak would be measured at this height or above if it is assumed that the data only
consists of Gaussian noise with no periodic signals. The peaks at periods of 0.011 days and
0.039 days have false alarm probabilities of 0.62 and 0.60 respectively. Therefore, the false
alarm probability is high and so the peaks are unlikely to be real. In order to decrease the
false alarm probability, further and more precise time series data needs to be taken.
Manser et al. (2019) observed a 123.4 minute period in the gaseous component to the disc
surrounding WD 1226+110, this period is not observed in the dust emission. The vertical
dashed line in Figure 2.13 shows the 123.4 minute period found in the gaseous component,
no peaks in the periodogram are observed around this period.
2.2.3 Discussion
As with the UKIRT survey over timescales of years, white dwarfs displaying large amplitude
near-infrared variability appear to also be rare over shorter timescales of hours–days. From
the UKIRT survey it was hypothesised that large events leading to KS band variability are rare
and could be occurring on shorter timescales and quickly become stable, therefore, predicting
variability over shorter periods. However, this is not observed in this work. Comparing
historic near-infrared magnitudes confirmed no variability in the near-infrared over timescales
of years. This is especially important for the three white dwarfs that did not overlap with
the UKIRT survey (WD 0959−57, EC 05365−4749, WD 2115−560), where the historic
magnitudes were all consistent within 1σ to the SOFI/NTT magnitudes. These conclusions
are limited as the sample is small, with limited sets of JHK data. With more white dwarfs
4https://www.astropy.org
2.2 Dust variability 65
0.00 0.05 0.10 0.15 0.20 0.25 0.30
BJD - 58593 (d)
−2.5
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
∆
K
(m
ag
)
16.13
15.85
16.07
16.55
Offset
Fig. 2.11 The lightcurves of the four stars in the field of view of WD 1226+110 that were
used to perform differential photometry, each offset from one another. ∆K is the output
KS band magnitude subtracted from the median magnitude of the lightcurve, such that > 0
is brighter than the median magnitude and < 0 is fainter. The median KS band magnitude
of each comparison star is labelled. The lightcurve labelled ‘offset’ is the calculated offset
from the four stars that was applied to the WD 1226+110 lightcurve to perform differential
photometry.
66 Dust Variability
0.05 0.10 0.15 0.20 0.25
BJD - 58593 (d)
−3
−2
−1
0
1
2
∆
K
(m
ag
)
Fig. 2.12 K band lightcurve spanning∼ 6 hours for WD 1226+110. ∆K is the output KS band
magnitude subtracted from the median magnitude of the lightcurve, such that > 0 means
WD 1226+110 is brighter than the median magnitude and < 0 means it is fainter. The errors
are large due to non-photometric conditions.
10−2 10−1
Period (d)
0.00
0.05
0.10
0.15
0.20
0.25
P
ow
er
123.4 min
Fig. 2.13 Lomb-Scargle periodogram for WD 1226+110 using the lightcurve in Figure 2.12.
The vertical dashed line shows the 123.4 minute period observed by Manser et al. (2019) in
the gaseous component of the disc for WD 1226+110. The periodogram reveals two peaks at
0.011 days and 0.039 days but have false alarm probabilities of 0.62 and 0.60 respectively
and are unlikely to be real.
2.2 Dust variability 67
with infrared excesses being discovered and confirmed (e.g. Lai et al., 2021), those which
are brighter and have a more significant KS band excess could be targeted to truly rule out
near-infrared variability.
WD 1226+110
Variability in both the circumstellar dust and gas has been previously observed for the white
dwarf WD 1226+110. Xu et al. (2018b) observed significant changes in the infrared dust
flux for WD 1226+110 with a 20% (3σ ) flux drop in Spitzer mid-infrared bands, and a
13% (2.7σ ) drop in K band was observed between 2007 and 2015. Subsequent K band
observations demonstrated that it remained at the same level for the following years, as seen
in Section 2.1.2. Manser et al. (2016a) reported evolution of the calcium infrared triplet gas
emission features over periods of 24–30 years, and interpreted it as the precession of the disc.
Additional variability in the gaseous emission features was observed with a 123.4 minute
period reported with a likely explanation of a planetesimal orbiting within the disc (Manser
et al., 2019).
Although variability has been previously observed in both the circumstellar dust and
gas emission, no K band variability is reported in this work. The work by Manser et al.
(2019) proposed that the planetesimal could interact with the dust which causes the gaseous
disc component and varying intensity pattern within the disc. If the planetesimal is first
interacting with the dust, it may be expected that this 123.4 minute signal is mimicked in
the dust emission. No 123.4 minute signal is observed in the KS band lightcurve. Therefore,
there doesn’t appear to be a correlation between the dust and gas. This could imply: that the
dust is not involved in causing the variable gaseous disc component, that the dust and gas are
not co-orbital, or that dust variability associated with this interaction is undetectable.
These conclusions are limited by the observations. These observations were conducted
over 6 hours which is roughly three times the length of the 123.4 minute period. Additional
K band time series data which covers more periods would help to determine whether there
truly is no 123.4 minute period. Also, observations taken under photometric conditions
are preferable to help to reduce the measurement errors and result in detections of smaller
amplitude variations. Furthermore, a wider field of view would enable more calibration
stars to be included such that LIGHTCURVES could be utilised to produce high precision
differential lightcurves for WD 1226+110.
68 Dust Variability
2.2.4 Conclusions from the NTT/SOFI survey
This work reports a near-infrared monitoring campaign to search for dust variability over
timescales of hours–days. Seven white dwarfs had multiple sets of J, H, and KS band
photometry measured over the space of hours and followed up again over timescales of
days. A ∼ 6 hour continuous KS band lightcurve was obtained for WD 1226+110 to study
timescales of minutes/hours in detail and search for a dust variability signal equivalent to the
123.4 minute signal in the gaseous component of the disc. The main results are summarised
as follows.
1. The KS band flux, which of the near-infrared bands is most sensitive to the dust, was
stable within the error of the survey for all observations of the eight white dwarfs,
where the observation sampling rates were on the order of hours and days. Comparing
with historic K band magnitudes, no statistically significant changes were observed.
2. The constraints from the UKIRT survey implied that if these large tidal disruption
events that cause near-infrared variability occur, they do so on short time-scales, and
quickly become stable within a few years. This limited sample does not support short
term variability. WD J0959−0200 (Xu & Jura, 2014) and WD 1226+110 (Xu et al.,
2018b) remain the only white dwarfs to show significant K band variability from
previous studies emphasising the rarity of K band variability. It is also interesting to
note that both these system display detectable circumstellar gaseous discs hinting at a
link between K band variability and the most extreme collisions.
3. No significant variability is detected in the 6 hour continuous KS band lightcurve of
WD 1226+110. The dust does not appear to be varying over these short timescales
despite a 123.4 minute period variation in the gaseous component to the disc. This
may imply there is no link between the dust and the gas variability.
4. Swan et al. (2019a) and Swan et al. (2020) show that mid-infrared variability appears to
be more common than in the near-infrared. In depth modelling is required to understand
these systems and the links between the near and mid infrared. This can be difficult due
to degeneracies between the distance of the dust from the white dwarf, the dust size,
the dust composition and albedo. It is crucial to model the near and mid infrared dust
emission and variability to understand the temperatures, sizes and compositions of the
grains, and how this material ultimately ends up in the white dwarf photosphere. With
developing technologies such as GRAVITY+, it may become possible to obtain images
of the spatially resolved dust for some of the brightest infrared excess white dwarfs.
2.2 Dust variability 69
This would help to calculate the radial extent of the dust, breaking the degeneracy
between dust size and dust distance from the white dwarf.

Chapter 3
Metal line variability
The events that lead to planetary material ultimately accreting onto white dwarfs are violent
and variable. The dynamic and stochastic nature of these systems consequently predicts the
accretion rate to also vary. For warm DAZ white dwarfs (12,000 K – 25,000 K), sinking
timescales of pollutant metals are of the order days – months. Therefore, any temporal
variations in the accretion rate or amount of material in the photosphere of the white dwarf,
should be detectable with spectroscopic monitoring over timescales longer than the sinking
timescales. von Hippel & Thompson (2007) reported an increase of ∼ 70% in the equivalent
width of the Ca II K line in G29-38 over 3 years. However, a follow up study by Debes
& López-Morales (2008) found no evidence for changes in the equivalent width of the Ca
II K line, nor a number of other spectral lines, and hypothesised that the variations found
previously were due to differing spectral resolutions. Papers reporting time series of circum-
stellar dust or gas observations of individual objects investigate whether the photospheric
lines appear to change as a by product (Wilson et al., 2014; Farihi et al., 2018), with no
further detections of variability. There have been no studies investigating a sample of DAZ
white dwarfs systematically to search for variability and constrain the level of variability in
the accretion rate.
This Chapter reports a spectroscopic monitoring campaign of five DAZ white dwarfs
using two medium resolution spectrographs. Each white dwarf was observed over a total
baseline of >10 years with between 12–30 data sets obtained, covering timescales of days,
months and years. This samples between 50–2000 sinking timescales, depending on the white
dwarf properties, so if the accretion rate were to change this should be discovered. However,
no unambiguous changes in accretion rate are discovered. Section 3.1 reports the target
selection, spectroscopic observations of the selected targets, and the data reductions and
processing. Section 3.2 discusses the methods used to determine the equivalent width over
72 Metal line variability
time. Finally Sections 3.4 and 3.5 discuss and conclude the results from the spectroscopic
monitoring survey.
3.1 Observations and Data Reduction
3.1.1 Target Selection
When searching for variability in the metal lines, target selection is crucial. For this reason,
five white dwarfs that satisfy particular physical conditions were selected, as shown in
Table 3.1. Firstly, the targets must be warm DAZ white dwarfs. DAZ white dwarfs have
sinking timescales on the order of days–years, so if changes in the amount of material
in the white dwarfs’ photosphere occurs, it should be detectable over the baseline of the
observations (see Table 3.2), whereas DBZ white dwarfs have much longer sinking timescales
on the order of 102 to 106 years. The targets must have temperatures which aren’t too cold
< 10,000 K such that the sinking timescales of the different elements are of the order of
days–months rather than tens of years (Koester, 2009), and not too hot such that radiative
levitation becomes a dominant mechanism to bring heavy elements to the photosphere
(> 20 – 25,000 K) (Chayer et al., 1995a,b; Barstow et al., 2014). One of the hottest target,
WD 1929+011, was found to have a negligible radiative levitation contribution of material
in comparison to accreted material (Koester et al., 2014). Finally, the white dwarfs must
show evidence for atmospheric pollution at a strong level with detections of at least Ca and
Mg, with abundances of [Ca/H]> −7.0 and [Mg/H]> −6.0, as shown in Table 3.2. Four of
the five white dwarfs display an infrared excess associated with circumstellar dust, however,
this wasn’t a requirement for the programme. G29-38 was included in this programme, as
studied by both von Hippel & Thompson (2007) and Debes & López-Morales (2008). The
latter paper highlighted the importance of observing using similar resolution instruments,
therefore, this work will re-visit the results from these studies using two medium resolution
spectrographs.
3.1.2 Spectroscopic observations
Debes & López-Morales (2008) highlighted the importance of systematic observations to
search for variability in the metal features. Their R∼40,000 spectra gave a median equivalent
width value of 260 mA, however, when re-binning this R∼40,000 spectra down to resolutions
of R∼500 they found significant deviations in the derived equivalent width with values
between 140 mA and 350 mA, significantly discrepant from the R∼40,000 equivalent width
of 260 mA. Therefore, it is crucial to study white dwarf metal variability using the same
3.1 Observations and Data Reduction 73
Table 3.1 The sample of polluted white dwarfs stating their effective temperature and log(g)
derived from a spectroscopic fit in previous works. The dust column highlights whether they
are confirmed to have an infrared excess from circumstellar dust.
WD Name Other Name Gaia eDR3 Number Te f f log(g) Dust?
WD 0106−328 HE 0106−3253 5026963661794939520 17350 α 8.12 α Yes1
WD 0408−041 GD 56 3251748915515143296 15300 β 8.09 β Yes2
WD 1457−086 ... 6332172027974304512 22200 β 7.99 β - ∗
WD 1929+011 GALEX J193156.8+011745 4287654959563143168 21200 γ 7.91 γ Yes3
WD 2326+049 G29-38 2660358032257156736 11800 δ 8.40 δ Yes4
Temperature/log(g) References: (α) Xu et al. (2019), (β ) Gianninas et al. (2011), (γ) Gänsicke et al.
(2012), (δ ) Xu et al. (2014).
Dust References: (1) Farihi et al. (2010b), (2) Jura et al. (2007b), (3) Rocchetto et al. (2015), (4) Zuckerman
& Becklin (1987).
∗ Dust emission candidate but photometry likely contaminated (Dennihy et al., 2017).
Table 3.2 The pollution levels and sinking timescales for the sample of white dwarfs. Sinking
timescales interpolated from Koester et al. (2020).
WD Name [Ca/H] [Mg/H] τCa (d) τMg (d) log(q)
WD 0106−328 −5.93±0.11 1 −5.57±0.20 1 1.13 1.83 −16.71
WD 0408−041 −6.86±0.20 1 −5.55±0.20 1 2.75 4.58 −16.19
WD 1457−086 −6.23±0.20 1 −5.47±0.20 1 5.50 9.59 −15.78
WD 1929+011∗ −5.83±0.10 2 −4.10±0.10 2 4.39 7.48 −16.00
WD 2326+049 −6.58±0.12 3 −5.77±0.13 3 80.45 86.01 −14.00
References: (1) Xu et al. (2019), (2) Melis et al. (2011), (3) Xu et al. (2014).
∗The white dwarf parameters used in this work are from Gänsicke et al. (2012), so abundances will not be
directly comparable.
74 Metal line variability
or similar spectrographs to reduce systematics. This work focuses on spectra taken from
two similar mid-resolution echelle spectrographs. Tables 3.3–3.7 report the observations
highlighting the instrument, date of observation, exposure time, and signal-to-noise ratio
(SNR). The SNR was calculated per pixel from the continuum normalised spectra, the median
signal around the line of interest was divided by the median absolute deviation (multiplied
by 1.48 to give the standard deviation).
HRS/SALT
Spectroscopic observations of the white dwarfs were taken with the High Resolution Spectro-
graph (HRS) mounted on The Southern African Large Telescope (SALT) at the Sutherland
Observatory in South Africa. Observations spanned across 7 semesters from Semester 2017/1
to 2020/2 covering 3.5 years. The HRS (Barnes et al., 2008) is a dual-beam (370–550 nm &
550–890 nm) fiber fed, echelle spectrograph. The LR mode was used to yield a resolution of
∼14,000. This was a queue based programme with both high priority time, where up to 3
sets of spectra were taken consecutively for each white dwarf to obtain high SNR data, and
low priority time, where one spectrum was obtained as a filler between other programmes or
during poor weather. Therefore, for each observing night, the exposure times and SNR varied.
The data were reduced by the MIDAS pipeline which produced flat fielded, wavelength
calibrated and merged spectra (Kniazev et al., 2016; Kniazev et al., 2017). There is little
overlap between the orders so no spectral lines fall into multiple orders. For the observations
where multiple consecutive spectra were obtained, they were normalised individually and
stacked weighted by their inverse variance.
MIKE/Magellan
Spectra were taken between 2007–2011 on the MIKE spectrograph at the Magellan Clay
Telescope at the Las Campanas Observatory in Chile (Bernstein et al., 2003) (PI: Debes). The
MIKE spectrograph is a double echelle spectrograph with two arms covering wavelengths
of 3350–5000 Å (blue) and 4900–9500 Å (red). The data were obtained under varying
atmospheric conditions but almost always using the 0.7" x 5" slit. This gave a spectral
resolution of ∼ 35,000 for the red arm and 46,000 for the blue arm. The spectra were binned
at 2 x 2 and had a slow readout speed. The data were reduced using the CarPy suite of MIKE
reduction tools to produce calibrate spectra.
3.1 Observations and Data Reduction 75
Table 3.3 WD 0106−328 observation details. SNR determined from the continuum around
the Mg II line at 4481.125 Å as defined in Section 3.1.2.
Instrument Date Exp Time (s) SNR
MIKE 2007-10-25 1800 42.3
MIKE 2007-10-26 2400 12.8
MIKE 2008-08-20 1800 49.9
MIKE 2008-08-21 1800 53.0
MIKE 2008-08-22 1800 45.8
MIKE 2009-10-15 3600 39.7
SALT 2019-06-08 1800 9.5
SALT 2019-09-06 1800 21.5
SALT 2020-07-29 1450 22.0
SALT 2020-08-07 2900 12.6
SALT 2020-09-17 2900 22.9
SALT 2020-10-24 2900 36.4
Table 3.4 WD 0408−041 observation details. SNR determined from the continuum around
the Mg II line at 4481.125 Å as defined in Section 3.1.2.
Instrument Date Exp Time (s) SNR
MIKE 2007-10-25 3600 51.6
MIKE 2007-10-26 3600 35.9
MIKE 2008-08-21 4800 61.0
MIKE 2008-08-22 3600 57.2
MIKE 2008-08-23 3600 59.5
MIKE 2009-10-14 4800 67.2
SALT 2018-11-28 1800 8.5
SALT 2019-08-04 1800 14.2
SALT 2019-11-17 2900 23.5
SALT 2019-11-23 2900 17.3
SALT 2019-11-24 2900 24.2
SALT 2019-12-16 2900 23.2
SALT 2020-01-15 2900 10.7
SALT 2020-09-17 2900 17.9
SALT 2020-11-20 2900 17.4
SALT 2020-12-14 2900 9.1
76 Metal line variability
Table 3.5 WD 1457−086 observation details. SNR determined from the continuum around
the Mg II line at 4481.125 Å as defined in Section 3.1.2.
Instrument Date Exp Time (s) SNR
MIKE 2008-03-21 3600 70.1
MIKE 2008-03-22 3600 69.9
MIKE 2009-05-18 3600 61.8
MIKE 2010-06-17 3600 46.9
MIKE 2010-07-07 3600 13.5
MIKE 2010-08-03 3580 48.1
SALT 2018-06-05 2850 17.4
SALT 2020-05-31 3140 15.0
SALT 2020-06-15 3140 21.1
SALT 2021-04-02 3140 11.3
SALT 2021-04-10 3140 19.2
SALT 2021-04-14 1800 13.6
Table 3.6 WD 1929+011 observation details. SNR determined from the continuum around
the Mg II line at 4481.125 Å as defined in Section 3.1.2.
Instrument Date Exp Time (s) SNR
MIKE 2010-06-16 2687 21.2
MIKE 2010-06-17 1200 50.9
MIKE 2010-07-08 900 63.2
MIKE 2010-08-02 1800 77.4
MIKE 2010-08-03 1200 49.5
MIKE 2011-06-09 2400 64.9
SALT 2017-07-06 2700 18.4
SALT 2017-07-11 2700 17.8
SALT 2017-07-22 2700 39.4
SALT 2017-07-30 2700 25.7
SALT 2017-08-02 1800 41.9
SALT 2017-08-09 2700 43.4
SALT 2017-08-13 2700 19.9
SALT 2017-08-23 2700 44.8
SALT 2017-09-26 1800 39.3
SALT 2018-06-05 900 17.2
SALT 2018-06-11 900 18.0
SALT 2019-08-20 2900 34.3
SALT 2020-05-15 2400 44.1
SALT 2020-05-24 2400 38.2
SALT 2020-05-31 2400 36.4
SALT 2020-06-20 1200 31.3
SALT 2020-07-19 1200 26.8
SALT 2020-07-24 1200 30.6
SALT 2020-07-27 2400 28.2
SALT 2020-07-30 1200 32.0
SALT 2020-08-24 2400 57.5
SALT 2021-04-12 2400 28.9
SALT 2021-04-14 2400 26.6
SALT 2021-04-20 2400 21.7
3.1 Observations and Data Reduction 77
Table 3.7 G29-38 observation details. SNR determined from the continuum around the Mg II
line at 4481.125 Å as defined in Section 3.1.2.
Instrument Date Exp Time (s) SNR
MIKE 2007-10-25 600 71.9
MIKE 2007-10-26 600 59.2
MIKE 2007-10-27 600 49.5
MIKE 2008-08-20 900 110.8
MIKE 2008-08-21 1800 98.8
MIKE 2008-08-22 900 100.1
MIKE 2008-08-23 1200 96.7
MIKE 2009-05-18 1500 77.3
MIKE 2009-05-20 1600 65.3
MIKE 2009-10-14 2389 4.4
MIKE 2009-10-15 2400 91.2
MIKE 2010-06-16 1225 35.1
MIKE 2010-06-17 400 50.9
MIKE 2010-08-02 1200 101.0
MIKE 2011-06-09 3600 129.4
SALT 2017-07-05 1800 55.8
SALT 2017-07-29 1800 49.5
SALT 2017-08-02 1800 77.8
SALT 2017-08-05 1800 69.5
SALT 2017-09-02 1800 62.6
SALT 2017-09-10 1800 81.9
SALT 2017-09-17 1800 45.2
SALT 2017-09-23 1800 46.2
SALT 2019-11-15 2400 56.5
SALT 2019-11-23 2400 60.0
SALT 2019-11-24 2400 72.6
SALT 2019-11-25 2400 49.4
SALT 2020-06-24 2400 47.5
SALT 2020-08-21 2400 87.1
SALT 2020-08-23 1200 34.9
SALT 2020-09-07 2400 67.6
SALT 2020-11-02 2400 83.9
SALT 2020-11-13 2400 84.6
78 Metal line variability
3.2 Variability Analysis
Equivalent widths are most often used to quantify the strengths of spectral lines, this is a
measure of the area of the spectral line relative to the continuum level. Therefore, accurate
and precise continuum normalisation is critical. The continuum around the spectral line of
interest was fitted using an iterative sigma clipping process where a low order polynomial
(order 2–4) was fitted to the continuum around each line. Experiments with higher order
polynomials tended to over-fit the continuum and include the wings of the lines, therefore,
subsequent equivalent width measurements were systematically lower. To test the sensitivity
of the equivalent width to the normalisation, the equivalent width was calculated whilst
varying the parameters for the continuum normalisation. The order of the polynomial was
varied between 2–4 and the wavelength range between 5–20 Å either side of the line of
interest. From these experiments, the maximum variation in equivalent width was found to
be 6%.
Voigt profiles are a convolution of the Gaussian and Lorentzian profiles and show the
combined effect of both the Doppler broadening and pressure broadening of spectral lines in
white dwarfs. Consequently, Voigt profiles are a good model to fit the shapes of spectral lines
(Armstrong, 1967). A Markov Chain Monte Carlo (MCMC) approach was implemented to
explore the range of Voigt profiles which fit the fluxes and associated errors for each spectral
line; this better quantifies the uncertainties. A five parameter Voigt profile was used, allowing
the continuum level to also be a free parameter. The Voigt profile doesn’t have a defined
equation but is related to the real part of the Faddeeva function, w(z), with z= x+iy
σ
√
2
:
V =
Re[w(z)]
σ
√
2π
(3.1)
V = O+A
Re[w(x− x0+1 jγ)]
σ
√
2π
(3.2)
where σ is the standard deviation of the Gaussian profile, γ is the half-width at half-maximum
of the Lorentzian profile, x0 is the wavelength value marking the center of the line, A is
the amplitude, and O is the flux offset. The python package SCIPY1 was implemented to
find the optimal Voigt profile parameters for a particular spectral line in a data set, these
parameters were used as an input for the MCMC. The EMCEE2 python package was used to
implement the MCMC sampling. 10 walkers were used to sample the posterior distributions
of the parameters with 22,000 iterations each; 2,000 iterations were run and discarded for
1https://scipy.org
2https://emcee.readthedocs.io/en/stable
3.3 Results 79
the burn-in phase. The chains were thinned by approximately the auto-correlation time, the
number of iterations required for the walkers to ‘forget’ their initial position, to ensure the
parameters in the chain were independent. For each set of Voigt model parameters in the
chain (O, A, x0, σ , γ), the equivalent width was evaluated. The Voigt profile was integrated
with bounds of ± 3 times the full-width at half-maximum of the Voigt model, and divided
by the continuum to give the equivalent width for that set of parameters. From this chain,
the median value of the equivalent width is calculated and the errors are quoted using the
16th and 84th percentiles. These errors were combined in quadrature with the 6% continuum
normalisation error.
The MIKE/Magellan spectra have significant overlap between consecutive orders and
often the spectral lines fall on multiple orders. For the spectral lines where this occurred, the
data were normalised individually and then were stacked weighted by their inverse variance.
However, the sensitivity of the detector can drop off steeply towards the edges of the orders.
For WD 1929+011, the Mg II 4481.125 Å line overlapped between two orders, one line was
in the centre of its order and the other on the edge of the consecutive order. The equivalent
widths were calculated separately to ensure that the line close to the order edge did not bias
the results. The discrepancies between the equivalent widths derived from the two orders
were up to 30%. Therefore, spectral lines which were within ∼ 5 Å from the order edge or
fell on the steepest parts of the sensitivity curve were not used for the final equivalent width
measurements.
When comparing data obtained from different spectrographs, variations in the spectral
resolution can significantly bias the results (Debes & López-Morales, 2008). Before the
equivalent width was determined, the MIKE/Magellan spectra were linearly interpolated to
match the wavelengths of the HRS/SALT data to reduce this bias.
3.3 Results
This work reports spectroscopic monitoring campaigns of five DAZ white dwarfs to determine
whether the mass of material in their photosphere changes over time. 6–15 data sets were
obtained between 2007 and 2011 using MIKE/Magellan, and 6–24 data sets were taken with
HRS/SALT between 2017 and 2021. For the warm DAZ white dwarfs the Mg II doublet at
4481.125 Å is most often the strongest metal line; Figures 3.1–3.5 show the evolution of the
Mg II spectral line across the data sets for each white dwarf. G29-38 is the coolest white
dwarf in the sample, and its strongest metal line is instead the Ca II K line at 3933.663 Å,
Figure 3.6 shows this line for all observations taken in the MIKE data-set. It should be noted
that the HRS/SALT is not sensitive around the 3933.663 Å line.
80 Metal line variability
This section reports the results from the MCMC analysis to robustly determine the
equivalent width of the spectral lines over time. For the strongest line/s, an equivalent width
can be obtained from each data set, therefore probing timescales from days–years. For the
weaker lines, all spectra obtained with one spectrograph were stacked together to obtain one
high SNR spectrum. This resulted in one measure of equivalent width for the MIKE/Magellan
data set and one measure for HRS/SALT, probing an equivalent width change over timescales
of ∼ 10 years. Results for each white dwarf are reported separately.
3.3.1 WD 1929+011
WD 1929+011 is a heavily polluted white dwarf with strong lines from numerous elements
(Mg, Ca, Si, Fe, O) in the optical range. From Figure 3.4, the shape and depth of the Mg
II doublet appears consistent between the spectra. The lack of variation in the Mg II line
is quantified in the top panel of Figure 3.7. The equivalent width measurements are all
consistent within 1σ . A horizontal line model was fitted to the data points to investigate if
the equivalent widths are consistent with no variability using the chi squared statistic (χ2),
and the reduced chi squared statistic (χ˜2 = χ2/N(do f ), where N(do f ) is the number of
degrees of freedom). A χ˜2 of 1 implies that a horizontal line model is a good fit to the data,
χ˜2 < 1 implies the model is over-fitting the data, χ˜2 > 1 implies the model is under-fitting
the data, and χ˜2 ≫ 1 implies the model is a poor fit to explain the data. The best fitting
equivalent width for the Mg II doublet was 464.0 mÅ with a χ˜2 fit of 0.42. Therefore,
the model describing a constant equivalent width over time can explain the data, although
appears to be over-fitting the data. The over-fitting is likely a consequence of inflated errors
from the normalisation; due to the strength of this absorption line, the true normalisation
error is likely < 6%. This analysis was also done for the strongest lines of Ca and Si for
WD 1929+011. Figure 3.7 shows that for the Ca and Si lines, the equivalent widths over
time are also consistent with a constant equivalent width model. Consequently, the mass and
abundance of the material present in the photosphere of WD 1929+011 is constant over time.
The MIKE/Magellan spectra and HRS/SALT spectra were stacked separately to produce
two higher SNR spectra separated by ∼ 10 years. The MCMC equivalent width analysis
was run on the stacked spectra. Table 3.8 compares the output equivalent width values from
the Mg II doublet and Table 3.8 reports values from other lines that are well resolved in the
stacked spectra. These data are reported graphically in Figure 3.8. Nearly all the lines have
statistically the same equivalent widths, with the exception of a few weak Fe lines.
3.3 Results 81
4477.5 4480.0 4482.5 4485.0
Wavelength (A)
1
2
3
4
5
6
N
or
m
al
is
ed
F
lu
x
2007-10-25
2007-10-26
2008-08-20
2008-08-21
2008-08-22
2009-10-15
2019-09-06
2020-07-29
2020-08-07
2020-09-17
2020-10-24
Fig. 3.1 The Mg II 4481.125 Å spectral line from the MIKE/Magellan (blue) and HRS/SALT
(orange) spectra spanning more than a decade for WD 0106−328. The spectra have been
continuum normalised and are offset by 0.5. Spectra with SNR < 10 are not plotted.
82 Metal line variability
4477.5 4480.0 4482.5 4485.0
Wavelength (A)
1
2
3
4
5
6
7
N
or
m
al
is
ed
F
lu
x
2007-10-25
2007-10-26
2008-08-21
2008-08-22
2008-08-23
2009-10-14
2019-08-04
2019-11-17
2019-11-23
2019-11-24
2019-12-16
2020-01-15
2020-09-17
2020-11-20
Fig. 3.2 The Mg II 4481.125 Å spectral line from the MIKE/Magellan (blue) and HRS/SALT
(orange) spectra spanning more than a decade for WD 0408−041. The spectra have been
continuum normalised and are offset by 0.5. Spectra with SNR < 10 are not plotted.
3.3 Results 83
4477.5 4480.0 4482.5 4485.0
Wavelength (A)
1
2
3
4
5
6
N
or
m
al
is
ed
F
lu
x
2008-03-21
2008-03-22
2009-05-18
2010-06-17
2010-07-07
2010-08-03
2018-06-05
2020-05-31
2020-06-15
2021-04-02
2021-04-10
2021-04-14
Fig. 3.3 The Mg II 4481.125 Å spectral line from the MIKE/Magellan (blue) and HRS/SALT
(orange) spectra spanning more than a decade for WD 1457−086. The spectra have been
continuum normalised and are offset by 0.5.
84 Metal line variability
4477.5 4480.0 4482.5 4485.0
Wavelength (A)
1
2
3
4
5
6
7
8
N
or
m
al
is
ed
F
lu
x
2018-06-05
2018-06-11
2019-08-20
2020-05-15
2020-05-24
2020-05-31
2020-06-20
2020-07-19
2020-07-24
2020-07-27
2020-07-30
2020-08-24
2021-04-12
2021-04-14
2021-04-20
4477.5 4480.0 4482.5 4485.0
Wavelength (A)
1
2
3
4
5
6
7
8
N
or
m
al
is
ed
F
lu
x
2010-06-16
2010-06-17
2010-07-08
2010-08-02
2010-08-03
2011-06-09
2017-07-06
2017-07-11
2017-07-22
2017-07-30
2017-08-02
2017-08-09
2017-08-13
2017-08-23
2017-09-26
Fig. 3.4 The Mg II 4481.125 Å spectral line from the MIKE/Magellan (blue) and HRS/SALT
(orange) spectra spanning more than a decade for WD 1929+011. The spectra have been
continuum normalised and are offset by 0.5.
3.3 Results 85
4480 4485
Wavelength (A)
1.0
1.5
2.0
2.5
3.0
3.5
N
or
m
al
is
ed
F
lu
x
2017-07-05
2017-07-29
2017-08-02
2017-08-05
2017-09-02
2017-09-10
2017-09-17
2017-09-23
2019-11-15
2019-11-23
2019-11-24
2019-11-25
2020-06-24
2020-08-21
2020-08-23
2020-09-07
2020-11-02
2020-11-13
4480 4485
Wavelength (A)
1.0
1.5
2.0
2.5
3.0
N
or
m
al
is
ed
F
lu
x
2007-10-25
2007-10-26
2007-10-27
2008-08-20
2008-08-21
2008-08-22
2008-08-23
2009-05-18
2009-05-20
2009-10-15
2010-06-16
2010-06-17
2010-08-02
2011-06-09
Fig. 3.5 The Mg II 4481.125 Å spectral line from the MIKE/Magellan (blue) and HRS/SALT
(orange) spectra spanning more than a decade for G29-38. The spectra have been continuum
normalised and are offset by 0.15. Spectra with SNR < 10 are not plotted.
86 Metal line variability
3930.0 3932.5 3935.0 3937.5
Wavelength (A)
1
2
3
4
5
6
7
N
or
m
al
is
ed
F
lu
x
2007-10-25
2007-10-26
2007-10-27
2008-08-20
2008-08-21
2008-08-22
2008-08-23
2009-05-18
2009-05-20
2009-10-15
2010-06-16
2010-06-17
2010-08-02
2011-06-09
Fig. 3.6 The Ca II 3933 Å spectral line from the MIKE/Magellan (blue) for G29-38. The
spectra have been continuum normalised and are offset by 0.5. Spectra with SNR < 10 are
not plotted.
3.3 Results 87
400
500
Mg II: 4481.125 A EW: 464.4
χ˜2: 0.45
40
60
E
W
(m
A
) Ca II: 3933.663 A EW: 52.7
χ˜2: 0.45
4000 5000 6000 7000 8000 9000 10000
MJD - 50000 (d)
150
200
250 Si II: 5055.984 A EW: 190.4
χ˜2: 1.07
Fig. 3.7 The Mg II (top), Ca II (middle), and Si II (bottom) equivalent width (EW) measure-
ments over time for WD 1929+011. Measurements from MIKE/Magellan are reported as
blue data points between 5000–6000 days, and measurements from HRS/SALT are reported
as orange data points after 7000 days.
Table 3.8 The median equivalent width (mÅ) and error for the HRS/SALT (S) data and
the MIKE/Magellan (M) data obtained from the stacked spectra for the Mg II doublet at
4481.125 Å.
WD 0106 WD 0408 WD 1457 WD 1929 G29-38
(mÅ) (mÅ) (mÅ) (mÅ) (mÅ)
MIKE/Magellan 99.7±6.4 142±8.8 81.0±5.0 455±28 43.3±3.0
HRS/SALT 134±9.1 155±12 86.5±8.8 464±29 39.2±2.0
88 Metal line variability
Table 3.9 The median equivalent width and error for the stacked HRS/SALT (S) data and the
MIKE/Magellan (M) data for weaker lines for WD 0106−328, WD 1929+011, and G29-38.
Element λair WD 0106 EW (mÅ) WD 1929 EW (mÅ) G29-38 EW (mÅ)
Å M S M S M S
Ca I 4226.727 - - - - 18.2±1.3 22.3±2.3
Fe II 4923.927 - - 16.1±1.35 10.9±1.07
Fe II 5018.440 16.5±2.6 16.8±3.8 24.6±2 20.7±1.6 - -
Fe II 5169.033 18±2.2 13±12 30.8±2.1 25.1±1.9 - -
Si II 5041.024 - - 111±6.9 106±7 - -
Si II 5055.984 - - 198±12 186±12 - -
Si II 5957.560 - - 45.2±3.1 44.6±3.5 - -
Si II 5978.930 - - 55.5±4.1 43.2±3.0 - -
Si II 6347.100 - - 152±9.3 145±9.3 - -
Si II 6371.360 - - 106±6.5 108±6.7 - -
Mg I 5172.683 - - - - 19.3±1.3 18.3±1.4
Mg I 5183.602 - - - - 36.1±2.3 35.2±2.2
Mg II 7877.054 - - 56.5±4.1 73±5.3 - -
Mg II 7896.366 - - 99.8±7.6 129±9.6 - -
O I 7771.944 - - 41.2±3.8 41.1±3.4 - -
Fig. 3.8 Comparison of the equivalent width (EW) measurements from the MCMC analysis
on the MIKE/Magellan (M) and HRS/SALT (S) stacked spectra for WD 1929+011. Markers
represent different lines of Mg, Si, Fe and O with their transition wavelength along the x axis.
3.3 Results 89
3.3.2 G29-38
G29-38 is a cooler DAZ white dwarf, with sinking timescales of ∼ 80 days (Table 3.2).
G29-38 is a ZZ Ceti pulsator and therefore experiences periodic changes in brightness of
between 1–3%. These pulsations can result in equivalent widths that are discrepant from
the mean equivalent width. Longer integration times (≫ 20 minutes - approximately the
maximum pulsation period, Kleinman et al., 1998) average out the effects of the pulsations
on the equivalent widths (von Hippel & Thompson, 2007). Therefore, for spectra taken on
consecutive days, these are stacked and processed together to obtain a longer total exposure
to gain more accurate measure of equivalent width.
For G29-38, the strongest line is the Ca II K line, the evolution of this line from the
MIKE/Magellan data is shown in Figure 3.6. No obvious change in the shape or depth of the
line is evident. Figure 3.5 shows the evolution of the Mg II doublet over time for both the
MIKE/Magellan and HRS/SALT spectra. This line is much weaker than the Ca II K line; it
should be noted that each spectrum is offset by 0.15 compared with 0.5 for the Ca II K line,
so the high SNR of the spectra (up to ∼ 130 for 2011-06-09) means this line can be resolved
above the noise in each individual spectrum, although some detections are marginal.
Figure 3.9 shows the equivalent width over time for the 4481.125 Å Mg II doublet, the
Ca II K line (3933.663 Å), and the 5183.602 Å Mg I line. The HRS/SALT is not sensitive
bluewards of∼ 4000 Å, and therefore only the data from MIKE/Magellan are reported for the
Ca II K line. χ˜2 < 1, so the constant equivalent width model fits the data here, and again due
to the strength of the line, it is likely that the true normalisation error is < 6%, accounting
for the apparent over-fitting of the model to the data. For the Mg II and Mg I lines, the χ˜2
is 1.90 and 1.52 respectively. To assess whether these values of χ˜2 imply that the data can
not be fit by a constant equivalent width model (the null hypothesis) the critical value of χ2
(χ2crit) is used. Given a probability level, if χ˜
2
measured > χ˜
2
crit then the null hypothesis can be
rejected. For a probability of 99.9% (> 3σ ) the χ˜2crit is 2.19, as the χ˜
2
measured values lie below
the critical value, there is no evidence to reject the null hypothesis of constant equivalent
width over time.
The MCMC equivalent width analysis was run on the stacked MIKE/Magellan spectra and
HRS/SALT spectra. Table 3.8 reports the values from the Mg II doublet and Table 3.9 reports
values from other lines that are well resolved in the stacked spectra. The derived equivalent
width for the Mg II doublet, the Ca I line at 4226.727 Å , the Mg I line at 5172.683 Å , and the
Mg I line 5183.602 Å are consistent within 1σ between the MIKE/Magellan and HRS/SALT
stacked spectra. Therefore, based on these data, there has been no change in the mass or
abundances of the material in the photosphere of G29-38.
90 Metal line variability
25
50
75
Mg II: 4481.125 A EW: 40.3
χ˜2: 1.90
250
300
E
W
(m
A
) Ca II: 3933.663 A EW: 257.3
χ˜2: 0.50
4000 5000 6000 7000 8000 9000 10000
MJD - 50000 (d)
25
50
Mg I: 5183.602 A EW: 35.9
χ˜2: 1.52
Fig. 3.9 The Mg II doublet (top), Ca II K line (middle), and Mg I line, 5183.602 Å
(bottom) changes of equivalent width (EW) over time for G29-38. Measurements from
MIKE/Magellan are reported as blue data points between 5000–7000 days, and measure-
ments from HRS/SALT are reported as orange data points after 7000 days.
3.3 Results 91
3.3.3 WD 0106−328
The evolution of the Mg II doublet over time for WD 0106−328 is shown in Figure 3.1. The
metal lines are particularly narrow in this white dwarf, and therefore the two Mg lines in the
doublet are resolved in the MIKE/Magellan data, and partially resolved in the HRS/SALT
data.
The top panel in Figure 3.11 shows the equivalent width of the Mg II doublet over time.
There appears to be a significant offset between the equivalent widths measured from the
MIKE/Magellan data and those measured from the HRS/SALT data. Indeed the χ˜2measured
value is high at 6.83. The χ˜2crit value is 3.10, and as the measured value lies above the critical
value so the null hypothesis, that there is no equivalent width variability, can be ruled out
with 99.9% confidence based on the equivalent width measurements of the Mg II doublet.
This result is also seen when the MCMC equivalent width analysis was run on the
stacked MIKE/Magellan spectrum and the stacked HRS/SALT spectrum. A significant
(>3σ ) increase in equivalent width of the Mg II doublet is seen between the MIKE/Magellan
the HRS/SALT stacked spectra. This is also shown in Figure 3.10.
As mentioned previously, the metal lines for this white dwarf are particularly narrow so
obtaining an equivalent width for all spectra for other metal lines is not possible. However, the
MIKE/Magellan and HRS/SALT stacked spectra revealed weak lines that can be compared
between the two epochs. As reported in Table 3.9, the 5018.440 Å and 5169.033 Å Fe II
lines are consistent within 1σ between the MIKE/Magellan and HRS/SALT data. From these
weaker Fe lines there is no strong evidence that the equivalent widths have changed over
time. In order to distinguish whether accretion rate variability occurred, further high SNR
spectra are required.
3.3.4 WD 0408−041
The evolution of the Mg II doublet over time for WD 0408−041 is seen in Figure 3.2. The
MIKE/Magellan data has a higher SNR than the HRS/SALT making it difficult to compare
the lines by eye.
The middle panel in Figure 3.11 shows the equivalent width of the Mg II doublet over
time for WD 0408−041. The variance of the equivalent widths is larger for the HRS/SALT
data, likely due to the lower SNR. The χ˜2measured value is 1.99 and the χ˜
2
crit value is 2.74,
and as the measured value lies below the critical value, the null hypothesis of no change in
equivalent width can not be ruled out.
The MCMC equivalent width analysis was run on the stacked MIKE/Magellan spectrum
and the stacked HRS/SALT spectrum. The results are reported in Table 3.8. The derived
92 Metal line variability
4480.5 4481.0 4481.5 4482.0 4482.5 4483.0 4483.5
Wavelength (A)
0.7
0.8
0.9
1.0
1.1
N
or
m
al
is
ed
F
lu
x
HRS/SALT
MIKE/Magellan
MIKE R=14,000
Fig. 3.10 The stacked MIKE/Magellan and SALT/HRS data for the Mg II doublet for
WD 0106−328. The darker blue line is the MIKE/Magellan spectra interpolated and con-
volved to the resolution of HRS/SALT.
3.4 Discussion 93
equivalent width for the Mg II line from the stacked spectra are consistent within 1σ .
Therefore, based on these data, there has been no change in the mass of material in the
photosphere of WD 0408−041.
3.3.5 WD 1457−086
Figure 3.3 shows the evolution of the Mg II doublet over time for WD 1457−086. Similar
to WD 0408−041, the MIKE/Magellan data has a higher SNR than the HRS/SALT again
making it difficult to compare the lines by eye.
The bottom panel of Figure 3.11 shows the output of the MCMC analysis with the
equivalent width of the Mg II doublet over time for WD 1457−086. The χ˜2measured value is
1.49, and for a confidence level of 99.9%, the χ˜2crit value is 2.96. The measured value lies
below the critical value and so the null hypothesis of no equivalent width change can not be
ruled out. The equivalent width derived from the stacked data as reported in Table 3.8 show
that the Mg II doublet is consistent within 1σ . Therefore, based on these data, there has been
no change in the mass of material in the photosphere of WD 1457−086.
3.4 Discussion
The aim of this work was to investigate whether the mass of the pollutants in the photosphere
of five warm DAZ white dwarfs changed over time. With such dynamic circumstellar
environments, variability in the accretion rates and therefore amount of material in the
photosphere, is predicted. For four of the five white dwarfs, no statistically significant
variability was observed. For one of the white dwarfs, WD 0106−328, these data were
inconclusive.
3.4.1 Discussion of methods
Using optimisation and MCMC methods allows a full exploration of the posterior distribution
of the parameters. However, for weaker lines and low SNR data, the MCMC struggled to
converge. This meant that low SNR data-sets (<10) were omitted from the analysis. Also,
for WD 1929+011 one of the sets of data demonstrated extra absorption ∼ 1.5 Å bluewards
of the Mg II doublet, see Figure 3.4 date 2017-07-11. This skewed the Voigt profile such
that the wings were broad, giving a large equivalent width value. If this is additional Mg
absorption, the absorption was at a different radial velocity so is not photospheric. This data
set was therefore omitted from the analysis.
94 Metal line variability
50
100
150
WD0106-328
EW: 112.0
χ˜2: 6.83
100
200
E
W
(m
A
) WD0408-041
EW: 149.4
χ˜2: 1.99
4000 5000 6000 7000 8000 9000 10000
MJD - 50000 (d)
50
100
WD1457-086
EW: 85.2
χ˜2: 1.49
Fig. 3.11 The equivalent width of the Mg II doublet over time for WD 0106−328,
WD 0408−041, and WD 1457−086.
3.4 Discussion 95
The first three sets of data for G29-38 from MIKE/Magellan (2007-10-25, 2007-10-26
and 2007-10-27) are the same as those reported in Debes & López-Morales (2008), allowing
a direct comparison between methods to determine equivalent widths. The equivalent
widths derived here for these data sets are consistent within 1σ to those reported in Debes
& López-Morales (2008). Slight discrepancies between measurements could be due to
differing handling of the continuum normalisation or the equivalent width measurement.
Debes & López-Morales (2008) normalised the regions around the spectral lines using high-
order polynomials between third and twelfth order. Whereas, this work fitted lower order
polynomials using a sigma clipping method, and then allowed the continuum to be a free
parameter in the Voigt model. Also, Debes & López-Morales (2008) integrated the line
profile from the data, whereas this work modelled the lines with Voigt profile. The fact that
the results agree within 1σ where identical data sets are used is reassuring for this analysis.
This work is only sensitive to equivalent width variations of the order of 10% or larger.
Therefore, variability in the equivalent widths at the level of a few percent will be hidden.
3.4.2 G29-38
Searches for equivalent width changes for G29-38 have been studied previously by von
Hippel & Thompson (2007) and Debes & López-Morales (2008). von Hippel & Thompson
(2007) found evidence for large scale variability with the Ca II K line changing from 165 mÅ
to 280 mÅ . Whereas, Debes & López-Morales (2008) found the equivalent widths to be
consistent with a median of 264 mÅ and proposed that the variability found previously was
likely due to comparing low resolution data (R∼500) with higher resolution data. In this
work the best fitting equivalent width across the MIKE/Magellan observations was 257 mÅ
for the Ca II K line, with no statistically significant variations found. Therefore, this work
corroborates the findings of Debes & López-Morales (2008).
3.4.3 WD 0106−328
For WD 0106−328, there appears to be a significant increase in the equivalent width of
the Mg II doublet. The MIKE/Magellan spectrum was interpolated and convolved to the
same resolution as HRS/SALT (R∼14,000) to check whether the differing resolutions were
impacting the results. As shown in Figure 3.10 there remains a significant difference in line
profiles between the HRS/SALT and MIKE/Magellan stacked spectra. However, the Fe II
5018.440 Å line reported in Table 3.9 is not consistent with the same increase in variability.
Also, as WD 0106−328 has particularly narrow metal lines, for HRS/SALT the resolution of
the spectrograph is close to the line width. This could therefore be affecting the line profiles
96 Metal line variability
Table 3.10 The inferred accretion rates assuming a bulk Earth composition for the best
fitting [Mg/H] abundance for the 2020-08-24 data set (−4.25, in italics), and for abundance
+0.2, +0.4, −0.2, and −0.4 dex from the measure [Mg/H] value. Macc, 10 yrs reports the mass
of material that would accrete over a 10 year baseline. Assuming the abundance in the
photosphere changed from [Mg/H] = −4.25, ∆Macc, 10 yrs reports the change in mass between
the new [Mg/H] value and [Mg/H] = −4.25 that would accrue over 10 years, reported as a
fraction of the mass of Ceres, a dwarf planet in the asteroid belt, and the fraction of the mass
of Comet Halley.
[Mg/H] M˙ (g/s) Macc, 10 yrs (g) ∆Macc, 10 yrs
MCeres MC.Halley
−4.65 6.0×108 1.9×1017 −3.2×10−8 −1.3
−4.45 9.6×108 3.0×1017 −1.9×10−8 −0.8
−4.25 1.5×109 4.8×1017 0.0 0.0
−4.05 2.4×109 7.6×1017 +3.0×10−8 +1.3
−3.85 3.8×109 1.2×1018 +7.9×10−8 +3.3
and equivalent width measurements with the HRS/SALT. Therefore, this variability analysis
is inconclusive, and follow up spectra using MIKE/Magellan would be required to confirm
the variability.
3.4.4 Accretion rates
The equivalent width limit can be converted to a limit on the metal abundance of the pollutant,
and therefore accretion rate. This was calculated for the strongest line across the five DAZ
white dwarfs, the Mg II doublet for WD 1929+011. Figure 3.12(a) shows the best fitting
model to the highest SNR spectrum from HRS/SALT for WD 1929+011 (2020-08-24). The
best fitting Mg abundance is [Mg/H] = −4.25. Models are plotted every 0.2 dex spreading
to +/- 1.0 dex in [Mg/H]. The equivalent widths for these models were added to Figure
3.12(b); this work would have been sensitive to an increase or decrease of 0.2 dex in the
abundance of material accreted by the white dwarf. The inferred mass accretion rates are
calculated in Table 3.10, assuming magnesium makes up 15.8% of the total mass, as in Bulk
Earth. Xu et al. (2019) demonstrated that this was the most reliable and consistent way of
measuring and comparing accretion rates. If the accretion rate changed between the sets of
MIKE/Magellan and HRS/SALT observations, over a ∼ 10 year baseline, this work would
be sensitive to changes of mass accretion down to Comet Halley sized objects. Therefore,
the mass accretion rate was stable and consequently, there is no evidence for new scattered
bodies being accreted by WD 1929+011.
Polluted white dwarf systems are dynamic, with variability observed in the circumstellar
material from as short as hours (e.g. Vanderburg et al., 2015) to as long as decades (e.g.
3.4 Discussion 97
4479 4480 4481 4482 4483 4484
Wavelength (A)
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
N
or
m
al
is
ed
F
lu
x
-3.25
-3.45
-3.65
-3.85
-4.05
-4.25
-4.45
-4.65
-4.85
-5.05
-5.25
5000 6000 7000 8000 9000 10000
MJD - 50000 (d)
0.2
0.3
0.4
0.5
0.6
0.7
E
W
(A
)
-3.85
-4.05
-4.25
-4.45
-4.65
-4.85
-5.05
Fig. 3.12 (a) The best fitting model to the 2020-08-24 HRS/SALT spectrum of the Mg-
II doublet WD 1929+011. The best fitting Mg abundance is [Mg/H] = −4.25. Models
are plotted every 0.2 dex spreading to +/- 1 dex in [Mg/H]. Models kindly provided by P.
Dufour (Dufour et al., 2012). (b) The equivalent width of the Mg II doublet over time for
WD 1929+011. The equivalent width for each model in (a) is plotted, showing the expected
equivalent width values for each [Mg/H] abundance.
98 Metal line variability
Farihi et al., 2018). The dynamic and stochastic nature of these systems predicts for periods
of increased accretion onto these white dwarfs. If the accretion is dominated by smaller
asteroids scattered often, then the subsequent accretion rates can increase by up to an order of
magnitude (Wyatt et al., 2014; Trierweiler et al., 2022), (Trierweiler, private communications).
The lack of variability found in this study implies that scattering events that lead to variable
accretion occur on timescales longer than decades.
3.4.5 White dwarf models
Theory predicts that the accretion rates are on the order of days for DAZ white dwarfs,
but these are based on 1D models. Understanding mixing mechanisms (e.g. convection,
diffusion, thermohaline instability) at the surfaces of white dwarfs is crucial to ensure accurate
sinking timescales. Cunningham et al. (2019) performed 3D models that included convective
instabilities. The onset of convective instabilities occurs at 18,000–18,250 K, white dwarfs
cooler than this may therefore be unstable to convection which consequently may increase the
diffusion timescales by 1.5–3 orders of magnitude (Cunningham et al., 2019). WD 0106−328,
WD 0408−041, and G29-38 lie in this temperature regime and may therefore have longer
sinking timescales than those reported in Table 3.2. Figure 3.13 compares the results from
Cunningham et al. (2019) for sinking timescales of Ca, Mg, and Fe as a function of white
dwarf effective temperature. For WD 0106−328 the sinking timescale increases to 4.0 days
for Ca and 6.4 days for Mg (factor 3.5 increase), for WD 0408−041 it increases to 33.3 and
37.6 days for Ca and Mg respectively (factor 8 increase), and G29-38 increases to 658.3
and 549.2 days for Ca and Mg respectively (factor 8 increase). Therefore, especially for
G29-38, these observations cover a limited number of sinking timescales, and further follow
up spectra would be required to definitively rule out variability. It has been hypothesised
that warm DAZ white dwarfs (> 10,500 K) do not spread the metals homogeneously across
the surface, therefore predicting surface abundance variations of the metals (Cunningham
et al., 2021). The rotation periods of white dwarfs are longer than the spectroscopic exposure
times in this work, and therefore, this work should have been sensitive to surface feature
changes, providing the abundance variations would be significant enough. Therefore, this
may imply that the accretion is spherically homogeneous. Thermohaline instabilities are
predicted to affect the amount of material in the photosphere and have been used to explain
the orders of magnitude lower accretion rates of DA’s than DB’s (Bauer & Bildsten, 2019),
this can consequently affect the diffusion times. The longer diffusion times predicted from
vertical mixing theory would align with the results of no detectable variability, however, the
horizontal spreading is at odds with this. Continued efforts in modelling mixing in these
3.4 Discussion 99
12000 14000 16000 18000
Temperature (K)
−3
−2
−1
0
lo
g τ
(y
rs
)
WD0106WD0408G29-38
Mg
Ca
Fe
Fig. 3.13 The updated sinking timescales using 3D models including convection. The
1D sinking timescales reported in Table 3.2 are plotted for the three white dwarfs in the
temperature regime of interest. Figure adapted from Cunningham et al. (2019) Figure 22.
systems will enable further understanding as to whether variability in the metal abundances
in the photospheres are expected.
3.4.6 The link with circumstellar variability
Four of the white dwarfs have confirmed infrared excesses due to circumstellar dust (Table
3.1). All five white dwarfs have Spitzer epoch photometry (Swan et al., 2020), with at least
two observations separated by 2000 days. Four of the white dwarfs have near-infrared K
band data from Rogers et al. (2020) with at least two measurements spanning a baseline of
up to three years. The variability analysis of these data is reported in Table 3.11 and shown
graphically in Figure 3.14. There is overlap between the optical spectroscopic monitoring
campaigns of the metal features and the infrared data.
WD 0106−328, WD 0408−041 and G29-38 show significant mid-infrared variability,
whereas WD 1929+011 and WD 1457−086 do not. For WD 1457−086 this is unsurpris-
ing as it is suspected that this white dwarf does not have detectable circumstellar dust.
WD 1929+011 appears to have no variability either in the circumstellar dust nor the accretion
rate. No recent collisional or tidal disruption event has occurred and so the processes driving
100 Metal line variability
Table 3.11 Infrared variability from previous studies. The K band data is from Rogers et al.
(2020) where the variability measure is an upper limit that corresponds to the measurement
limit of the observations. The Spitzer data are from Swan et al. (2020) showing the percentage
change and significance of the data.
WD Name K Sp Ch1 Sp Ch2
WD 0106−328 <3.9% 9.0% (6σ ) 10% (6σ )
WD 0408−041 <1.1% 16% (9σ ) 26% (13σ )
WD 1457−086 - 2.0% (1σ ) 0.8% (0.5σ )
WD 1929+011 <0.64 1.0% (0.7σ ) 2.0% (2σ )
G29-38 <1.0% 12% (7σ ) 9.0% (4σ )
the accretion of the circumstellar material are stable. G29-38 is a pulsator and consequently
there can be pulsation induced infrared variability. Xu et al. (2018b) predicts the effects of
pulsations on the infrared fluxes for different wavebands, these maximum infrared variations
are plotted in Figure 3.14 as filled in regions. Therefore, the infrared variability cannot be
unambiguously associated with the dust for G29-38. For WD 0106−328, this work studying
variability in the equivalent width is inconclusive. However, the mid-infrared flux is signifi-
cantly decreasing across the∼ 10 year baseline between the MIKE/Magellan and HRS/SALT
observations. If the increase in equivalent width over time for the Mg II line is confirmed,
this may provide evidence for the inner disc quickly evaporating and accreting such that
there is anti-correlation between the infrared flux, and the accretion rate, as predicted in Xu
& Jura (2014). WD 0408−041 shows significant variability in the mid-infrared flux, with
increases and decreases in the dust flux between ∼4000–8500 days (MJD−50,000) (Farihi
et al., 2018). There is no evidence for a change in the equivalent width of the spectral lines
from this work, and therefore no evidence for change in accretion rate onto this white dwarf.
This implies that either physical processes are acting to stabilise the accretion rate, such as
an inner viscous gas disc, or that there is a significant time delay between the delivery time
of solids and a change in the accretion onto the white dwarf. If it is the latter then continual
follow up spectroscopic monitoring of WD 0408−041 is crucial.
3.5 Conclusions
A spectroscopic monitoring campaign of five DAZ white dwarfs using two medium resolution
spectrographs has been conducted. Each white dwarf was observed over a total baseline of
>10 years with between 12–30 data sets obtained, covering timescales of days, months, and
years. This samples between 50–2000 sinking timescales depending on the properties of the
white dwarfs, or 6–1500 sinking timescales if considering updated sinking timescales from
3.5 Conclusions 101
800
850
900
950
1000
1050
1100
F
lu
x
(µ
Jy
)
WD1929+011 S1
S2
K
4000
6000
8000
10000
F
lu
x
(µ
Jy
)
G29-38
100
150
200
250
300
350
F
lu
x
(µ
Jy
)
WD0106-328
4000 5000 6000 7000 8000 9000 10000
MJD - 50000 (d)
600
800
1000
1200
1400
F
lu
x
(µ
Jy
)
WD0408-041
Fig. 3.14 The infrared fluxes of the white dwarfs with confirmed dust emission over time.
S1 and S2 are the Spitzer channels 1 and 2 with data from Swan et al. (2020) (private
communications). The K band data are from Rogers et al. (2020), as reported in Chapter 2.
The horizontal dashed lines are the median values for each photometric band.
102 Metal line variability
Cunningham et al. (2019). Therefore, if there was a change in accretion rate or abundance of
the metals in the photosphere, it should have been detected above a particular level.
The equivalent widths of the spectral features were calculated across the sample. For
four of the five white dwarfs in this sample, no statistically significant variation in the
equivalent widths were observed. For one of the white dwarfs, WD 0106−328, these data
were inconclusive. This was inconclusive as only one metal line could be resolved in each
spectrum, and as the lines are particularly narrow in this white dwarf, of the order of the
resolution of the HRS/SALT, comparisons between the data from the two spectrographs is
difficult. Follow-up observations with MIKE/Magellan will help to confirm this variability.
No unambiguous variability in the equivalent widths of the spectral lines has been found.
This may imply that the underlying source of the accretion is surprisingly steady. This has
implications for models of the inner regions of the circumstellar environments as it may imply
the need of a viscous gas accretion disc to regulate the accretion rate. Pollution is expected to
be as a result of the scattering of small bodies, this work predicts that these scattering events
must be less frequent than every 10 years. On the contrary, lack of variability could imply
that the sinking timescales in the white dwarfs are orders of magnitude longer than the current
models predict. These models are only just beginning to explore sinking timescales using 3D
atmosphere models and mixing mechanisms, therefore, unknown mixing mechanisms may
therefore increase the sinking timescales.
It should be noted that this work cannot rule out variability completely, as variability below
that which can be detected with this programme is likely. This work shows that studying the
metal lines with similar spectrographs allows for reduced systematic uncertainties such that
smaller equivalent width changes can be probed. Therefore, further spectroscopic monitoring
should be done with similar medium resolution spectrographs.
Chapter 4
Tracing the composition of exoplanetary
building blocks
Observations of planetary material polluting the atmospheres of white dwarfs provide a
unique means to probe the bulk composition of exoplanetary material. Less than one
percent of polluted white dwarfs host both observable circumstellar dust and gas discs; it
is unknown whether these systems represent an early phase in the disruption and accretion
of planetary bodies, or if they are accreting larger planetary bodies. This work presents
medium- and high-resolution optical spectroscopy of seven such white dwarfs to reveal the
chemical composition and history of the accreted exoplanetary material. The white dwarfs
are accreting planetary bodies with a wide range of volatile contents; two show evidence of
accreting oxygen-rich material, potentially from water-rich bodies, whilst others are accreting
dry, rocky material similar to asteroids in the solar system. The accretion of highly refractory
material, similar to CAIs, would explain both the high Ca/Mg in the planetary material
accreted by Gaia J0347+1624 and the high blackbody temperature of its circumstellar dust.
Based on the limited spectral lines, there is an indication that up to three of the white dwarfs
could be accreting fragments of a core-mantle differentiated body; core-mantle differentiation
and disruptive collisions appear commonplace in exoplanetary systems. White dwarfs with
circumstellar gas are good targets for studying photospheric abundances as they yield many
detectable elements, and there is no substantial evidence for significant differences in the
accreted abundance ratios for those polluted white dwarfs with or without circumstellar gas.
This work reports observations of seven white dwarfs with circumstellar dust and gas,
where the abundances of the planetesimals that have polluted their atmospheres has been
determined, and the population of these extreme systems is compared to the general popula-
tion of polluted white dwarfs. This chapter is structured as follows. Section 4.1 describes
the optical spectra of these seven systems taken with VLT/X-shooter, KECK/HIRES and
104 Tracing the composition of exoplanetary building blocks
Table 4.1 Stellar parameters derived from the spectroscopic (spec) and photometric (phot)
fitting methods. Distances (D) are inferred from Gaia parallaxes.
WD Name SpT Spec Teff Spec log(g) Phot Teff Phot log(g) D (pc)
Gaia J0006+2858 DAZ 23921 (335) 8.04 (0.04) 22837 7.86 152
Gaia J0347+1624 DAZ 21815 (305)∗ 8.10 (0.04)∗ 18854 7.84 141
Gaia J0510+2315 DAZ 21700 (304)∗ 8.20 (0.04)∗ 18723 8.05 65
Gaia J0611−6931 DAZ 17749 (248) 8.14 (0.04) - - 143
Gaia J0644−0352 DBZA 18350 (422) 8.18 (0.05) 16999 7.98 112
WD 1622+587 DBZA 18850 (434)∗ 7.80 (0.05)∗ 20204 7.92 183
Gaia J2100+2122 DAZ 25565 (358) 8.10 (0.04) 21997 7.92 88
Notes:
No available SDSS or Pan-STARRS photometry for Gaia J0611−6931, so no photometric solution
was derived.
∗ Spectroscopic parameters from Melis et al. (2020).
Magellan/MIKE. Section 4.2 describes how the composition of the polluting body is inferred
from the optical spectra, with the results reported in Section 4.3. Section 4.4 investigates
whether the pollutants of these white dwarfs with detectable gaseous discs represent a special
sub-class of objects. Section 4.5 discusses the chemical and geological composition of the
pollutant exoplanetary material, and the conclusions are presented in Section 4.6.
4.1 Observations and Data Reduction
4.1.1 Targets
This work targets seven newly identified polluted white dwarfs discovered in Dennihy et al.
(2020) and Melis et al. (2020) as listed in Table 4.1. These systems all show evidence of
atmospheric pollution, infrared excess from circumstellar dust emission, and observable
circumstellar gaseous discs. With > 1000 polluted white dwarfs known, but only 21 systems
with both detectable circumstellar dust and gas (Gänsicke et al., 2006, 2007, 2008; Melis
et al., 2010; Farihi et al., 2012a; Melis et al., 2012; Brinkworth et al., 2012; Debes et al.,
2012b; Dennihy et al., 2020; Melis et al., 2020; Gentile Fusillo et al., 2020), this represents a
unique sub-sample of polluted white dwarfs.
4.1 Observations and Data Reduction 105
Ta
bl
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4.
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tio
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106 Tracing the composition of exoplanetary building blocks
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4.1 Observations and Data Reduction 107
4.1.2 X-shooter
Four of the white dwarfs were observed with the echelle spectrograph X-shooter (Vernet et al.,
2011) on Unit Telescope 2 (UT3, Melipal) of the Very Large Telescope (VLT) at Paranal
Observatory, Chile (PI: Xu). X-shooter allows simultaneous observations in the 3 arms:
UVB (300–559.5 nm), VIS (559.5–1024 nm) and NIR (1024–2480 nm). The white dwarfs
are too faint to have strong signals in the NIR arm, so the NIR data was excluded from this
study. The observations were taken between July–October 2019 during runs 0103.C-0431(B)
and 0104.C-0107(A). For all observations, stare mode was used, with a 1.0 and 0.9 arcsec
slit width for the UVB and VIS arms respectively, this gives an optimal resolution (λ/∆λ )
of 5400 and 8900. Two exposures were taken lasting 1700 and 1729 s each for the UVB
and the VIS band respectively. The data reduction was performed using esoreflex (v 2.11.3)
with the X-shooter pipeline version 2.9.1 (Freudling et al., 2013). The standard reduction
procedures were followed including minor alterations to optimise the signal to noise ratio
(SNR) of the output spectrum, and reduce the number of cosmic ray contaminants. The
details of the X-shooter observations are listed in Table 4.2. The SNR was calculated per
pixel from the spectra, the median signal around the line of interest was divided by the
median absolute deviation (multiplied by 1.48 to give the standard deviation). The SNR at
the continuum around the Ca II K (∼ 3993 Å) line was 30–134 for the UVB arm and the
SNR at the continuum around 6600Å was 35–127 for the VIS arms depending on the flux of
the white dwarf and observing conditions.
4.1.3 HIRES
Six of the white dwarfs were observed with the High Resolution Echelle Spectrometer
(HIRES) on the Keck I Telescope, Hawaii (Vogt et al., 1994) (PI: Xu, PI: Klein). This has 2
modes, HIRESb and HIRESr, with a wavelength coverage of approximately 3200–5750 Å
and 4700–9000 Å respectively. The C5 decker was used, which has a slit width of 1.148
arcsec and a spectral resolution of 37,000. The observations were taken between July 2019
and October 2020.
Data reduction including bias subtraction, flat fielding, wavelength calibration, and
spectral extraction were performed using MAKEE (as in Xu et al., 2016). The final spectra
were continuum normalised using low order polynomials and combined using IRAF functions
(as in Klein et al., 2010). The details of the HIRES observations are listed in Table 4.2. The
SNR was calculated in the same way as for X-shooter (Section 4.1.2) for one observation was
32–89 around the continuum at the Ca K line for HIRESb and 31–73 around the continuum
at 6600 Å for HIRESr.
108 Tracing the composition of exoplanetary building blocks
4.1.4 MIKE
Gaia J0611−6931 was observed with the Magellan Inamori Kyocera Echelle (MIKE) spec-
trograph (Bernstein et al. 2003) on the 6.5 m Magellan Clay Telescope at Las Campanas
Observatory on 27 August 2021 with one exposure of 1800 s followed by a second of 1300 s
(PI: Weinberger). Observations were taken at airmass 1.5 with the atmospheric dispersion
corrector installed, but possibly not correcting the spectrum optimally, which would result
in a lower SNR than expected in the blue. The SNR of the continuum was approximately
15 near the Ca infrared triplet, calculated in the same way as reported in Section 4.1.2. The
seeing was 0.8 arcsec, and the employed 1′′ slit produces spectral resolution of R≈ 28,000
on the blue side (3500–5060 Å) and 22,000 on the red side (5000–9400 Å). ThAr lamps taken
before and after the exposures were used for wavelength calibration. Data reduction with the
standard Carnegie Python MIKE pipeline included extraction, flat-fielding, and wavelength
calibration using methods described in Kelson et al. (2000); Kelson (2003).
4.2 Modelling Methods
The white dwarf model atmospheres were kindly provided by P. Dufour using models from
the Montreal white dwarf group to derive stellar parameters, and measure the abundance of
the polluting material (Dufour et al., 2012).
4.2.1 White Dwarf Parameters
Two methods were used to derive the stellar parameters for each white dwarf. The first fitted
white dwarf models to broad band photometry (the photometric method), and the second
fitted white dwarf models to the pressure broadened hydrogen and helium spectral lines (the
spectroscopic method). The derived values for the spectroscopic and photometric methods
are reported in Table 4.1. These methods are discussed in more detail below.
For the photometric method, white dwarf models were fitted to SDSS and Pan-STARRS
broad band photometry to extract the best-fitting effective temperature and log(g). Parallaxes
from Gaia were required to obtain log(g) and the mass of the white dwarf. SDSS to AB
corrections were included as outlined in Eisenstein et al. (2006). Reddening becomes
important for objects > 100 pc, and five of the white dwarfs fall into this distance range. For
these white dwarfs the observational data were de-reddened using the method as described in
Genest-Beaulieu & Bergeron (2019) before fitting. When available, a combination of SDSS
and Pan-STARRS ugrizy were used to constrain the white dwarf parameters1. As discussed
1Photometry listed on: https://montrealwhitedwarfdatabase.org
4.2 Modelling Methods 109
in Genest-Beaulieu & Bergeron (2019), this provides the most accurate and consistent results.
Otherwise, either the SDSS ugriz, or Pan-STARRS grizy were used. In the future Gaia DR3
BP/RP spectrophometry can be used to improve the photometric fitting methods.
The spectroscopic method fits white dwarf atmospheric models to the hydrogen and
helium absorption lines to extract the best-fitting effective temperature and log(g). For the
four white dwarfs with X-shooter data, updated stellar parameters were found and for the
three objects without X-shooter data, the parameters derived in Melis et al. (2020) were
used. The model fits to the Balmer lines for the three DA white dwarfs (Gaia J0006+2858,
Gaia J0611−6931, and Gaia J2100+2122) are shown in Fig. 4.1. For the DBAZ white dwarf,
GaiaJ0644−0352, models were fitted to the Helium lines, trace H is also present, and
this abundance was also determined in this fit. Metals and hydrogen in cool DBZ stars
may affect the pressure/temperature structure and therefore affect the derived white dwarf
parameters (Dufour et al., 2012; Coutu et al., 2019). For GaiaJ0644−0352 it was tested
whether including metals in the models affected the derived parameters; as this white dwarf
is hot (Teff ∼ 20,000K), the inclusion of metals had a negligible affect on the derived white
dwarf parameters. The best-fitting white dwarf model is shown in Fig. 4.2.
The uncertainties in the spectroscopically derived effective temperature and log(g) for
DA white dwarfs are from Genest-Beaulieu & Bergeron (2019), 1.4% in Teff and 0.042 dex
in log(g). For the two DBA white dwarfs, the uncertainties derived in (Bergeron et al., 2011)
are used, 2.3% in Teff and 0.052 dex in log(g).
To assess the reliability of the stellar parameters, SEDs of the white dwarfs were used to
compare the X-shooter spectrum (where available) and the photometry from SDSS and/or
Pan-STARRS, with the white dwarf models derived from the photometric method and spec-
troscopic method (Appendix 2: Fig. 7.1). Additionally, GALEX photometry is used to assess
the reliability of the white dwarf models. UV wavelengths are sensitive to reddening so the
GALEX photometry points may lie below the photometric models, few physical explanations
exist that could cause the GALEX photometric points to lie above the photometric model, so
to explain this, a higher temperature white dwarf model would be required. Gaia J0510+2315
and Gaia J2100+2122 have GALEX fluxes which lie significantly above the expected flux
from the photometric models. It is likely that a hotter model, more consistent with the
spectroscopic models, is required for these systems. Neither white dwarf has SDSS ‘u’ band
photometry, reinforcing the idea that in order to obtain accurate photometric parameters,
SDSS ‘u’ is required (Bergeron et al., 2019).
110 Tracing the composition of exoplanetary building blocks
Fig. 4.1 Model fits (red lines) to the Hydrogen Balmer line profiles from the X-shooter
spectra for Gaia J0006+2858, Gaia J0611−6931, and Gaia J2100+2122. The best-fitting
model parameters are labelled on each panel. Doubled peaked emission lines from the
circumstellar gas discs can be seen in the wings of the hydrogen lines.
4.2.2 Line Identification
A multitude of metal lines were identified in the spectra of each white dwarf. Using the
IRAF task SPLOT (Tody, 1986) the equivalent width, line centre, and radial velocity of each
spectral line was measured. For the equivalent width, a Voigt function was fitted to the profile
of the line five times whilst changing the region used for the continuum fitting. From this the
average equivalent width and standard deviation for each line was found, this was compared
to a direct flux summation to ensure accuracy. The uncertainty on the equivalent width
was calculated by combining in quadrature the standard deviation of the equivalent width
measurements and the SPLOT fitting error. Appendix 2: Tables 7.1 – 7.7 list the spectral lines
identified, the derived equivalent widths, line centres, and radial velocities.
4.2.3 Abundance of planetary material
The abundance of the planetary material that has polluted each white dwarf was measured
using white dwarf models kindly provided by P. Dufour following Dufour et al. (2012).
The spectra were divided into regions of 5–15 Å around each metal absorption line. The
white dwarf effective temperature and log(g) was inputted, and the best-fitting abundance
4.2 Modelling Methods 111
Fig. 4.2 Model fits (red lines) to the X-shooter Helium lines for Gaia J0644−0352. The
best-fitting white dwarf parameters and hydrogen abundance are labelled. The green lines
show the points used to re-normalise the spectrum to the models.
112 Tracing the composition of exoplanetary building blocks
3932.0 3932.5 3933.0 3933.5 3934.0 3934.5 3935.0
Wavelength (A)
0.6
0.7
0.8
0.9
1.0
1.1
1.2
N
or
m
al
is
ed
F
lu
x
10kG
0kG
6368 6369 6370 6371 6372 6373 6374
Wavelength (A)
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
N
or
m
al
is
ed
F
lu
x
10kG
0kG
6344 6345 6346 6347 6348 6349
Wavelength (A)
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
N
or
m
al
is
ed
F
lu
x
10kG
0kG
Norma
lised	Fl
ux
Ca	II Si	II Si	II
Fig. 4.3 Model fits to the HIRES data using the average abundances for WD 1622+587.
Dashed orange line shows the model for a magnetic field of 0kG, and the blue solid line
shows the model for a magnetic field of 10kG.
for that spectral line was found. The abundances of the lines were found using the effective
temperature and log(g) from the photometric and spectroscopic methods separately. When
more than one line of a particular element are present in the 5–15 Å region, the lines are
fitted together. For each spectral line in both the X-shooter and HIRES data, the best-fitting
abundance was derived, these are reported in Appendix 2: Tables 7.1 – 7.7.
A magnetic DB white dwarf
The widths of the absorption lines for WD 1622+587 are significantly wider than expected
from pressure broadening for this DBZ white dwarf. A possible explanation is the presence
of a weak magnetic field. The formulation presented in Dufour et al. (2015) is used (see
also Hardy et al., 2017) but kept the surface magnetic field constant for simplicity (i.e. no
geometry). Fig. 4.3 shows that a constant 10 kG field may account for the extra broadening
of the Ca and Si lines.
Absorption features in the presence of emission features
Some absorption lines also have gaseous emission features present at the same wavelength
which makes it difficult to disentangle the contribution from the photospheric absorption
from the circumstellar emission. In Appendix 2: Tables 7.1 – 7.7. those lines which have
photospheric absorption at the same wavelength as the gaseous emission features are noted.
High order polynomials are fitted to the spectra to normalise out the broader gaseous emission
features. In Klein et al. (2010) it is noted that through tests which varied the order of the
normalisation polynomial, the effect of continuum normalisation on narrow absorption lines
4.2 Modelling Methods 113
in the presence of bumpy features was < 1%. However, in this sample, the spectra contain
both broad and sharp gaseous emission features which are less trivial to normalise out in
order to obtain accurate equivalent widths of the photospheric features. To test how the
sharp gaseous emission features affect the derived equivalent widths, tests were performed
on the 3933 Å Ca II line in Gaia J0006+2858 and 7771 Å O I line in Gaia J0510+2315.
The equivalent widths were measured using SPLOT, as explained in Section 4.2.2, using
both the un-normalised and normalised HIRES spectra. The average equivalent width
deviation was found to be 12%. For those spectral lines with gaseous emission features, this
additional error of 12% was added in quadrature with the SPLOT fitting error. The equivalent
width errors quoted in Appendix 2: Tables 7.1 – 7.7 include the additional error for those
photospheric lines which lie in the presence of gaseous emission features. Gaia J0006+2858
has abundances determined from two calcium lines, 3179 Å and 3933 Å, where the latter
has a weak gaseous emission feature at the same wavelength. The calcium abundance
derived from 3933 Å and that derived from 3179 Å are consistent within the errors of 0.1
dex, providing confidence that the derived abundances in the presence of gaseous emission
features are accurate.
Spectroscopic versus photometric white dwarfs parameters used to derive abundances
The spectroscopic and the photometric methods for determining white dwarf parameters
result in different sets of absolute abundances derived for the pollutant planetary material. All
derived white dwarf temperatures are hotter (except the magnetic white dwarf WD 1622+587)
for the spectroscopic method, than for the photometric method. Derived heavy element
abundance correlates with temperature, so the abundances of heavy elements when compared
to the abundance of the principal element (H or He) as derived from the spectroscopic white
dwarf parameters are larger. When considering the abundance ratios of heavy elements
rather than absolute abundances, the discrepancy between the spectroscopic and photometric
parameters disappears within the 1σ error, and the choice of white dwarf parameters little
affects the abundance pattern and interpretation.
Upper limits
Some important elements are not detected, and so an equivalent width upper limit that would
have resulted in a 3σ spectral line detection was calculated. Either a detection or upper limit
was determined for these elements for each white dwarf: O, Na, Mg, Al, Si, Ca, Ti, Cr, Fe and
Ni. Around the strongest optical line for a particular element, a spectral line was artificially
inserted at decreasing values of equivalent width, corresponding to decreasing abundance.
114 Tracing the composition of exoplanetary building blocks
From this, the significance of the absorption feature was calculated, and repeated 10,000
times. The equivalent width upper limit was taken to be the point at which 99.7% of the lines
were detected at 3σ for a certain equivalent width. The equivalent width upper limits are
reported in Appendix 2: Table 7.8. The Montreal white dwarf models were used to convert
from equivalent width to abundance assuming the spectroscopically derived temperature and
log(g); the abundance upper limits are reported in Table 4.3. As mentioned previously, the
hotter the temperature of the white dwarf used in the models, the larger the abundance is for
the same spectral line and equivalent width. Therefore, the abundance upper limits consider
the abundance error associated with temperature, and are applicable to both the spectroscopic
and photometric abundances, with the exception of WD 1622+587.
Final Abundances of the accreted material
The final abundances are reported in Table 4.3. The abundances are reported as an average of
X-shooter and HIRES abundances (or X-shooter and MIKE abundances for Gaia J0611−6931),
weighted by the number of absorption lines for each element. If only one line of a particular
element is present, the measurement uncertainty is propagated for the abundances and the
error was set to 0.1 dex. If an element has a number of detected spectral lines then the uncer-
tainty is dominated by the range of abundances derived for each element, and the standard
deviation of the abundances is taken as the abundance error. Appendix 2: Figs. 7.2–7.7 show
the average model abundance fit to the strongest spectral line for each element in each white
dwarf, for WD 1622+587 the abundance fits are shown in Fig. 4.3. The average abundance is
plotted which is derived from multiple spectral lines, so sometimes the fit to individual lines
can be discrepant.
4.2.4 Interpreting the observed abundances
Bayesian Models
In order to interpret the final abundances of the accreted material, the PYLLUTEDWD soft-
ware package was kindly run by A. Buchan on the abundances (Buchan et al., 2022)2. This
was used to find the most likely explanation for the observed compositions, taking into ac-
count the differential sinking of elements in the white dwarf photosphere and the abundances
of the accreted planetary material. Fundamentally, the model focuses on the volatile content
and geological history of the planetary bodies accreted by the white dwarfs (Harrison et al.,
2018, 2021; Buchan et al., 2022). The model assumes that only a single planetary body is
2https://github.com/andrewmbuchan4/PyllutedWD_Public
4.2 Modelling Methods 115
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
[Mg/Ca] - [Mg/Ca]¯
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
[S
i/
C
a]
-
[S
i/
C
a]
¯
Heating
Sinking
GaiaJ0006
GaiaJ0347
GaiaJ0510
GaiaJ0611
GaiaJ0644
WD1622
GaiaJ2100
(a)
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
[O/Ca] - [O/Ca]¯
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
[F
e/
C
a]
-
[F
e/
C
a]
¯
Heating
Sinking
CMF
(b)
Fig. 4.4 (a) [Mg/Ca] vs [Si/Ca] abundance ratios of the pollutant, normalised to solar, derived
from the spectroscopically determined white dwarf parameters. The ellipses show a 1σ error
ellipse on the abundance ratio. The Hypatia catalogue (Hinkel et al., 2014) of nearby main
sequence stars is plotted as scatter points with a density histogram in the densest regions
(around solar values - dashed lines at 0, 0). The red arrows show how sinking in the white
dwarf atmosphere and heating affects the abundance ratios. Limits are shown with arrows.
(b) [O/Ca] vs [Fe/Ca] abundance ratios normalised to solar, for reference the value of [O/Ca]
normalised to solar for Bulk Earth is -0.7. An additional red arrow describes how the [Fe/Ca]
ratio changes as the core-mass-fraction (CMF) of the planetary body is increased.
116 Tracing the composition of exoplanetary building blocks
currently present in the white dwarf atmosphere. This is clearly a wide-reaching assumption,
but as discussed in Turner & Wyatt (2020); Harrison et al. (2018), it is likely that the mass
currently in the atmosphere is dominated by the most massive, single body accreted. The
composition of this planetary body has potentially been altered due to differential sinking
rates of elements in the atmosphere of the white dwarf. Additionally, three main processes are
considered that dominate changes to the planetary body’s composition. First, the composition
of the initial material available for planet formation may differ from the solar system. Second,
the planetary bodies may lose volatiles due to the high temperatures experienced during
formation. Third, if there is sufficient heating that large-scale melting occurs, the segregation
of the iron melt leads to the formation of a core and a mantle; additionally the influence of
the internal pressure and oxygen fugacity are considered. Subsequent collisions or other
processing that leads to fragmentation, can change the amount of core or mantle material
that is accreted by the white dwarf.
The model uses a Bayesian framework to compare the likelihood of a basic primitive
model explaining the abundances of the white dwarf pollutant, with a range of more complex
models. The basic free parameters are listed below, with the additional more complex
parameters listed as optional:
• ‘Initial Composition’: the body accreted by the white dwarf could have formed in
planetary systems with a range of initial compositions, later altered by volatile depletion
of metal-silicate segregation. The compositions of nearby stars is a good proxy for this
range of initial compositions, utilising the catalogue of Brewer & Fischer (2016). In
most cases, the white dwarf is equally likely to have accreted material that started with
a wide range of initial compositions.
• ‘Pollution fraction’: the mass fraction of the white dwarf convection zone that is made
up of observable metals MZ/MCVZ .
• ‘Time since accretion onto the white dwarf’ and ‘accretion event time-scale’: the
model finds the most likely time since accretion started and length of time for which
accretion lasted based on the abundances and relative settling of the detected elements.
The diffusion time-scales used in the models are obtained from Koester (2009)3. It
should be noted that there are model dependent differences in settling time-scales
which contributes an additional uncertainty, see Figure A2 in Swan et al. (2019b)
for further details. Based on this, the model finds whether it is more likely to be in
build-up, steady-state or declining phase, these phases were discussed in detail in
Chapter 1 Section 1.4.2. As all the objects in this sample have circumstellar gas and
3http://www1.astrophysik.uni-kiel.de/~koester/astrophysics/astrophysics.html
4.2 Modelling Methods 117
dust reservoirs, accretion is likely ongoing and dominated by one singular body. This
is almost certainly occurring for the hot DA white dwarfs, with settling timescales on
the order of days.
• ‘Temperature’ (optional complex model): the depletion of volatiles is linked to the
temperature (pressure) conditions at a certain location in the protoplanetary disc. This
assumes that patterns of volatile depletion occur due to the incomplete condensation of
hot gas in the inner regions of a protoplanetary disc. In reality it is not known when in
the history of the planetesimal the heating occurred; collisions, impacts, or heating on
the red giant branch may also alter the abundances, albeit in the same way as modelled
here. Therefore, the ‘Temperature’ parameter informs of any kind of volatile loss.
• ‘Feeding Zone Size’ (optional complex model): the abundances of some planetary
material are best explained by a mixture of material that experienced different tempera-
tures. This would occur in reality when planetary bodies accrete material from a range
of radial locations, or their feeding zone.
• ‘Fragment Core Fraction’ (optional complex model): the white dwarf may have
accreted material that is dominated by the core or the mantle of a larger planetary body.
This is quoted by both number fraction and mass fraction.
• ‘Differentiation pressure’ and ‘oxygen fugacity’ (optional complex model): these
parameters determine the composition of the core (mantle) based on the conditions
that were present during core-mantle differentiation, notably the pressure and the
availability of oxygen and its degree of oxidisation, parameterised by oxygen fugacity.
The composition of the core or mantle most notably the Cr, Si, Ni content, is constrained
based on a model for elemental partitioning during core formation, this model allows
the core composition to differ from Earth’s core and has 2 free parameters: core mantle
boundary pressure (‘differentiation pressure’) and ‘oxygen fugacity’ at the time of
core formation (note this is different to oxygen fugacity of the final planetary body,
as considered in Doyle et al. (2019)). The pressure and oxygen fugacity of the Earth
as reported in Buchan et al. (2022) are roughly 45 GPa and −1.3. An asteroidal body,
with significant lower pressure than Earth, would have a core with significantly higher
Ni/Fe than Earth’s core.
These Bayesian models were initially written and developed by John Harrison; the priors of
the Bayesian models for the above parameters are defined in Table 1 of Harrison et al. (2021).
Buchan et al. (2022) developed these Bayesian models to include differentiation pressure
and oxygen fugacity during formation of the parent body. A uniform prior distribution
118 Tracing the composition of exoplanetary building blocks
between 0 and 60 GPa was used for differentiation pressure, and −3 and −1 for the oxygen
fugacity, see Doyle et al. (2019) for the formal definition of oxygen fugacity. All priors for
the model parameters use a uniform distribution between two values to ensure that the priors
are uninformative and not biasing the results towards a specific outcome.
The Bayesian framework compares the basic primitive model with no additional complex
free parameters included (null hypothesis, M0), with more complex models which incor-
porate additional free parameters, (alternative hypothesis, M1). It is assessed whether the
introduction of additional free parameters results in an improved Bayesian evidence using the
Bayes factor. This compares the likelihood of the data given the alternative hypothesis, M1,
to the likelihood of the data given the null hypothesis, M0. A Bayes factor of > 1 implies
evidence for the alternate hypothesis, and a Bayes factor of > 100 implies extreme evidence
for an alternate hypothesis. Additionally, this is converted to a frequentist statistic (Nσ ) to
also show the significance of the model. The abundances and output of the Bayesian models
are discussed in the results section below.
Oxygen Budget
In order to determine whether the pollutant is water rich, has any iron in metallic form,
or is dry, rocky material, oxygen budgeting is done following the method used by Klein
et al. (2010). O is assigned to: MgO, SiO2, Al2O3, CaO, and FeO, if there is excess
oxygen, this was probably in the form of water in the parent body. The abundances are
corrected for sinking assuming the accretion is occurring in the steady state. If there is not a
measured abundance for one or more of the major rock forming elements (Mg, Si, Al, Ca
and Fe) then the abundance of that element predicted from the Bayesian model is used in the
calculation. The oxidisation state of Fe is unknown and Fe could be in a number of forms
(or a combination) including: FeO, Fe2O3 or metallic Fe. Therefore, the oxygen budgeting
method is used to determine if there is excess oxygen rather than to explore the exact water
content of a body. As well as the O assignment described above, the most conservative case
possible is also considered, which is entirely ferric Fe (i.e. forming Fe2O3). This calculation
does not consider carbon ices, including CO2 ices, as in equilibrium these would only form
at significantly lower temperatures than water ice.
4.3 Results from individual systems
Interpretation of the observed abundances for the planetary material that were accreted by
each white dwarf is discussed here, whilst interpretation of the entire population is presented
in Section 4.4. In what follows, the abundances obtained based on the spectroscopically
4.3 Results from individual systems 119
derived stellar parameters are used (see the discussion for additional details). However, as
noted in Section 4.2.3, when considering abundance ratios rather than absolute abundances,
the two sets of measurements agree within a 1σ error. When discussing abundances,
abundances by number are used unless stated otherwise. The derived abundances are
reported in Table 4.3, plots showing the average abundance fits to the spectra can be found
in Appendix 2: 7.4 and Fig. 4.3 for WD 1622+587. The photospheric abundances for each
target inform our understanding of the history and state of the planetary material accreted.
These interpretations are presented first, followed by more detailed insights derived from the
Bayesian models discussed in Section 4.2.4. The best-fitting parameters from the Bayesian
models are reported in Appendix 2: 7.5 in Table 7.9.
4.3.1 Gaia J0006+2858
The exoplanetary body that polluted Gaia J0006+2858 has Si/Mg and Ca/Mg abundances
that are close to solar and within the abundance range of nearby stars, as shown in Fig. 4.4a.
The system is most likely in steady-state given the short settling time-scale of a few days.
The derived oxygen upper limit provides no information about the volatile content of the
accreted object.
These conclusions are supported by the Bayesian models which find that the abundances
are most likely explained by the accretion of a primitive body in steady state.
4.3.2 Gaia J0347+1624
The abundance of the exoplanetary body that polluted Gaia J0347+1624 demonstrates super-
solar values of Ca/Mg (Fig. 4.4a). One explanation is that a portion of the polluting body
contained material depleted in moderate volatiles, including Mg-rich minerals, with respect
to highly refractory calcium-rich minerals. This may be the result of experiencing hot
temperatures, as seen in Fig. 4.4a the abundance follows the ‘heating’ arrow. As this white
dwarf is a hot DAZ with short sinking time-scales, it is most likely to be accreting in
steady-state phase.
The model with the highest Bayesian evidence invokes the accretion of a planetary body
with a highly refractory composition (depleted in moderate volatiles) with Bayes factor of
2.1×1013 (8.1σ ), as reported in Appendix 2: Table 7.9.
120 Tracing the composition of exoplanetary building blocks
4.3.3 Gaia J0510+2315
The oxygen abundance of the body that polluted Gaia J0510+2315 is high when compared
to more refractory species, such as: Mg, Si, and Ca, as shown in Fig. 4.4b. Based on the
available optical spectra, Fe is not detected in the atmosphere of this white dwarf and the
upper limit provides no further insights into the oxygen budget. The oxygen abundance
is consistent with the accretion of a volatile rich body and has a similar abundance ratio
to solar, rather than depleted in volatiles which the case for the rocky material typically
accreted by white dwarfs. If the iron abundance was also found to be solar, consistent with
the non-detection, the oxygen abundance is too high to account for all the metals, and thus
there would be excess oxygen that may imply that Gaia J0510+2315 accreted a water-rich
body. The abundances are most likely accreting in steady-state, as it is unlikely to catch the
system in build-up phase given the settling time-scales of days.
The Bayesian model finds that the most likely explanation for the observed abundances
is the accretion of a volatile rich body accreting in steady state. In order to consider the
oxygen budget, iron is considered likely to be no more abundant than seen in nearby stars.
Using the Bayesian models inference for iron the contribution of oxygen to the metal
oxides can be estimated, as described in Section 4.2.4. If iron were significantly higher
than the abundances seen in nearby stars, it is likely that this iron would take the form of
Fe (metal) in a planetary core, rather than FeO, however, Ni or Cr abundances would be
needed to confirm this interpretation. The remaining fraction of oxygen once the metals
(including the Fe prediction) have been oxidised is 0.74 (0.48 water mass fraction) if Fe
is in the form of FeO; this oxygen can bond with hydrogen as water. In order for the Fe
abundance to balance the oxygen budgeting, the Fe abundance would have to be 1.1 dex
higher than the range of stellar abundance from Brewer & Fischer (2016). Future UV
spectra will confirm whether this system is indeed accreting a volatile rich body as the UV is
sensitive to numerous of absorption lines from volatile species (e.g. O, C, N) enabling robust
abundance determinations and limits to be obtained for the pollutant. Gaia J0510+2315 is a
DA, so hydrogen from an accreted body cannot be spectroscopically distinguished from the
hydrogen envelope of the white dwarf. The oxygen circumstellar gaseous emission features
are particularly strong implying there could also be volatile-rich circumstellar material. Full
radiative transfer calculations such as those in Gänsicke et al. (2019); Steele et al. (2021) are
required to investigate whether the circumstellar gas is as rich in volatiles as the photosphere
appears to be; this is beyond the scope of this chapter.
4.3 Results from individual systems 121
GaiaJ0611 GaiaJ0644
0.0
0.2
0.4
0.6
0.8
1.0
F
ra
ct
io
n
of
O
as
si
gn
ed
Excess O
MgO
MgO
SiO2
SiO2
Al2O3
CaO
FeO
FeO
MgO
SiO2
Al2O3
CaO
FeO
Excess O
Fig. 4.5 The likely division of the observed oxygen abundance between metal oxides
(MgO, SiO2, Al2O3, CaO, and FeO) and water-ice (yellow), for Gaia J0611−6931 and
Gaia 0644−0352. The approach is described in Section 4.2.4, using abundances adjusted
for sinking in steady-state. For Gaia J0611−6931 the fraction of excess oxygen is 0.48, this
excess oxygen is likely carried in water-ice. For Gaia 0644−0352, the oxygen can all be
accounted for in metal oxides, and the pollutant was most likely dry and rocky.
122 Tracing the composition of exoplanetary building blocks
4.3.4 Gaia J0611−6931
Gaia J0611−6931 has accreted a planetary body with approximately solar abundances of
Ca/Mg, Si/Mg, and O/Mg. Solar (or close to) abundances of oxygen are seen in Kuiper belt
objects from the cold outer regions of the solar system. The planetary body also has a super-
solar abundance of Fe/Mg, as shown in Fig. 4.6. This iron abundance lies 5.8σ above that
of solar. The high iron abundance is typical of planetary cores, indicating that the accreted
object appears to be dominated by its iron core. The body accreted by Gaia J0611−6931 is
both rich in iron and oxygen, as seen in Fig. 4.4b.
Oxygen budgeting was done on this system using the bulk composition of the parent body.
The most likely accretion state is steady-state so the abundances are adjusted to consider the
effects of differential sinking of elements. Assuming steady-state accretion, the measured
oxygen abundance (Table 4.3) is sufficiently large that extra oxygen is indicated, over and
above that which can be accounted for in metal oxides, see Fig. 4.5. The excess oxygen
was calculated using two Fe oxidisation states: FeO and the more conservative Fe2O3. The
oxidisation state of Fe (FeO or Fe2O3) leads to small uncertainty in the potential water
fraction. Both oxidisation strategies show a significant oxygen excess: 0.48 for FeO and
0.31 for Fe2O3 which is equivalent to accreting a body with 0.22 and 0.14% water by mass
respectively. Additionally some Fe could be metallic and so the oxygen excess is a lower
limit.
The most likely Bayesian model is that of a volatile rich and core-mantle differentiated
body; this is preferred over a primitive model with Bayes factor 4.3×104 (5.0σ ). From
Appendix 2: Table 7.9, a fragment number core fraction of 0.26+0.06−0.05 is inferred, which
equates to a core mass fraction of 0.52+0.07−0.07, the equivalent core mass fraction for Earth is
only 0.325. Gaia J0611−6931 has accreted material that is dominated by core-rich material,
likely a core-rich portion of a larger parent body. The model determined that the body
accreted by Gaia J0611−6931 was oxygen-rich, and inferred a correspondingly oxygen-rich
mantle composition (87% by number). Assuming a single body was accreted by the white
dwarf, the oxygen level is too high to be explained with standard oxidation of the rock
forming elements, suggesting an additional oxygen reservoir, for example, a hydrosphere.
4.3.5 Gaia J0644−0352
Gaia J0644−0352 has solar abundances of Al, Ti, Ca, Cr, and Si, when compared to Mg, but
has sub-solar O and Fe, as shown in Fig. 4.7. The oxygen abundance is depleted by > 3σ
indicating the accretion of dry and rocky material, oxygen budgetting calculations were
performed which found that sufficient metals are present such that the oxygen likely arrived
4.3 Results from individual systems 123
Ca Fe Si O
−1.00
−0.75
−0.50
−0.25
0.00
0.25
0.50
0.75
1.00
[X
/M
g]
Solar
Bulk Earth
CI Chondrites
GaiaJ0611
GaiaJ2100
Fig. 4.6 The number ratio of elemental abundances in the parent body relative to Mg, nor-
malised to solar (grey dash dot line). Abundances for the white dwarfs, Gaia J0611−6931 and
Gaia J2100+2122, are shown as green diamond and black hexagon data points respectively,
with 1σ errors, derived using the spectroscopic temperature and log(g). Abundances have
been adjusted for sinking assuming steady state. The Fe/Mg for Gaia J0611−6931 lies 5.8σ
above solar, and for Gaia J2100+2122 the Fe/Mg value lies 3.2σ above solar; both systems
are enhanced in Fe compared to Mg.
124 Tracing the composition of exoplanetary building blocks
in the form of metal oxides within the errors, as shown by Fig. 4.5. The low Fe abundance
could be due to the accretion of a mantle-rich fragment which would naturally explain a
depletion in iron.
The most likely explanation for the observed abundances (highest Bayesian evidence) is
the accretion of volatile depleted material. The pollutant went through significant heating
(∼1381+182−80 K) to fit the volatile depletion in this accreted body, as shown as the blue ‘max
Z’ model in Fig. 4.7. The low Fe abundance observed for Gaia J0644−0352 is consistent
with the accretion of mantle-rich material. A model in which Gaia J0644−0352 accreted
mantle-rich material is a good fit to the data points, as shown by the grey median model with
differentiation included in Fig. 4.7. A mantle-rich model does not have a higher Bayesian
evidence than a model where the white dwarf accretes volatile depleted material (Bayes
factor with ‘max Z’ model as null hypothesis and mantle-rich model as alternate hypothesis
gives 0.4). Although the model including core-mantle differentiation is a better fit to the
data points, the Bayesian model does not favour such a solution due to the additional model
parameters. As there are measurements of nine abundances, the model renders it likely that
the abundance of one of the elements could be discrepant from its true abundance by 2σ ,
where σ is the measurement uncertainty, as required for the ‘max Z’ volatile-depleted model
to explain the low Fe. The true Fe abundance could be significantly higher than that observed
due to statistical uncertainties and observational errors. This is a limitation of the Bayesian
model.
4.3.6 WD 1622+587
The Ca/Mg and Si/Mg abundances of the exoplanetary body that polluted WD 1622+587 are
primitive and reflect bulk Earth, or compositions seen in nearby stars. The oxygen upper
limit suggests the accreted body was rocky material, rather than volatile-rich.
4.3.7 Gaia J2100+2122
The Si/Mg abundance in the exoplanetary body that polluted Gaia J2100+2122 is primitive
and reflects bulk Earth, or compositions seen in nearby stars. However, there is an enhance-
ment of Ca and Fe in comparison to solar, as shown in Fig. 4.6. The Fe/Mg lies 3.2σ above
that of solar, when assuming steady state accretion. This could be explained by the accretion
of a core-rich fragment. There is insufficient information from the oxygen upper limit to
constrain the volatile content for the body that was accreted by this white dwarf.
The Bayesian model that invokes core-mantle differentiation is preferred over a primitive
model with a Bayes factor of 4.6×102 (3.9σ ). The fragment core number fraction is
4.3 Results from individual systems 125
Fig. 4.7 The number ratio of elemental abundances in the pollutant material relative
to Mg, normalised to solar (dashed line). Observed abundances for the white dwarf,
Gaia J0644−0352, are shown as black points, with 1σ errors, derived using the spectroscopic
temperature and log(g). Sinking effects are included in the model. The blue line represents
the Bayesian model with the maximum likelihood (max Z). The black line represents the
maximum likelihood median model with differentiation included and a 1σ error as the shaded
dark grey region. The body that was accreted by Gaia J0644−0352 may be mantle rich, but
there is insufficient statistical evidence to include an additional parameter in the model fit.
The shaded light grey region indicates the range of abundances seen in nearby stars using the
catalogue from Brewer & Fischer (2016).
126 Tracing the composition of exoplanetary building blocks
14000 16000 18000 20000 22000 24000 26000
Temperature (K)
106
107
108
109
1010
1011
1012
A
cc
re
ti
on
ra
te
(g
/s
)
H
He
H with Gas
He with Gas
H (this work)
He (this work)
Fig. 4.8 The accretion rates of polluted white dwarfs with and without detectable gaseous
discs in emission as a function of their effective temperatures. The data for the accretion
rates of polluted white dwarfs without circumstellar gaseous discs are from Figure 3 in Xu
et al. (2019), see reference for details. The accretion rates for gaseous disc systems are from
Table 4.4 including the seven reported in this work.
0.30+0.11−0.08, and the equivalent core mass fraction is 0.52
+0.12
−0.11, this is higher than bulk Earth
which has a core mass fraction of 0.325.
4.4 Comparing pollution in white dwarfs with and without
detectable circumstellar gas
The white dwarfs in this sample represent 7 of just 21 polluted white dwarf systems with de-
tectable circumstellar gas and dust. The presence of circumstellar gas is not fully understood.
One possibility is that it represents an early stage in the accretion process, which is followed
by dust-rich accretion and then no detectable circumstellar material. Alternatively, detectable
4.4 Comparing pollution in white dwarfs with and without detectable circumstellar gas 127
−0.5 0.0 0.5 1.0 1.5
[Ca/Mg] - [Ca/Mg]¯
600
800
1000
1200
1400
1600
1800
2000
B
B
D
us
t
T
em
p
er
at
ur
e
(K
)
GaiaJ0347
Mg/Si/Fe
Ca
Al
Fig. 4.9 Single blackbody dust temperature for the dust emission from the literature versus
the [Ca/Mg] ratio, normalised to solar, of the pollutant body. Those in this work are black
squares, and those from the literature are grey. Horizontal dashed grey lines show apparent
condensation temperatures for Al, Ca, Mg, Si and Fe (Lodders, 2003). The material pol-
luting Gaia J0347+1624 is depleted in moderate volatiles and has a composition most like
Ca-Al–rich inclusions, it is hypothesised that the material underwent incomplete conden-
sation during formation explaining the extreme [Ca/Mg]. Therefore the dust surrounding
Gaia J0347+1624 can survive to higher temperatures, and so the dust emission has a hotter
overall inferred blackbody temperature.
128 Tracing the composition of exoplanetary building blocks
quantities of circumstellar gas may only be produced in the disruption of the largest planetary
bodies, or those with the most violent collisions.
Previous work has found that detectable circumstellar gas is a rare phenomena in polluted
white dwarfs (Manser et al., 2020). Xu et al. (2019) compared pollution levels for those white
dwarfs with and without detectable circumstellar dust, compiling their work with data from
the literature (Koester et al., 2011, 2014; Koester & Kepler, 2015; Hollands et al., 2018). No
strong difference in total mass accretion rate or abundance of polluting material was found
between those white dwarfs with detectable circumstellar dust and those without, although
it should be noted that the authors consider there to be bias in the sample. Here the work
of Xu et al. (2019) is expanded to compare the pollution between white dwarfs with and
without detectable circumstellar gaseous discs, where without refers to all polluted white
dwarfs without any evidence of circumstellar gas in emission.
4.4.1 Accretion rates
Previous studies investigating the link between the presence of a detectable gaseous disc and
accretion rate based on a handful of systems found no correlation between accretion rate
and the presence of circumstellar gas (Manser et al., 2016b, 2020). However, gas drag may
cause enhanced accretion rates above what may be expected from PR drag alone. Combining
white dwarfs with detectable circumstellar gas discs from the literature (which have reported
abundances of at least Ca, and Mg in their photosphere) with the seven in this work, the
sample size is doubled. The following discussion revisits whether white dwarfs with a
circumstellar gas disc accrete planetary material at higher levels, compared to the population.
In order to compare the mass accretion rates between white dwarfs with and without
detectable circumstellar gas discs, a systematic approach must be taken. The mass accretion
rates were calculated from the magnesium abundance, assuming magnesium makes up 15.8%
of the total mass, as in Bulk Earth. Xu et al. (2019) demonstrated this as the most reliable and
consistent way to measure and compare accretion rates for a sample of polluted white dwarfs.
The coolest white dwarf discovered with a circumstellar gaseous disc is WD 0145+234, with
a temperature of 12,720 K (Melis et al., 2020), thus, when comparing to the population,
the lower temperature cut off was set at T> 12,720 K. There is no correlation between
temperature (white dwarf cooling age) and accretion rate above 10,000 K (Xu et al., 2019;
Wyatt et al., 2014).
The accretion rates as a function of white dwarf temperature are plotted in Fig. 4.8, which
compares those with detectable circumstellar gas discs to the population. The white dwarfs
with gas discs tend to be hotter white dwarfs, which could be an observational bias, and
can have accretion rates that match the upper end of the population. Given the statistics of
4.4 Comparing pollution in white dwarfs with and without detectable circumstellar gas 129
small numbers, at this time such a comparison is limited by this. The figure also highlights
how the accretion rates of He dominated white dwarfs are higher than those in H dominated
atmospheres (Farihi et al., 2012b; Xu et al., 2019). This may be due to the orders of magnitude
longer settling time-scales for He dominated white dwarfs and therefore the rates represent
an average historical accretion rate. Direct impacts onto the white dwarf (Brown et al.,
2017; McDonald & Veras, 2021), or the disruption of massive asteroids ∼500 km which can
collisionally evolve to produce enhanced accretion on short time-scales (Wyatt et al., 2014;
Brouwers et al., 2022) can contribute to larger measured average accretion rates for DBZ
white dwarfs. Alternatively, thermohaline mixing could explain the differences between
DA and DB accretion rates. DBZ white dwarfs experience less thermohaline mixing than
DAZ white dwarfs (Bauer & Bildsten, 2019). When including thermohaline mixing into the
white dwarf models, larger accretion rates are required in order to account for this instability
(Bauer & Bildsten, 2018). As it disproportionally affects DA white dwarfs, the accretion
rates would need to be orders of magnitude larger for the DA white dwarfs to account for the
thermohaline mixing.
130 Tracing the composition of exoplanetary building blocks
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4.5 Discussion 131
4.4.2 Metal abundances
The photospheric abundances of white dwarfs with circumstellar gas provide crucial informa-
tion regarding the planetary bodies accreted. In this section, it is investigated whether there
are differences in the composition of the planetary bodies accreted by white dwarfs with and
without detectable circumstellar gas which might shed light on their respective histories.
The presence of circumstellar gas may reflect an early stage in the accretion history,
or alternatively, the accretion of larger planetary bodies. Volatiles sublimate in the cooler
regions, further from the star, whilst refractories sublimate close to the star. One could
postulate that preferential production of volatile-rich gas occurs early in the lifetime of a
circumstellar disc. This would be reflected in a volatile-rich photospheric composition. The
abundances of volatile material polluting white dwarfs with and without circumstellar gas
are shown in Fig. 4.10b. Given the small number statistics, there is no preference for the
accretion of volatile rich material for those systems with gaseous discs when compared to
those without gaseous discs.
The lithophilic abundances (Si, Ca, Mg) are compared between those white dwarfs
which show detectable levels of circumstellar gas, and those without, as shown in Fig. 4.10a.
Only white dwarfs with detections of Ca, Mg and Si are plotted, with the addition of
Gaia J0347+1624 from this work which only has measurements of Ca and Mg. The abundance
distribution cannot be explained by invoking a solar or local stellar abundance. The range
of Ca, Mg, Si abundances seen in the atmospheres of white dwarfs with and without gas
detections show similar trends, influenced only by their relative sinking and another process
that enhances Ca relative to Mg. This might be due to the depletion of Mg-rich minerals in
favour of highly refractory-rich minerals, containing Ca, Al, Ti, that would occur if a portion
of the body experienced temperatures higher than ∼1250 K during formation or in the red
giant phase. However, these conclusions, and those discussed above, are limited by small
number statistics and therefore, require further detections of white dwarfs with circumstellar
gaseous discs to be conclusive. Over the coming years surveys such as 4MOST and WEAVE
will discover numerous new polluted white dwarfs with circumstellar gaseous discs, allowing
these conclusions to be revisited in future studies.
4.5 Discussion
This chapter presents the abundances of the planetary material that was accreted by seven
white dwarfs with circumstellar gas and dust, along with interpretation of the observed
compositions in terms of the history of the accreted planetary body. The results reveal
planetary bodies that have accreted material with a large range of volatile contents, from pure
132 Tracing the composition of exoplanetary building blocks
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
[Mg/Ca] - [Mg/Ca]¯
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
[S
i/
C
a]
-
[S
i/
C
a]
¯
Heating
Sinking
H no gas
He no gas
H with Gas
He with Gas
H (this work)
He (this work)
(a)
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
[O/Ca] - [O/Ca]¯
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
[F
e/
C
a]
-
[F
e/
C
a]
¯
Heating
Sinking
CMF
H no gas
He no gas
H with Gas
He with Gas
H (this work)
He (this work)
(b)
Fig. 4.10 (a) Comparison of the [Si/Ca] against [Mg/Ca] composition of the material that
has polluted white dwarfs which have a detectable circumstellar gaseous disc compared to
those without. (b) Comparison of the [Fe/Ca] against [O/Ca] composition. The grey ellipses
show a 1σ , 2σ and 3σ error ellipse based on solar abundances with Ca, Mg and Si errors
of 0.1 dex. If a white dwarf accreted material of solar abundance with typical errors of 0.1
dex, the contours show the distribution of expected abundances. The arrows show how the
abundances are affected by: sinking in the white dwarfs atmosphere, heating of the pollutant
and increasing the core mass fraction (CMF).
4.5 Discussion 133
rock, to rock and water-ice mixtures that are similar to Kuiper belt objects in the solar system.
Evidence is presented for the geological process of core formation, and the accretion of
highly refractory grains onto Gaia J0347+1624. In the following discussions, the robustness
and implications of these conclusions are discussed.
The absolute abundances in the white dwarf photosphere are most affected by uncertain-
ties in the derived stellar parameters, discussed in Section 4.5.1, as well as the quality of the
spectroscopic data and the white dwarf models used to analyse and obtain the abundances.
Crucially, interpretation of the observed compositions, which is based on elemental ratios, are
less affected by uncertainties in the stellar parameters. However, limitations are introduced
by uncertainties in relative sinking of various elements, uncertainties in the modelling of the
atmospheres of white dwarfs, as well as by missing information regarding key species that
evaded detection.
4.5.1 Effects of uncertainties on elemental abundances
In order to determine elemental abundances from the data, a number of systematics must
be considered. Sometimes only one (or few) absorption line(s) of a particular element are
present in the spectrum (see Appendix 2: Tables 7.1 – 7.7 for details). This is especially
important for the five DAZ white dwarfs where there are few metal absorption lines and
they can be weak. Both Gaia J0611−6931 (Section 4.3.4) and Gaia J2100+2122 (Section
4.3.7) have enhanced Fe/Mg abundances, however, each has just one Fe absorption line in the
spectra, adding additional uncertainties to the conclusions. The abundances are also limited
by the white dwarf models, for example, 3D mixing effects such as convection may affect
the derived abundances (Cunningham et al., 2019). It should also be noted that UV-optical
discrepancies in derived abundances have been observed (e.g. Gänsicke et al., 2012; Xu et al.,
2019).
This work corroborates previous studies which identified the differences in deriving
white dwarf parameters from spectral analysis compared to those derived from broad band
photometry. Spectroscopic temperatures can exceed photometric temperatures by 5–10%
above 14,000 K (Genest-Beaulieu & Bergeron, 2019). All white dwarfs in this study fall into
this temperature range, and indeed this is reflected in the derived stellar parameters. The most
accurate white dwarf parameters derived from broad band photometry are those that include
the SDSS ‘u’ band with additional optical photometry, e.g. Pan-STARRS (Bergeron et al.,
2019). Only three of the target white dwarfs have SDSS photometry, and as noted in Section
4.2.1, the photometrically derived parameters for Gaia J0510+2315 and Gaia J2100+2122 are
less reliable due to comparison with GALEX photometry. Therefore, there are significant
systematic uncertainties associated with the stellar parameters. It is likely that a hybrid
134 Tracing the composition of exoplanetary building blocks
approach similar to Izquierdo et al. (2021) may result in improved parameters, however, this
still requires SDSS ‘u’ band data and so is not performed in this study.
The metal abundance uncertainties quoted in Table 4.3 are measurement errors and
do not include systematic errors arising from uncertain white dwarf parameters. Instead
the abundances based on the two sets of stellar parameters are considered. The difference
in temperature and log(g) between the two sets of stellar parameters are between 1000–
3000 K and 0.1–0.25 dex respectively. In order to obtain reliable and accurate absolute
abundances of the accreted planetary material it is crucial to obtain accurate stellar parameters.
However, the relative elemental ratios, which are used to interpret the observed compositions,
are consistent within 1σ between the abundances derived from the spectroscopic stellar
parameters compared with the photometric stellar parameters. The ratios are less sensitive
to the derived stellar parameters. The Bayesian models were run for all the white dwarfs
based on both sets of parameters. For all the white dwarfs, the best-fitting models are the
same between the two sets of parameters. Therefore, until the uncertainties on the absolute
abundances can be reduced, the differences between the photometric and spectroscopic
temperatures and log(g) will not affect the results of the abundance analysis. If absolute
abundances are important, (as when deriving accretion rates), the measurement errors as
well as systematic errors associated with uncertain stellar parameters should be included and
propagated.
4.5.2 Volatiles in exoplanetary systems
This work shows that there is a wide range in volatile content of the planetary material
accreted by the white dwarfs in the sample. Gaia J0510+2315 and Gaia J0611−6931 show
approximately solar levels of oxygen, this is significantly in excess to the oxygen abundance
of bulk Earth. Without an iron detection for Gaia J0510+2315 it is not possible to assess
the true volatile content of the planetary body that was accreted; future UV observations
should detect iron, allowing improved oxygen budgeting calculations. Oxygen budgeting for
Gaia J0611−6931 demonstrated a significant oxygen excess above that which could form
metal oxides as discussed in Section 4.3.4. The accreted body is best explained by a mixture
of rocks and water-ice. This adds to the handful of polluted white dwarf systems discovered
that have accreted water rich bodies (Farihi et al., 2011, 2013; Raddi et al., 2015; Xu et al.,
2017; Hoskin et al., 2020; Klein et al., 2021). On the other hand, Gaia J0347+1624 and
Gaia J0644−0352 (discussed in Sections 4.3.2 and 4.3.5) appear to be accreting bodies that
are dry and rocky, much like asteroids or terrestrial planets in the solar system.
A number of uncertainties affect the conclusions drawn here. To determine the oxygen ex-
cess, the oxygen was assigned to Fe, Ca, Al, Si and Mg; but not all the rock forming elements
4.5 Discussion 135
are detected. Al has a low abundance, and therefore the absence of Al for Gaia J0611−6931
is unlikely to influence the oxygen budget. It should be noted that the quantity of the oxygen
excesses and therefore water fraction of the body is uncertain. This is largely due to the fact
that the form of iron is unknown. Fe could be in the form of FeO, Fe2O3, or metallic Fe. The
latter is especially important for Gaia J0611−6931 given that the most likely composition of
this body was core rich, so it is probable that a significant fraction of the Fe would be in the
form of metallic Fe. Therefore, the fraction of excess oxygen that could have been in the form
of water may be as high as 0.8 if all Fe were in the form of metallic Fe. This is equivalent
to accreting a body with 37% water by mass. The conclusion regarding Gaia J0611−6931
accreting a volatile rich planetary body appears robust.
Gaia J0611−6931 accreting a volatile rich body demonstrates that volatiles can survive
stellar evolution to the white dwarf phase. The fact that the sample of white dwarfs is
accreting material with a wide range of volatile content implies that they are accreting
material from a wide range of radial locations. Terrestrial planets are thought to form
within the ice lines of volatile elements, and therefore form primarily dry. However, the
Earth contains more volatiles than would be expected based on a formation distance of 1 au.
Although various mechanisms that could deliver water early have been proposed, studies of
the composition of the forming core and mantle over time demonstrated that the Earth was
initially reduced and accreted volatiles later (Wood et al., 2008; Rubie et al., 2011). Volatiles
delivered later by planetesimals originating past the snow lines and destabilised by Jupiter
and Saturn are one potential pathway for water delivery to Earth (Morbidelli et al., 2000,
2012; Raymond & Izidoro, 2017). Discovery of water-rich planetesimals in other planetary
systems is important as it informs us that volatile rich bodies can survive formation and
subsequent evolution, and can deliver volatiles to planetary systems as late as in the white
dwarf phase. Additional discoveries of water rich planetary bodies across the Milky Way can
be linked to questions regarding extra-terrestrial life.
4.5.3 Evidence for the accretion of multiple bodies?
The simplest possible assumption to make is that the planetary material currently in the
atmosphere of the white dwarf represents a single body, which is the assumption used
throughout this work. However, if white dwarfs are polluted by many small asteroids (Jura,
2008), it is possible that currently, or historically, any given white dwarf may contain material
from multiple planetary bodies. Also, models often assume that the bodies accreted are from
the same planetesimal reservoir around the white dwarf.
Gaia J0611−6931 is accreting material that is both enhanced in Fe and O, as discussed
in Section 4.3.4. This white dwarf may be accreting material from two bodies: one that is
136 Tracing the composition of exoplanetary building blocks
enhanced in Fe and is a fragment of a core rich body, and the other enhanced in O and is
a fragment of a water-rich body. When a planetary body undergoes large-scale melting to
produce an iron-rich core, in general, temperatures are sufficiently high that volatiles, such
as water, are lost (Lichtenberg et al., 2019). Unless the body was particularly large such that
volatiles are retained in an atmosphere, or it accreted a substantial population of icy pebbles
long after cooling, it is more difficult for a single planetary body to be both core-mantle
differentiated and icy.
Gaia J0644−0352 is accreting dry, volatile depleted material, however, trace hydrogen is
detected and there could be multiple origins. Hydrogen can be accreted from the ISM, be
primordial and remain after stellar evolution or it could be interpreted as the accretion of
water-rich material (Gentile Fusillo et al., 2017), which could have occurred at any point in
its history as the hydrogen would stay on the surface of the white dwarf. If this hydrogen is
truly from the accretion of a volatile-rich body in its past and isn’t due to ISM accretion or
is primordial, then the current abundance is conflicting. As Gaia J0644−0352 is currently
accreting volatile depleted material inferred from the heavy elements, but in the past may have
accreted volatile rich material, this implies that it is accreting material from a wide range of
radial locations. It is highly unlikely that the current pollutant material for Gaia J0644−0352
contains significant water as oxygen budgeting reveals the heavy elements balance the oxygen
and all oxygen can be in the form of metal oxides (see Fig. 4.5). This is a robust conclusion
as all major rock-forming elements are detected, with between three and 11 spectral lines
being used to determine the average abundance for each element. If this white dwarf did
accrete a water-rich planetesimal, it did so when it was much younger, with the hydrogen
remaining on the surface.
Evidence for the accretion of multiple bodies would be exciting support for the widely
supported theory of the accretion of many small asteroids leading to white dwarf pollution
(Turner & Wyatt, 2020). The diverse compositions in these bodies indicate that in a single
system, planetary bodies can arrive onto the star from a wide range of radial locations in the
planetary system. This has implications for scattering models used to explain how bodies
get perturbed onto star grazing orbits, as there must be mechanisms which can stochastically
scatter bodies from a wide range of orbits.
4.5.4 Are high Ca/Mg ratios explained by the accretion of a high pro-
portion of refractory material?
Gaia J0347+1624 is accreting material with one of the highest Ca/Mg ratios observed, higher
than even GD 362 (Jura & Xu, 2012). The accretion of material with high Ca/Mg could
4.5 Discussion 137
be explained by the depletion of moderately volatile species, including Si, Mg and Fe-rich
minerals, occurring at temperatures greater than 1250 K. Neither sinking nor geological pro-
cessing can explain the high Ca/Mg abundance. In order to explain the observed abundances,
it is hypothesised that a portion of the accreted body experienced temperatures higher than
1550±20 K during formation in the inner region of the disc, much like CAIs in the solar
system, or during the red giant phase of stellar evolution.
The temperature of the circumstellar dust around Gaia J0347+1624 when modelled by a
single blackbody is 1760 K (Dennihy et al., 2020), the hottest dust surrounding any white
dwarf with detectable circumstellar gas and dust. Fig. 4.9 shows how the Ca/Mg abundance
ratio of the accreted planetary material relates to the blackbody dust temperature for white
dwarfs in this study and from the literature (Dennihy et al., 2020; Rocchetto et al., 2015);
there is a weak correlation between dust temperature and Ca/Mg ratio. The material accreting
onto Gaia J0347+1624 is depleted in Mg-rich moderate volatiles, explaining the extreme
Ca/Mg abundance, and so Gaia J0347+1624 is accreting refractory rich dust. This refractory
rich dust can survive to hotter temperatures around the white dwarf explaining why the dust
temperature is so extreme.
For Gaia J0347+1624, the conclusion is based on the abundance determination of two
elements, where only one or two lines per element are present in the spectrum. Also, no
optical spectrum is available red-ward of 6000 Å so no assessment can be made regarding
more volatile species such as oxygen or sodium. It is vital to obtain follow up data to
investigate the volatiles for this intriguing system.
4.5.5 Evidence for the formation of iron cores in exoplanetary systems
The high (low) Fe abundances relative to lithophile species (Ca, Mg, Si) are best explained by
the accretion of a fragment that is dominated by core (mantle) material, potentially produced
in a destructive collision of a larger body. Within the sample there is evidence for the
accretion of core rich (Gaia J0611−6931 and Gaia J2100+2122) and possibly mantle rich
(Gaia J0644−0352) exoplanetary fragments.
For Gaia J2100+2122 and Gaia J0611−6931, these conclusions are based on the enhanced
iron in comparison to solar abundance. However, it is important to note that only one iron
line was detected for each white dwarf, the 5169 Å line in Gaia J0611−6931 and the 3227 Å
line in Gaia J2100+2122 (see Section 4.5.1). Both detections lie above solar to a significance
of > 3σ , however, the true iron abundance may be different from that derived here. In
terms of composition analysis, it is difficult to explain enhanced iron in any way other than
invoking the accretion of a core-rich exoplanetary body. The maximum uncertainty for a
DA white dwarf that has multiple detected lines of a particular element is 0.19 (see Table
138 Tracing the composition of exoplanetary building blocks
4.3). The results are tested by including an uncertainty of 0.19 on the Fe abundance in the
Bayesian models; the Fe is still significantly enhanced and differentiation is required, albeit
to less significance. Upper limits for other elements are included (e.g. Cr and Ni), these
are in agreement with the conclusions regarding the accretion of a core-rich fragment. For
Gaia J0644−0352, on the other hand, whilst the accretion of a mantle-rich fragment is a
good model for the data, as discussed in Section 4.3.5, there is insufficient evidence to rule
out alternate explanations. A Ni or Cr detection might support the mantle-rich nature of the
material (Harrison et al., 2018; Buchan et al., 2022).
The evidence for the accretion of up to three core-mantle differentiated fragments pre-
sented in this work indicates that core-mantle differentiation in exoplanetary systems is
commonplace, as are the large destructive collisions required in these planetary systems to
produce the observed fragments. Planetesimal belts are collisional systems, as witnessed by
debris disc observations (e.g. Wyatt, 2021). This implies that during the post main sequence
phase either massive planetesimal belts must be present, or there are high levels of collisional
excitation, or both.
In the solar system, large-scale melting in asteroids is fueled by the decay of short-lived
radioactive nuclides including 26Al, as they are not massive enough to generate heat via
gravitational potential energy (Urey, 1955; Elkins-Tanton et al., 2011). If the total mass of
an accreted body is of asteroid-size, then differentiation requires the presence of a sufficient
complement of short-lived radioactive nuclides such as 26Al. The budget of short-lived
radioactive nuclides across exoplanetary systems is unclear, with estimates ranging from
suggestions that the solar system level abundances of 26Al are very rare, accounting for ∼ 1%
of systems (Gounelle, 2015), to suggestions that solar system levels of 26Al are common
(Young, 2016). If the bodies accreted by white dwarfs are truly asteroid size, as indicated
by the typical accretion rates observed, this would provide evidence that planetary systems
enriched in short-lived radioactive nuclides are common. If the planetesimals that act as
planet building blocks undergo large-scale melting and form iron cores it can inform planet
formation models and in particular their volatile content, as differentiation has implications
for how rocky exoplanets form.
4.5.6 Magnetic field of WD 1622+587
The first magnetic white dwarf was discovered in 1970 (Kemp et al., 1970), and since then
several hundred magnetic white dwarfs have been discovered from observations of Zeeman
splitting of absorption lines or by spectropolarimetry (see references in Kepler et al., 2021)).
However, there are few examples of magnetic white dwarfs with atmospheric pollution
and circumstellar dust and gas, and especially the absence of magnetic fields around hotter
4.6 Conclusions 139
polluted white dwarfs (>10,000 K) (Kawka & Vennes, 2014; Kawka et al., 2019; Ferrario
et al., 2015; Hollands et al., 2015). WD 1622+587 is a hot DBZA white dwarf which possibly
has a weak magnetic field of ∼10 kG. Schreiber et al. (2021) explains the high rate of weak
magnetic fields in old metal polluted white dwarfs by beginning crystallisation of the cores.
The hottest magnetic polluted white dwarf in their sample, WD 2105−820 (T∼11000 K)
was explained as being massive enough that the crystallisation begins at hotter temperatures.
However, at ∼18850 K and with a mass of ∼0.5 M⊙, this explanation would not be valid
for WD 1622+587. The magnetic field hypothesised here is weak, so a higher resolution
spectrograph would be required to fully resolve the Zeeman splitting components of the lines
and confirm the magnetic field. It should be noted that previous surveys have not had the
sensitivity or resolution to probe magnetic fields down to 10 kG for polluted white dwarfs,
and so it is likely that further hot polluted white dwarfs with magnetic fields are yet to be
discovered.
Hogg et al. (2021) suggests that magnetic white dwarfs should circularise circumstellar
dust faster due to magnetic drag forces. The disc lifetime is also decreased, for optically thick
discs this occurs >∼10 kG and for optically thin discs this occurs > 100 kG, a more thorough
understanding of the structure and lifetime of the circumstellar disc of WD 1622+587 could
help to disentangle whether the discs are predominantly optically thick or thin. Hogg et al.
(2021) modelled a 10,000 K white dwarf and found that the dominant drag force on the dust
changes between PR drag and magnetic drag at around 10 kG. WD 1622+587 is much hotter
than 10,000 K, and as diametric drag dominance scales with inverse temperature squared, it
will dominate out to a smaller radii. This would be within the sublimation radii of the white
dwarf, and so it isn’t expected that magnetic drag will dominate at the tidal disruption radius.
Assuming the dust is optically thick, order of magnitude calculations reveal that PR drag
accretion rates are broadly consistent with the accretion rate derived for WD 1622+587 in
this work (Rafikov, 2011b), so given the current data, this system doesn’t show evidence for
enhanced accretion above that from PR drag. WD 1622+587 with a hypothesised magnetic
field of ∼ 10 kG is an interesting case for further study on the nature of white dwarf debris
discs, and the relation between magnetic drag and accretion rates.
4.6 Conclusions
This work presents X-shooter/VLT, HIRES/KECK and MIKE/Magellan optical spectroscopy
of seven polluted white dwarfs that host both detectable circumstellar gas and dust emission.
Calcium, and at least one other element is detected in the photosphere of each white dwarf,
with the most elements detected in the atmosphere of Gaia J0644−0352 (O, Mg, Al, Si, Ca,
140 Tracing the composition of exoplanetary building blocks
Ti, Cr, Fe). The observations inform processes that determine the composition of exoplanetary
material, including volatile loss and core formation. The key findings are as follows:
• White dwarfs accrete planetary bodies with a range of volatile contents from dry, rocky
bodies to water-rich bodies. Across the seven white dwarfs observed here, the accreted
planetary material has experienced a range of temperatures, as indicated by different
levels of volatile depletion observed. Planetary bodies can be perturbed onto white
dwarfs from a wide range of locations across exoplanetary systems, with no particular
preference for close-in orbits.
• White dwarfs with circumstellar gas are good targets for studying photospheric abun-
dances. Not only do they accrete at high levels, yielding many detectable elements, but
the distribution of accreted abundances is consistent with systems without detectable
gas.
• Generally, Ca, Mg and Si abundances in the accreted material can be explained by
relative sinking rates, but the accretion of highly refractory (Ca, Al-rich) material
provides a plausible explanation to explain the high Ca/Mg of some white dwarfs.
• Gaia J0611−6931 has a high oxygen abundance in comparison to bulk Earth. Oxygen
budgeting revealed it has likely accreted a water-rich body, potentially originating from
the outer regions of the surviving planetary system.
• The material accreted by Gaia J0611−6931 appears to be both water-rich, and core-rich.
Gaia J0644−0352 shows evidence for currently accreting a dry, rocky, body but, in the
past, having accreted at least one water-rich body. Both these indicate that multiple
bodies, from different radial locations, have been accreted by these white dwarfs.
• To explain its broad spectral lines, WD 1622+587 must have a magnetic field of at least
10 kG. This is the first ‘hot’ polluted white dwarf with a detected magnetic field and
circumstellar gas and dust.
Chapter 5
Conclusions and Future Work
5.1 Conclusions
As we transition to an era where exoplanets are the norm rather than the exception, charac-
terising and understand exoplanets is crucial. This thesis focused on white dwarfs polluted
with planetary material as they are powerful laboratories to study the bulk composition of
exoplanets, the architecture and evolution of planetary systems, and ultimately reveal the
eventual fate of the solar system.
Dust provides crucial information regarding how planetary material arrives into the
atmosphere of the white dwarfs. A growing number of observations reveal a shifting
paradigm away from the flat, opaque disc (Jura, 2003), where PR drag causes the material to
migrate inwards, sublimate, and accrete onto the white dwarf. Dust variability can reveal
information about the optical depth and geometry of the circumstellar dust. Therefore,
it is crucial to determine how frequently variability is within the population and at what
wavelengths this variability is dominant. The first dust variability was reported in Xu &
Jura (2014) where a 35 percent mid-infrared, and 18.5 percent near-infrared flux drop was
observed. Motivated by this, a large near-infrared JHK monitoring campaign was conducted
using the WFCAM/UKIRT sampling ∼ 80 percent of the known white dwarfs with dust
emission at the time across a time span of 3 years (as reported in Chapter 2). Surprisingly,
no statistically significant variation is found in the dust emission in all three near-infrared
bands. Specifically, variability at ∼ 1.3% was ruled out for the 13 white dwarfs brighter
than 16th mag in K band, and at ∼ 10% for the 32 white dwarfs brighter than 18th mag over
time-scales of three years. As the dust emission is stronger at 3–4 µm, some systems do not
have strong K band emission; for those with significant K band excesses, any white dwarf
with a similar large amplitude (> 18.5%) near-infrared variability from Xu & Jura (2014) on
short (< 3 year) time-scales should have been found with the survey. Additionally, a small
142 Conclusions and Future Work
near-infrared monitoring campaign using the SOFI/NTT ruled out K band variability over
timescales of hours–days for a sample of eight white dwarfs with dust emission, therefore,
dust variability that leads to K band variability is consequently rare.
Contradictory to the near-infrared monitoring campaigns finding no variability, Swan
et al. (2019a, 2020) found that most white dwarfs with infrared excesses show significant
variability in the mid-infrared. If the emission of the dust in the near and mid infrared is
dominated by the distance from the star rather than grain size, then the K band represents
the closest in (<0.001 AU), hottest dust and the mid-infrared represents the further out,
cooler dust. The cooler dust is experiencing dynamic and large variability events, but once
the dust reaches the inner hot disc there is no variability. One hypothesis is that the outer
disc is dominated by optically thin dust, where destructive collisions and/or tidal disruption
events are occurring, therefore, explaining the extreme mid-infrared variability. As the dust
collisionally grinds down and migrates via PR drag to the inner disc, physical processes are
acting to stabilise the dust resulting in no K band variability. The inner disc may therefore
be an optically thick, razor thin disc, and this can explain accretion rates up to 108 g. The
two white dwarfs that have previously displayed K band variability, WD J0959−0200 and
WD 1226+110, have circumstellar gas emission in additional to dust emission. If the gas is
produced in the most violent collisions then this could be mimicked in the K band, predicting
that K band variability would only be found in those systems with detectable levels of
circumstellar gas.
Theory maintains that once this material arrives in the atmosphere of the white dwarf, the
material should sink to the core (where it is not observable) on incredibly short timescales,
from days to weeks for Hydrogen dominated white dwarfs (Koester, 2009). Chapter 3
reports the optical spectroscopic monitoring campaigns that were conducted for five DAZ
white dwarfs with HRS/SALT and MIKE/Magellan over a total baseline of ∼ 14 years.
The equivalent widths of the metal absorption lines were calculated; for four of the five
white dwarfs no statistically significant variation in the equivalent widths were observed.
For one of the white dwarfs, WD 0106−328, these data were inconclusive. Therefore, no
unambiguous change in the amount of material present in the white dwarf photosphere
and therefore accretion rate was observed. This implies that either the processes which
maintain the accretion of the planetary material are surprisingly stable, or there are unknown
mechanisms in the white dwarf photospheres that are acting to increase the sinking timescales
and therefore result in no variability.
Combining the results from Chapter 2 on the near-infrared monitoring, and Chapter 3 on
the metal line monitoring, inferences can be made about the accretion disc of metallic gas.
Although theory predicts this accretion disc as a vessel for the accretion of material from
5.1 Conclusions 143
the circumstellar dust disc to the atmosphere, it has not been observed. Chapter 3 reports
no change in the amount of material present in the atmosphere of the white dwarf implying
the accretion rate onto the white dwarf is constant. If the hypothesis of the inner disc being
stable is true, as inferred from the near infrared monitoring in Chapter 2, it predicts that the
material leaves the dust disc and arrives in the atmosphere at a constant rate and the accretion
disc just acts as a vessel for the accretion. However, if this hypothesis is incorrect and the
entire dust disc is dynamic and variable (with variability hidden from K band studies), then
the metallic accretion disc must be acting to dampen out dust variability via gas viscosity for
it to arrive in the atmosphere at a constant rate.
Previous works have argued that gas drag may cause enhanced accretion rates above
what may be expected from PR drag alone (e.g. Rafikov, 2011a). If this is the case, and
the gaseous emission is higher at the same radial location as the dust, then white dwarfs
with circumstellar gaseous discs should be accreting at higher levels in comparison to the
population. Chapter 4 reports the accretion rates of the bodies accreting onto white dwarfs
with circumstellar gas discs. The range of accretion rates of those systems with gaseous discs
spans a similar range to those without, with both high accretors and low accretors. These
results hint that the presence of gas does not affect the accretion rate, however, due to small
number statistics, definitive conclusions are impossible.
As more polluted white dwarfs are discovered with Gaia and large spectroscopic surveys,
it is crucial to ensure that the most promising systems are followed up with high resolution
spectroscopy such that in depth studies of the pollutant composition and geological history
can be studied. We are transitioning to an era of population statistics, and it is imperative to
include these highly polluted white dwarfs in the statistics. Chapter 4 reports abundances
for the exoplanetary material that were accreted by seven white dwarfs which all have
circumstellar gaseous discs. Circumstellar dust and gas around white dwarfs tell us about
the current, potentially violent accretion of planetary material. These systems are extreme
examples of polluted white dwarfs, and as such they are perfect targets for studying high
levels of pollution in their atmospheres. These white dwarfs with gas discs all reveal
multiple detected elements from ground based optical spectroscopy. Solar system material
appears commonplace in exoplanetary systems as all but one of the white dwarfs has an
equivalent composition within the solar system. Gaia J0006+2858 and WD 1622+587 have
refractory compositions close to that of bulk Earth. Gaia J0644−0352 and Gaia J2100+2122
have compositions consistent with accreting material similar to Earth’s mantle and core
respectively. Core-mantle differentiation with an iron rich core and iron poor mantle, and
disruptive collisions appear commonplace in exoplanetary systems, agreeing with previous
findings (e.g. Bonsor et al., 2020). Gaia J0510+2315 is accreting a rocky body enhanced
144 Conclusions and Future Work
in volatiles similar to volatile-rich bodies in the Kuiper-belt. Gaia J0347+1624 is refractory
rich with a [Ca/Mg] of 0.09, few white dwarfs have such extreme [Ca/Mg] ratios (Jura &
Xu, 2012), in the solar system CAI’s have even more extreme [Ca/Mg] ratios, these formed
in the inner regions of the solar system during formation under high temperatures. The
high [Ca/Mg] may also explain the high blackbody temperature of its dust emission as these
refractory grains can survive closer in to the white dwarf. Gaia J0611−6931 appears to be
both core-rich and water-rich with abundances that don’t fit with bulk abundances of a single
body in the solar system.
Gaia J0510+2315 and Gaia J0611−6931 have swallowed a body with exceptionally high
oxygen in comparison to bulk Earth, these bodies were likely rich in water. This adds to the
handful of other white dwarfs which also show evidence for the accretion of volatile-rich
exoplanetary material. The discovery of water-rich planetesimals in other planetary systems
is crucial as it informs us that volatile rich bodies can survive formation, and subsequent
evolution, and can deliver volatiles to planetary systems as late as in the white dwarf phase.
For the Earth, volatiles are crucial for life, but it is hypothesised that the Earth formed dry
and accreted volatiles later. Additional discoveries of water rich planetary bodies across the
Milky Way, can be linked to questions regarding terrestrial and extra-terrestrial life.
When analysing the abundances of the body that was accreted by the white dwarf, it
is assumed to be a single body accreting from one reservoir of planetesimals. However,
Chapter 4 highlights two examples where this may not be the case. The material accreted
by Gaia J0611−6931 appears to be both water-rich, and core-rich. Gaia J0644−0352 shows
evidence for currently accreting a dry, rocky, body but in the past having accreted at least one
water-rich body. These findings indicate that it is likely that the assumption of a single body
being accreted by the white dwarf is incorrect for some systems, providing evidence for the
predicted accretion of many smaller bodies with high probabilities of observing multiple
bodies in the white dwarf at any one time (e.g. Turner & Wyatt, 2020). Also, as both white
dwarfs may be accreting bodies from different radial locations, this can give an insight into
the architecture of these exoplanetary systems. In depth modelling which can perturb bodies
from both the inner and outer system towards the white dwarf are required to explain these
observations.
5.2 Future Work
Dust emission
The discovery of ubiquitous mid-IR variability with Spitzer (Swan et al., 2020) was shortly
followed by operations ending in January 2020. No telescope will have the resolution and
5.2 Future Work 145
capabilities to perform a large mid-infrared monitoring campaign of white dwarfs with
circumstellar dust on short cadences. neoWISE will continue to survey the sky in the mid-
infrared with a cadence of 6 months, due to the large pixel sizes further high resolution
imaging is needed to rule out contaminants in the field of view. Nonetheless, for those systems
that are already known to be free from contaminants, neoWISE will be a useful resource
to continue variability searches. As the near-infrared is accessible with ground based high
resolution imaging instruments, large monitoring campaigns using the near-infrared are more
technically feasible. The two white dwarfs which have previously shown K band variability
(WD J0959−0200 and WD 1226+110) had observations separated by 7–8 years (although
it should be noted no intermittent observations were conducted). Therefore, following up
the targets with the most significant K band excesses on decade long timescales will provide
useful insight into whether K band variability is the norm or the exception. Also, targeting
systems with known gaseous emission discs may reveal whether K band variability only
occurs when the most violent collisions occur. In order to understand the link between the
near and mid infrared, and what this means about the distribution, temperature, and grain size
of the dust, it is crucial to obtain mid-infrared spectroscopy and perform in depth modelling
of the dust. The JWST MIRI instrument spans a wavelength range of 5–28.5µm covering
a large number of dust mineralogy features, allowing in depth studies of the circumstellar
dust. It will be particularly useful to obtain dust mineralogy for those systems with both
circumstellar dust and gas discs as the planetary material can be compared between the
dust, gas and the pollution. Gaia J0611−6931 is a particularly good target for this as it
has the most elements detected in emission in a gaseous disc, and it is heavily polluted.
Recent COS/Hubble UV spectra (PI: Rogers) of Gaia J0611−6931 have revealed a myriad
of pollution lines allowing further in depth analysis into the composition of the pollutant.
Monitoring metal lines
No unambiguous variability was found in the amount of material present in the photospheres
of five DAZ white dwarfs over timescales of > 10 years. In order to conclusively deter-
mine whether the equivalent width of the Mg II doublet varied in WD 0106−328, follow-up
MIKE/Magellan data is required. Theoretical efforts must be dedicated to resolving the accre-
tion and diffusion processes to explain the lack of variability considering diffusion timescales
of days. For example, further investigations into mixing processes in the photosphere of white
dwarfs. Recent X-ray observations of G29-38 revealed the X-ray luminosity and therefore in-
stantaneous accretion rate of material onto the white dwarf, independent of stellar atmosphere
models (Cunningham et al., 2022). The X-ray observations were taken between 22 and 27
September 2020, optical ground based spectra from HRS/SALT of G29-38 were obtained
146 Conclusions and Future Work
two weeks before, and one month after (as reported in Chapter 3). The sinking timescales for
G29-38 are of the order of 2–3 months, therefore, no changes should be expected between the
photosphere as measured by HRS/SALT and at the time of the X-ray observations. Therefore,
these spectra can be used to investigate the link between instantaneous accretion rates and
the accretion rates inferred from the photosphere. Follow-up X-ray observations of G29-38
may be more fruitful to investigate whether there is variability in the instantaneous accretion
rate, as this is independent of atmospheric models.
Increase the number of well studied polluted white dwarfs.
With > 350,000 white dwarfs discovered with Gaia eDR3 (Gentile Fusillo et al., 2021) and
large spectroscopic follow-up surveys (e.g. 4MOST, WEAVE, DESI, SDSS-V), thousands
of new polluted white dwarfs will be discovered. It is crucial that once identified, the
most promising polluted white dwarfs are followed up with high resolution ground-based
spectrographs, and space-based UV spectrographs to ensure the new polluted white dwarfs
are well studied and characterised. With increased numbers of polluted white dwarfs,
unbiased samples can be created such that the bulk composition of exoplanets, and their
distribution across the galaxy, can be well studied. Currently, there are only 19 systems
with detections or stringent upper limits of C and O, 42 systems are required in order to
distinguish the distribution of these volatiles across exoplanets. Future Hubble observations
in the upcoming cycle (PI: Rogers) will reach this number. Also, as mentioned previously,
there are insufficient numbers of white dwarfs with detectable gas discs, and especially those
with derived abundances for multiple elements. To conclusively discover whether white
dwarfs with circumstellar gas have enhanced accretion rates due to gas drag, the number of
gas systems discovered and characterised needs to be at least doubled. With upcoming large
spectroscopic surveys, this number will drastically increase.
References
Adams F. C., Laughlin G., 1997, Reviews of Modern Physics, 69, 337
Alexander C. M., McKeegan K. D., Altwegg K., 2018, Space science reviews, 214, 1
Armstrong B., 1967, Journal of Quantitative Spectroscopy and Radiative Transfer, 7, 61
Ballhaus C., et al., 2013, EPSL, 362, 237
Barber S. D., Kilic M., Brown W. R., Gianninas A., 2014, ApJ, 786, 77
Barnes S., et al., 2008, in Ground-based and Airborne Instrumentation for Astronomy II. pp
247–258
Barstow M. A., Barstow J., Casewell S., Holberg J., Hubeny I., 2014, MNRAS, 440, 1607
Batalha N. M., 2014, Proceedings of the National Academy of Sciences, 111, 12647
Bauer E. B., Bildsten L., 2018, ApJL, 859, L19
Bauer E. B., Bildsten L., 2019, ApJ, 872, 96
Becklin E., Farihi J., Jura M., Song I., Weinberger A., Zuckerman B., 2005, ApJL, 632, L119
Belardi C., Kilic M., Munn J. A., Gianninas A., Barber S. D., Dey A., Stetson P. B., 2016,
MNRAS, 462, 2506
Bergeron P., Saffer R. A., Liebert J., 1992, ApJ, 394, 228
Bergeron P., Wesemael F., Dufour P., Beauchamp A., Hunter C., et al., 2011, ApJ, 737, 28
Bergeron P., Dufour P., Fontaine G., Coutu S., Blouin S., Genest-Beaulieu C., Bédard A.,
Rolland B., 2019, ApJ, 876, 67
Bergfors C., Farihi J., Dufour P., Rocchetto M., 2014, MNRAS, 444, 2147
Bernstein R., Shectman S. A., Gunnels S. M., Mochnacki S., Athey A. E., 2003, in Instrument
Design and Performance for Optical/Infrared Ground-based Telescopes. pp 1694–1704
Bizzarro M., Connelly J. N., Krot A. N., 2017, in , Formation, evolution, and dynamics of
young solar systems. Springer, pp 161–195
Blackman J., et al., 2021, Nature, 598, 272
148 References
Bonsor A., Wyatt M., 2010, MNRAS, 409, 1631
Bonsor A., Mustill A., Wyatt M. C., 2011, MNRAS, 414, 930
Bonsor A., Farihi J., Wyatt M. C., van Lieshout R., 2017, MNRAS, 468, 154
Bonsor A., Carter P. J., Hollands M., Gänsicke B. T., Leinhardt Z., Harrison J. H., 2020,
MNRAS, 492, 2683
Borucki W. J., et al., 2010, Science, 327, 977
Brahic A., 1977, A&A, 54, 895
Brewer J. M., Fischer D. A., 2016, ApJ, 831, 20
Brinkworth C., Gänsicke B. T., Marsh T., Hoard D. W., Tappert C., 2009, ApJ, 696, 1402
Brinkworth C., Gänsicke B., Girven J., Hoard D., Marsh T., Parsons S., Koester D., 2012,
ApJ, 750, 86
Brouwers M. G., Bonsor A., Malamud U., 2022, MNRAS, 509, 2404
Brown J. C., Veras D., Gänsicke B. T., 2017, MNRAS, 468, 1575
Brown A., Vallenari A., Prusti T., De Bruijne J., Babusiaux C., Bailer-Jones C., Biermann
M., et al., 2018, A & A, 616, A1
Buchan A. M., Bonsor A., Shorttle O., Wade J., Harrison J., Noack L., Koester D., 2022,
MNRAS, 510, 3512
Budde G., Burkhardt C., Brennecka G. A., Fischer-Gödde M., Kruijer T. S., Kleine T., 2016,
EPSL, 454, 293
Burns J. A., Lamy P. L., Soter S., 1979, Icarus, 40, 1
Carpenter J. M., 2001, AJ, 121, 2851
Carroll B. W., Ostlie D. A., 2017, An introduction to modern astrophysics. Cambridge
University Press
Cassan A., et al., 2012, Nature, 481, 167
Charbonneau D., Brown T. M., Latham D. W., Mayor M., 1999, ApJ, 529, L45
Chayer P., Fontaine G., Wesemael F., 1995a, ApJS, 99, 189
Chayer P., Vennes S., Pradhan A., Thejll P., Beauchamp A., Fontaine G., Wesemael F., 1995b,
ApJ, 454, 429
Chu Y.-H., et al., 2011, AJ, 142, 75
Collaboration G., et al., 2016, arXiv preprint arXiv:1609.04153
Collaboration G., et al., 2022, A & A
References 149
Connelly J. N., Bizzarro M., Krot A. N., Nordlund Å., Wielandt D., Ivanova M. A., 2012,
Science, 338, 651
Coutu S., Dufour P., Bergeron P., Blouin S., Loranger E., Allard N., Dunlap B., 2019, ApJ,
885, 74
Crossfield I. J., 2015, PASP, 127, 941
Cunningham T., Tremblay P.-E., Freytag B., Ludwig H.-G., Koester D., 2019, MNRAS, 488,
2503
Cunningham T., et al., 2021, MNRAS, 503, 1646
Cunningham T., Wheatley P. J., Tremblay P.-E., Gänsicke B. T., King G. W., Toloza O., Veras
D., 2022, Nature, 602, 219
Davidsson B. J., 1999, Icarus, 142, 525
Debes J. H., López-Morales M., 2008, ApJ, 677, L43
Debes J. H., Sigurdsson S., 2002, ApJ, 572, 556
Debes J. H., Hoard D., Wachter S., Leisawitz D. T., Cohen M., 2011, ApJS, 197, 38
Debes J. H., Walsh K. J., Stark C., 2012a, ApJ, 747, 148
Debes J., Kilic M., Faedi F., Shkolnik E., Lopez-Morales M., Weinberger A., Slesnick C.,
West R. G., 2012b, ApJ, 754, 59
Dennihy E., Debes J. H., Dunlap B., Dufour P., Teske J. K., Clemens J., 2016, ApJ, 831, 31
Dennihy E., Clemens J., Debes J. H., Dunlap B., Kilkenny D., O’Brien P., Fuchs J., 2017,
ApJ, 849, 77
Dennihy E., Clemens J., Dunlap B., Fanale S., Fuchs J., Hermes J., 2018, ApJ, 854, 40
Dennihy E., et al., 2020, arXiv preprint arXiv:2010.03693
Dones L., 1991, Icarus, 92, 194
Dorn C., Khan A., Heng K., Connolly J. A., Alibert Y., Benz W., Tackley P., 2015, Astronomy
& Astrophysics, 577, A83
Doyle A. E., Young E. D., Klein B., Zuckerman B., Schlichting H. E., 2019, Science, 366,
356
Dufour P., Kilic M., Fontaine G., Bergeron P., Melis C., Bochanski J., 2012, ApJ, 749, 6
Dufour P., et al., 2015, in Astron. Soc. Pac. Conf. Ser. p. 37
Dufour P., Blouin S., Coutu S., Fortin-Archambault M., Thibeault C., Bergeron P., Fontaine
G., 2017, ASPC, 509, 3
Dupuis J., Fontaine G., Wesemael F., 1993, ApJS, 87, 345
150 References
Dye S., Warren S., Hambly N., Cross N., Hodgkin S., Irwin M., Lawrence A., et al., 2006,
MNRAS, 372, 1227
Eisenstein D. J., et al., 2006, ApJS, 167, 40
Elkins-Tanton L. T., 2012, Annual Review of EPS, 40, 2012
Elkins-Tanton L. T., Weiss B. P., Zuber M. T., 2011, EPSL, 305, 1
Farihi J., Zuckerman B., Becklin E., 2008, ApJ, 674, 431
Farihi J., Jura M., Zuckerman B., 2009, ApJ, 694, 805
Farihi J., Barstow M., Redfield S., Dufour P., Hambly N., 2010a, MNRAS, 404, 2123
Farihi J., Jura M., Lee J.-E., Zuckerman B., 2010b, ApJ, 714, 1386
Farihi J., Brinkworth C., Gänsicke B., Marsh T., Girven J., Hoard D., Klein B., Koester D.,
2011, ApJL, 728, L8
Farihi J., Gänsicke B., Steele P., Girven J., Burleigh M., Breedt E., Koester D., 2012a,
MNRAS, 421, 1635
Farihi J., Gänsicke B., Wyatt M., Girven J., Pringle J., King A., 2012b, MNRAS, 424, 464
Farihi J., Gänsicke B., Koester D., 2013, Science, 342, 218
Farihi J., Wyatt M., Greaves J., Bonsor A., Sibthorpe B., Panic´ O., 2014, MNRAS, 444, 1821
Farihi J., Parsons S., Gänsicke B., 2017, Nature Astronomy, 1, 0032
Farihi J., van Lieshout R., Cauley P., Dennihy E., Su K., Kenyon S., et al., 2018, MNRAS,
481, 2601
Ferrario L., de Martino D., Gänsicke B. T., 2015, Space Science Reviews, 191, 111
Fischer D. A., Howard A. W., Laughlin G. P., Macintosh B., Mahadevan S., Sahlmann J.,
Yee J. C., 2015, arXiv preprint arXiv:1505.06869
Fontaine G., Michaud G., 1979, ApJ, 231, 826
Fontaine G., Brassard P., Bergeron P., 2001, PASP, 113, 409
Freudling W., Romaniello M., Bramich D. M., Ballester P., Forchi V., García-Dabló C. E.,
Moehler S., Neeser M. J., 2013, , 559, A96
Gänsicke B. T., Marsh T., Southworth J., Rebassa-Mansergas A., 2006, Science, 314, 1908
Gänsicke B., Marsh T., Southworth J., 2007, MNRAS:L, 380, L35
Gänsicke B., Koester D., Marsh T., Rebassa-Mansergas A., Southworth J., 2008, MNRAS:L,
391, L103
Gänsicke B., Koester D., Farihi J., Girven J., Parsons S., Breedt E., 2012, MNRAS, 424, 333
References 151
Gänsicke B. T., Schreiber M. R., Toloza O., Fusillo N. P. G., Koester D., Manser C. J., 2019,
Nature, 576, 61
Gary B., Rappaport S., Kaye T., Alonso R., Hambschs F.-J., 2017, MNRAS, 465, 3267
Gaudi B. S., 2012, Annual Review of Astronomy and Astrophysics, 50, 2012
Gelman A., Rubin D. B., et al., 1992, Statistical science, 7, 457
Genest-Beaulieu C., Bergeron P., 2019, ApJ, 871, 169
Gentile Fusillo N., et al., 2015, MNRAS, 452, 765
Gentile Fusillo N. P., Gänsicke B. T., Farihi J., Koester D., Schreiber M. R., Pala A. F., 2017,
MNRAS, 468, 971
Gentile Fusillo N. P., Tremblay P.-E., Gänsicke B. T., Manser C. J., Cunningham T.,
Cukanovaite E., et al., 2018, MNRAS, 482, 4570
Gentile Fusillo N., et al., 2020, arXiv e-prints, pp arXiv–2010
Gentile Fusillo N., et al., 2021, MNRAS, 508, 3877
Gianninas A., Bergeron P., Ruiz M. T., 2011, ApJ, 743, 138
Girven J., Brinkworth C., Farihi J., Gänsicke B., Hoard D., Marsh T., Koester D., 2012, ApJ,
749, 154
Gounelle M., 2015, A & A, 582, A26
Graham J. R., Matthews K., Neugebauer G., Soifer B., 1990, ApJ, 357, 216
Grevesse N., Asplund M., Sauval A., 2007, Space Science Reviews, 130, 105
Guerrero N. M., et al., 2021, ApJSS, 254, 39
Hallis L., 2017, Philosophical Transactions of the Royal Society A: Mathematical, Physical
and Engineering Sciences, 375, 20150390
Hamers A. S., Portegies Zwart S. F., 2016, MNRAS:L, 462, L84
Hansen B. M., Liebert J., 2003, Annual Review of A&A, 41, 465
Hardy F., Dufour P., Jordan S., 2017, in 20th European White Dwarf Workshop. p. 205
Harrison J. H., Bonsor A., Madhusudhan N., 2018, MNRAS, 479, 3814
Harrison J. H., Bonsor A., Kama M., Buchan A. M., Blouin S., Koester D., 2021, MNRAS,
504, 2853
Hayashi C., 1981, Progress of Theoretical Physics Supplement, 70, 35
Hevey P. J., Sanders I. S., 2006, Meteoritics & Planetary Science, 41, 95
152 References
Hewett P. C., Warren S. J., Leggett S. K., Hodgkin S. T., 2006, MNRAS, 367, 454
Hinkel N. R., Timmes F., Young P. A., Pagano M. D., Turnbull M. C., 2014, AJ, 148, 54
Hogg M. A., Cutter R., Wynn G., 2021, MNRAS, 500, 2986
Holberg J., Wesemael F., Wegner G., Bruhweiler F., 1985, ApJ, 293, 294
Hollands M., Gänsicke B., Koester D., 2015, MNRAS, 450, 681
Hollands M., Koester D., Alekseev V., Herbert E., Gänsicke B. T., 2017, MNRAS, 467, 4970
Hollands M., Gänsicke B., Koester D., 2018, MNRAS, 477, 93
Hoskin M. J., et al., 2020, MNRAS, 499, 171
Irwin M. J., et al., 2004, in Optimizing scientific return for astronomy through information
technologies. pp 411–422
Irwin J., Irwin M., Aigrain S., Hodgkin S., Hebb L., Moraux E., 2007, MNRAS, 375, 1449
Izquierdo P., Toloza O., Gänsicke B. T., Rodríguez-Gil P., Farihi J., Koester D., Guo J.,
Redfield S., 2021, MNRAS, 501, 4276
Jura M., 2003, ApJL, 584, L91
Jura M., 2006, ApJ, 653, 613
Jura M., 2008, AJ, 135, 1785
Jura M., Xu S., 2012, AJ, 145, 30
Jura M., Young E., 2014, AREPS, 42, 45
Jura M., Farihi J., Zuckerman B., Becklin E., 2007a, AJ, 133, 1927
Jura M., Farihi J., Zuckerman B., 2007b, ApJ, 663, 1285
Jura M., Farihi J., Zuckerman B., 2009a, AJ, 137, 3191
Jura M., Muno M., Farihi J., Zuckerman B., 2009b, ApJ, 699, 1473
Jura M., Dufour P., Xu S., Zuckerman B., Klein B., Young E., Melis C., 2015, ApJ, 799, 109
Kawka A., Vennes S., 2014, MNRAS: Letters, 439, L90
Kawka A., Vennes S., Ferrario L., Paunzen E., 2019, MNRAS, 482, 5201
Kelson D. D., 2003, PASP, 115, 688
Kelson D. D., Illingworth G. D., van Dokkum P. G., Franx M., 2000, ApJ, 531, 159
Kemp J. C., Swedlund J. B., Landstreet J., Angel J., 1970, ApJ, 161, L77
Kenyon S. J., Bromley B. C., 2017a, ApJ, 844, 116
References 153
Kenyon S. J., Bromley B. C., 2017b, ApJ, 850, 50
Kepler S., Koester D., Pelisoli I., Romero A. D., Ourique G., 2021, MNRAS, 507, 4646
Kilic M., von Hippel T., Leggett S., Winget D., 2005, ApJ, 632, L115
Kilic M., von Hippel T., Leggett S., Winget D., 2006, ApJ, 646, 474
Klein B., Jura M., Koester D., Zuckerman B., Melis C., 2010, ApJ, 709, 950
Klein B., Jura M., Koester D., Zuckerman B., 2011, ApJ, 741, 64
Klein B. L., Doyle A. E., Zuckerman B., Dufour P., Blouin S., Melis C., Weinberger A. J.,
Young E. D., 2021, ApJ, 914, 61
Kleine T., Budde G., Burkhardt C., Kruijer T., Worsham E., Morbidelli A., Nimmo F., 2020,
Space Science Reviews, 216, 1
Kleinman S. J., et al., 1998, ApJ, 495, 424
Kniazev A., Gvaramadze V., Berdnikov L., 2016, MNRAS, 459, 3068
Kniazev A. Y., Gvaramadze V. V., Berdnikov L. N., 2017, in Balega Y. Y., Kudryavtsev D. O.,
Romanyuk I. I., Yakunin I. A., eds, Astronomical Society of the Pacific Conference Series
Vol. 510, Stars: From Collapse to Collapse. p. 480 (arXiv:1612.00292)
Koester D., 2009, A&A, 498, 517
Koester D., Chanmugam G., 1990, Rep. Prog. Phys., 53, 837
Koester D., Kepler S. O., 2015, A & A, 583, A86
Koester D., Napiwotzki R., Voss B., Homeier D., Reimers D., 2005, A & A, 439, 317
Koester D., Girven J., Gänsicke B., Dufour P., 2011, A & A, 530, A114
Koester D., Gaensicke B. T., Farihi J., 2014, A&A, 566, A34
Koester D., Kepler S., Irwin A., 2020, A & A, 635, A103
Lacombe P., Liebert J., Wesemael F., Fontaine G., 1983, ApJ, 272, 660
Lai S., et al., 2021, ApJ, 920, 156
Lichtenberg T., Golabek G. J., Burn R., Meyer M. R., Alibert Y., Gerya T. V., Mordasini C.,
2019, Nature Astronomy, 3, 307
Lodders K., 2003, ApJ, 591, 1220
Lomb N. R., 1976, Astrophysics and space science, 39, 447
Longstaff E., Casewell S., Wynn G., Page K., Williams P., Braker I., Maxted P., 2019,
MNRAS, 484, 2566
154 References
Madhusudhan N., 2019, arXiv preprint arXiv:1904.03190
Madhusudhan N., Nixon M. C., Welbanks L., Piette A. A., Booth R. A., 2020, ApJL, 891, L7
Manser C. J., Gänsicke B. T., Marsh T. R., Veras D., Koester D., Breedt E., et al., 2015,
MNRAS, 455, 4467
Manser C. J., et al., 2016a, MNRAS, 455, 4467
Manser C. J., Gänsicke B. T., Koester D., Marsh T. R., Southworth J., 2016b, MNRAS, 462,
1461
Manser C. J., Gänsicke B. T., Eggl S., Hollands M., Izquierdo P., Koester D., et al., 2019,
Science, 364, 66
Manser C. J., Gänsicke B. T., Gentile Fusillo N. P., Ashley R., Breedt E., Hollands M.,
Izquierdo P., Pelisoli I., 2020, MNRAS, 493, 2127
Marino S., 2022, arXiv preprint arXiv:2202.03053
Mayor M., Queloz D., 1995, Nature, 378, 355
McCook G. P., Sion E. M., 1999, ApJS, 121, 1
McDonald C. H., Veras D., 2021, MNRAS, 506, 4031
McDonough W., 2003a, Treatise on geochemistry, 2, 547
McDonough W., 2003b, Treatise on geochemistry, 2, 568
Melis C., Dufour P., 2016, ApJ, 834, 1
Melis C., Jura M., Albert L., Klein B., Zuckerman B., 2010, ApJ, 722, 1078
Melis C., Farihi J., Dufour P., Zuckerman B., Burgasser A. J., Bergeron P., Bochanski J.,
Simcoe R., 2011, ApJ, 732, 90
Melis C., Dufour P., Farihi J., Bochanski J., Burgasser A. J., Parsons S., Gänsicke B., et al.,
2012, ApJL, 751, L4
Melis C., Klein B., Doyle A. E., Weinberger A., Zuckerman B., Dufour P., 2020, arXiv
preprint arXiv:2010.03695
Mestel L., 1952, MNRAS, 112, 583
Metzger B. D., Rafikov R. R., Bochkarev K. V., 2012, MNRAS, 423, 505
Michel P., DeMeo F. E., Bottke W. F., 2015, Asteroids iv. University of Arizona Press
Mittlefehldt D. W., McCoy T. J., Goodrich C. A., Kracher A., 1998, Reviews in Mineralogy
and Geochemistry
Morbidelli A., Chambers J., Lunine J., Petit J.-M., Robert F., Valsecchi G., Cyr K., 2000,
Meteoritics & Planetary Science, 35, 1309
References 155
Morbidelli A., Lunine J. I., O’Brien D. P., Raymond S. N., Walsh K. J., 2012, Annual Review
of EPS, 40, 251
Mustill A. J., Villaver E., 2012, ApJ, 761, 121
Mustill A. J., Villaver E., Veras D., Gänsicke B. T., Bonsor A., 2018, MNRAS, 476, 3939
Nava C., López-Morales M., Haywood R. D., Giles H. A., 2019, AJ, 159, 23
Patil A., Huard D., Fonnesbeck C. J., 2010, Journal of statistical software, 35, 1
Payne M. J., Veras D., Holman M. J., Gänsicke B. T., 2016, MNRAS, 457, 217
Pelletier C., Fontaine G., Wesemael F., Michaud G., Wegner G., 1986, ApJ, 307, 242
Petrovich C., Muñoz D. J., 2017, ApJ, 834, 116
Prusti T., De Bruijne J., Brown A. G., Vallenari A., Babusiaux C., Bailer-Jones C., et al.,
2016, A & A, 595, A1
Quanz S. P., et al., 2021, arXiv preprint arXiv:2101.07500
Raddi R., Gänsicke B., Koester D., Farihi J., Hermes J., Scaringi S., Breedt E., Girven J.,
2015, MNRAS, 450, 2083
Rafikov R. R., 2011a, MNRAS, 416, L55
Rafikov R. R., 2011b, ApJL, 732, L3
Rajpaul V., Aigrain S., Osborne M. A., Reece S., Roberts S., 2015, MNRAS, 452, 2269
Rappaport S., Gary B., Kaye T., Vanderburg A., Croll B., Benni P., Foote J., 2016, MNRAS,
458, 3904
Rappaport S., Gary B., Vanderburg A., Xu S., Pooley D., Mukai K., 2017, MNRAS, 474, 933
Raymond S. N., Izidoro A., 2017, Icarus, 297, 134
Raymond S. N., Morbidelli A., 2022, in , Demographics of Exoplanetary Systems. Springer,
pp 3–82
Reach W. T., Kuchner M. J., von Hippel T., Burrows A., Mullally F., Kilic M., Winget D.,
2005, ApJL, 635, L161
Reach W. T., Lisse C., von Hippel T., Mullally F., 2009, ApJ, 693, 697
Rebassa-Mansergas A., Solano E., Xu S., Rodrigo C., Jiménez-Esteban F., Torres S., 2019,
MNRAS, 489, 3990
Robertson H., 1937, MNRAS, 97, 423
Rocchetto M., Farihi J., Gänsicke B., Bergfors C., 2015, MNRAS, 449, 574
156 References
Rogers L. K., Xu S., Bonsor A., Hodgkin S., Su K. Y., von Hippel T., Jura M., 2020, MNRAS,
494, 2861
Rubie D. C., et al., 2011, EPSL, 301, 31
Sanderson H., Bonsor A., Mustill A. J., 2022, arXiv preprint arXiv:2206.02505
Scargle J. D., 1982, ApJ, 263, 835
Schreiber M. R., Belloni D., Gänsicke B. T., Parsons S. G., 2021, MNRAS: Letters, 506, L29
Scott E. R., 2007, Annual Review of EPS, 35, 577
Seager S., Kuchner M., Hier-Majumder C., Militzer B., 2007, ApJ, 669, 1279
Smallwood J. L., Martin R. G., Livio M., Lubow S. H., 2018, MNRAS, 480, 57
Sohl F., Schubert G., 2007, Planets and Moons. Treatise on Geophysics, 10, 27
Stark J., 1913, Nature, 92, 401
Steckloff J. K., Debes J., Steele A., Johnson B., Adams E. R., Jacobson S. A., Springmann
A., 2021, ApJ:L, 913, L31
Steele A., Debes J., Xu S., Yeh S., Dufour P., 2021, ApJ, 911, 25
Stephan A. P., Naoz S., Zuckerman B., 2017, ApJL, 844, L16
Su K. Y., et al., 2007, ApJL, 657, L41
Swan A., Farihi J., Wilson T. G., 2019a, MNRAS:L, 484, L109
Swan A., Farihi J., Koester D., Hollands M., Parsons S., Cauley P. W., Redfield S., Gänsicke
B. T., 2019b, MNRAS, 490, 202
Swan A., Farihi J., Wilson T. G., Parsons S. G., 2020, arXiv preprint arXiv:2006.05999
Swan A., Kenyon S. J., Farihi J., Dennihy E., Gänsicke B. T., Hermes J., Melis C., von
Hippel T., 2021, MNRAS, 506, 432
Tody D., 1986, in Instrumentation in astronomy VI. pp 733–748
Trierweiler I. L., Doyle A. E., Melis C., Walsh K. J., Young E. D., 2022, arXiv preprint
arXiv:2205.07935
Turner S. G., Wyatt M. C., 2020, MNRAS, 491, 4672
Urey H. C., 1955, Proceedings of the National Academy of Sciences of the United States of
America, 41, 127
Van Dishoeck E. F., Bergin E. A., Lis D. C., Lunine J. I., 2014, arXiv preprint
arXiv:1401.8103
Van Horn H., 1971, in Symposium-International Astronomical Union. pp 97–115
References 157
Van Maanen A., 1917, PASP, 29, 258
VanderPlas J. T., 2018, ApJSS, 236, 16
Vanderbosch Z. P., et al., 2021, ApJ, 917, 41
Vanderburg A., Johnson J. A., Rappaport S., Bieryla A., Irwin J., et al., 2015, Nature, 526,
546
Vanderburg A., Plavchan P., Johnson J. A., Ciardi D. R., Swift J., Kane S. R., 2016, MNRAS,
459, 3565
Vanderburg A., et al., 2020, Nature, 585, 363
Vauclair G., Vauclair S., Greenstein J., 1979, A&A, 80, 79
Veras D., Wyatt M. C., Mustill A. J., Bonsor A., Eldridge J. J., 2011, MNRAS, 417, 2104
Veras D., Mustill A. J., Bonsor A., Wyatt M. C., 2013, MNRAS, 431, 1686
Veras D., Leinhardt Z. M., Bonsor A., Gänsicke B. T., 2014, MNRAS, 445, 2244
Veras D., Leinhardt Z. M., Eggl S., Gänsicke B. T., 2015, MNRAS, 451, 3453
Veras D., Georgakarakos N., Dobbs-Dixon I., Gänsicke B. T., 2016, MNRAS, 465, 2053
Vernet J., et al., 2011, A & A, 536, A105
Villaver E., Livio M., 2007, ApJ, 661, 1192
Vogt S. S., et al., 1994, in Instrumentation in Astronomy VIII. pp 362–375
Voss B., Koester D., Napiwotzki R., Christlieb N., Reimers D., 2007, A & A, 470, 1079
Wänke H., 1981, Philosophical Transactions of the Royal Society of London. Series A,
Mathematical and Physical Sciences, 303, 287
Warren P. H., 2011, EPSL, 311, 93
Weisberg M. K., McCoy T. J., Krot A. N., et al., 2006, Meteorites and the early solar system
II, 19, 19
Wilson D. J., Gänsicke B. T., Koester D., Raddi R., Breedt E., Southworth J., Parsons S. G.,
2014, MNRAS, 445, 1878
Wilson D. J., Gänsicke B. T., Koester D., Toloza O., Pala A. F., Breedt E., Parsons S. G.,
2015, MNRAS, 451, 3237
Wilson D. J., Gänsicke B. T., Farihi J., Koester D., 2016, MNRAS, 459, 3282
Wilson T. G., Farihi J., Gänsicke B. T., Swan A., 2019, MNRAS, 487, 133
Wolszczan A., Frail D. A., 1992, Nature, 355, 145
158 References
Wood B. J., Wade J., Kilburn M. R., 2008, Geochimica et Cosmochimica Acta, 72, 1415
Wyatt M. C., 2021, arXiv preprint arXiv:2110.04319
Wyatt M., Farihi J., Pringle J., Bonsor A., 2014, MNRAS, 439, 3371
Xu S., Bonsor A., 2021, arXiv preprint arXiv:2108.08384
Xu S., Jura M., 2012, ApJ, 745, 88
Xu S., Jura M., 2014, ApJL, 792, L39
Xu S., Jura M., Klein B., Koester D., Zuckerman B., 2013, ApJ, 766, 132
Xu S., Jura M., Koester D., Klein B., Zuckerman B., 2014, ApJ, 783, 79
Xu S., Ertel S., Wahhaj Z., Milli J., Scicluna P., Bertrang G.-M., 2015a, A&A, 579, L8
Xu S., Jura M., Pantoja B., Klein B., Zuckerman B., Su K., Meng H., 2015b, ApJL, 806, L5
Xu S., Jura M., Dufour P., Zuckerman B., 2016, ApJL, 816, L22
Xu S., Zuckerman B., Dufour P., Young E., Klein B., Jura M., 2017, ApJL, 836, L7
Xu S., Rappaport S., van Lieshout R., Vanderburg A., Gary B., Hallakoun N., Ivanov V.,
et al., 2018a, MNRAS, 474, 4795
Xu S., Su K., Rogers L., Bonsor A., et al., 2018b, ApJ, 866, 108
Xu S., Dufour P., Klein B., Melis C., Monson N. N., Zuckerman B., Young E. D., Jura M. A.,
2019, AJ, 158, 242
Xu S., Lai S., Dennihy E., 2020, arXiv preprint arXiv:2009.00193
Yoshizaki T., McDonough W. F., 2021, Geochemistry, 81, 125746
Young E. D., 2016, ApJ, 826, 129
Zuckerman B., Becklin E., 1987, Nature, 330, 138
Zuckerman B., Koester D., Reid I. N., Hünsch M., 2003, ApJ, 596, 477
Zuckerman B., Koester D., Melis C., Hansen B. M., Jura M., 2007, ApJ, 671, 872
Zuckerman B., Melis C., Klein B., Koester D., Jura M., 2010, ApJ, 722, 725
Zuckerman B., Koester D., Dufour P., Melis C., Klein B., Jura M., 2011, ApJ, 739, 101
van Roestel J., et al., 2021, ApJL, 919, L26
von Hippel T., Thompson S. E., 2007, ApJ, 661, 477
Chapter 6
Appendix 1: Additional tables and
figures from Chapter 2
6.1 Observation Information
Table 6.1 shows the dates of the observations for each white dwarf in the sample. Table 6.2
shows the frame numbers for each white dwarf in the sample.
160 Appendix 1: Additional tables and figures from Chapter 2
Ta
bl
e
6.
1
A
ll
th
e
po
llu
te
d
w
hi
te
dw
ar
fs
w
ith
an
in
fr
ar
ed
ex
ce
ss
ob
se
rv
ed
w
ith
th
e
U
K
IR
T
an
d
th
e
da
te
s
th
ey
w
er
e
ob
se
rv
ed
.
W
D
N
am
e
20
14
B
20
15
A
20
15
B
20
16
A
20
16
A
20
16
B
20
16
B
20
17
A
20
17
A
W
D
00
10
+2
80
03
/1
0/
14
N
N
N
N
06
/0
7/
16
N
N
N
W
D
01
06
−3
28
03
/1
0/
14
N
N
N
N
11
/1
0/
16
N
N
N
W
D
01
46
+1
87
03
/1
0/
14
N
N
N
N
12
/0
7/
16
N
N
N
W
D
03
00
−0
13
03
/1
0/
14
N
N
N
N
22
/0
7/
16
31
/0
1/
17
N
N
W
D
03
07
+0
77
03
/1
0/
14
N
N
N
N
10
/1
0/
16
N
N
W
D
04
08
−0
41
03
/1
0/
14
N
N
N
N
10
/1
0/
16
31
/0
1/
17
N
N
W
D
04
35
+4
10
03
/1
0/
14
N
31
/0
1/
16
N
N
10
/1
0/
16
N
N
N
W
D
J0
73
8+
18
35
N
03
/0
5/
15
N
29
/0
2/
16
N
10
/1
0/
16
28
/0
1/
17
N
N
W
D
J0
95
9−
02
00
09
/1
1/
14
02
/0
2/
15
N
05
/0
3/
16
07
/0
5/
16
N
N
23
/0
5/
17
N
W
D
10
15
+1
61
30
/1
0/
14
N
N
09
/0
5/
16
N
N
N
N
N
W
D
10
18
+4
10
30
/1
0/
14
N
N
09
/0
5/
16
N
N
N
N
N
W
D
10
41
+0
92
N
02
/0
5/
15
N
04
/0
3/
16
09
/0
5/
16
N
N
N
N
W
D
11
16
+0
26
N
02
/0
5/
15
N
05
/0
3/
16
10
/0
5/
16
N
N
30
/0
5/
17
N
W
D
11
45
+0
17
N
02
/0
5/
15
N
N
N
N
N
09
/0
5/
17
24
/0
5/
17
*
W
D
11
45
+2
88
N
02
/0
5/
15
N
23
/0
2/
16
09
/0
5/
16
N
N
30
/0
5/
17
N
W
D
11
50
−1
53
N
03
/0
5/
15
N
05
/0
3/
16
10
/0
5/
16
N
N
01
/0
6/
17
N
W
D
J1
22
1+
12
45
N
02
/0
5/
15
N
01
/0
3/
16
10
/0
5/
16
N
N
25
/0
5/
17
N
W
D
12
25
−0
79
N
03
/0
5/
15
N
04
/0
3/
16
10
/0
5/
16
N
N
25
/0
5/
17
N
W
D
12
26
+1
10
N
02
/0
5/
15
N
29
/0
2/
16
10
/0
5/
16
N
N
09
/0
5/
17
N
W
D
J1
23
4+
56
06
N
03
/0
5/
15
N
04
/0
3/
16
05
/0
6/
16
N
N
07
/0
6/
17
N
W
D
13
49
−2
30
N
03
/0
5/
15
N
04
/0
3/
16
06
/0
6/
16
N
N
30
/0
5/
17
N
W
D
14
56
+2
98
N
02
/0
5/
15
N
17
/0
2/
16
10
/0
5/
16
N
N
14
/0
5/
17
N
W
D
15
04
+3
29
N
01
/0
5/
15
N
29
/0
2/
16
08
/0
5/
16
N
N
12
/0
5/
17
N
W
D
15
36
+5
20
N
02
/0
5/
15
N
05
/0
3/
16
29
/0
5/
16
N
N
28
/0
5/
17
N
W
D
15
51
+1
75
N
01
/0
5/
15
N
03
/0
3/
16
31
/0
5/
16
N
N
14
/0
5/
17
N
W
D
15
54
+0
94
N
01
/0
5/
15
N
29
/0
2/
16
08
/0
5/
16
N
N
20
/0
5/
17
18
/0
7/
17
W
D
J1
61
7+
16
20
N
01
/0
5/
15
N
17
/0
2/
16
10
/0
5/
16
N
N
10
/0
5/
17
17
/0
7/
17
W
D
17
29
+3
71
N
02
/0
5/
15
02
/0
8/
15
28
/0
2/
16
10
/0
5/
16
N
N
12
/0
5/
17
17
/0
7/
17
W
D
19
29
+0
11
06
/1
0/
14
N
02
/0
8/
15
N
N
10
/0
7/
16
10
/0
5/
17
15
/0
7/
17
N
W
D
21
32
+0
96
N
03
/0
5/
15
09
/0
8/
15
21
/0
4/
16
N
10
/0
7/
16
N
11
/0
5/
17
15
/0
7/
17
W
D
22
07
+1
21
13
/1
0/
14
N
08
/0
8/
15
N
N
29
/0
6/
16
N
15
/0
7/
17
N
W
D
22
21
−1
65
30
/1
0/
14
N
09
/0
8/
15
N
N
13
/0
7/
16
N
N
N
W
D
23
26
+0
49
03
/1
0/
14
N
09
/0
8/
15
N
N
06
/0
7/
16
N
N
N
W
D
23
28
+1
07
N
N
08
/0
8/
15
01
/0
6/
16
N
06
/0
7/
16
N
02
/0
6/
17
15
/0
7/
17
(*
)F
or
W
D
11
45
+0
17
,t
he
re
ar
e
th
re
e
m
or
e
da
te
s
fo
r2
01
7A
:0
6/
06
/2
01
7,
21
/0
6/
20
17
an
d
22
/0
6/
20
17
.
6.2 SEDs 161
6.2 SEDs
SEDs of the targets in the survey. White dwarf models kindly provided by P. Dufour.
Figure B1.
Figure B1.
Figure B1.
Figure B1.
Figure B1. The spectral energy distributions for the 34 white dwarfs in this sample. The temperature and log(g) used within the models
are shown. R/D is the scaling factor used for the radii/distance needed in order for the models to fit the SDSS or Pan-STARRS optical
data. The 11 white dwarfs without a significant K band excess are: WD 0106−328, WD 0300−013, WD 0307+077, WD 1041+092, WD
1225−079, WD 1456+298, WD 2132+096, WD 2221−165, WD 2328+107, WD 1504+329, and WD 1551+175.
6.2 SEDs 167
Table 6.2 All the polluted white dwarfs with an infrared excess observed with the UKIRT
survey and the total number of frames. Each frame consists of a dithered stack of 5 exposures,
each with the corresponding frame time of 5 or 10 seconds. FT = frame time for each
individual exposure in the dithered stack, FN = total number of dithered stacks over all
observations.
WD Name FT J (secs) FN J FT H (secs) FN H FT K (secs) FN K
WD 0010+280 5 6 10 6 10 10
WD 0106−328 5 6 5 6 5 6
WD 0146+187 5 6 5 6 5 6
WD 0300−013 5 6 5 6 5 9
WD 0307+077 5 6 10 6 10 10
WD 0408−041 5 9 5 9 5 9
WD 0435+410 5 3 5 3 5 9
WD J0738+1835 10 9 10 27 10 75
WD J0959−0200 10 9 10 27 10 75
WD 1015+161 5 6 5 6 10 6
WD 1018+410 5 6 10 6 10 10
WD 1041+092 10 9 10 21 10 51
WD 1116+026 5 4 5 4 5 12
WD 1145+017 10 18 10 42 10 102
WD 1145+288 10 12 10 28 10 68
WD 1150−153 5 12 5 11 10 12
WD J1221+1245 10 12 10 36 10 100
WD 1225−079 5 4 5 4 5 12
WD 1226+110 5 12 10 12 10 20
WD J1234+5606 10 9 10 27 10 75
WD 1349−230 5 12 10 12 10 20
WD 1456+298 5 3 5 3 5 6
WD 1504+329 10 9 10 27 10 75
WD 1536+520 10 12 10 28 10 68
WD 1551+175 10 12 10 28 10 68
WD 1554+094 10 15 10 45 10 125
WD J1617+1620 5 19 10 23 10 45
WD 1729+371 5 19 5 19 10 23
WD 1929+011 5 6 5 10 5 20
WD 2132+096 5 20 5 22 10 26
WD 2207+121 10 18 10 36 10 76
WD 2221−165 5 6 5 6 5 6
WD 2326+049 5 3 5 3 5 9
WD 2328+107 5 19 5 19 5 23

Chapter 7
Appendix 2: Additional tables and
figures from Chapter 4
7.1 Spectral Energy Distributions
Spectral energy distributions for the seven white dwarfs are shown in Figure 7.1 showing the
best fitting white dwarf models derived both spectroscopically and photometrically.
7.2 Spectral Lines and abundances
For each of the white dwarfs, the stellar parameters were determined spectroscopically and
photometrically. For each set of parameters the abundances were obtained. Tables 7.1 – 7.7
show the spectral lines that were identified in the X-shooter, HIRES and MIKE data for the
seven white dwarfs, their associated equivalent width, radial velocity, and the abundance
derived.
7.3 Equivalent Width Upper Limits
Using the method discussed in Section 4.2.3 the equivalent width upper limits were derived,
as listed in Table 7.8. The strongest optical line was used to derive the equivalent width upper
limit.
The HIRES data were used to obtain the equivalent width upper limits as the higher
resolution allowed more stringent constraints to be used. For Gaia J0611−6931 the X-shooter
data was used to derive the upper limits. At the resolution of X-shooter it is difficult to
170 Appendix 2: Additional tables and figures from Chapter 4
0 2000 4000 6000 8000 10000 12000
Wavelength (A˚)
10−4
10−3
10−2
F
lu
x
(J
y)
GaiaJ0006+2858
X-shooter Scaled
Phot Model
Spec Model
SDSS
PS
GALEX
0 2000 4000 6000 8000 10000 12000
Wavelength (A˚)
10−4
10−3
10−2
F
lu
x
(J
y)
GaiaJ0347+1624
Phot Model
Spec Model
SDSS
PS
GALEX
0 2000 4000 6000 8000 10000 12000
Wavelength (A˚)
10−3
10−2
F
lu
x
(J
y)
GaiaJ0510+2315
Phot Model
Spec Model
PS
GALEX
0 2000 4000 6000 8000 10000 12000
Wavelength (A˚)
10−4
10−3
F
lu
x
(J
y)
GaiaJ0611-6931
X-shooter Scaled
Spec Model
GALEX
0 2000 4000 6000 8000 10000 12000
Wavelength (A˚)
10−3
F
lu
x
(J
y)
GaiaJ0644-0352
X-shooter Scaled
Phot Model
Spec Model
PS
GALEX
0 2000 4000 6000 8000 10000 12000
Wavelength (A˚)
10−4
10−3
F
lu
x
(J
y)
WD1622+587
Phot Model
Spec Model
SDSS
PS
GALEX
0 2000 4000 6000 8000 10000 12000
Wavelength (A˚)
10−3
10−2
F
lu
x
(J
y)
GaiaJ2100+2122
X-shooter Scaled
Phot Model
Spec Model
PS
GALEX
Fig. 7.1 Spectral energy distributions for the seven white dwarfs. The X-shooter spectra
for the four white dwarfs observed are shown in grey, this is scaled to fit the spectroscopic
models as the spectra suffer from flux loss due to non-ideal weather conditions and slit losses.
There is a gap in the data between 6360 Å– 6375 Å and telluric absorption features are present
in the reddest parts of the spectra. The photometric data points are given in black, errors are
plotted but are smaller than the data points. The photometric and spectroscopic model fits
are shown in orange (solid line) and blue (dashed line) where available. Missing GALEX
FUV or NUV fluxes implies either a non-detection in that band, or the flux was flagged as it
contained an artefact.
7.3 Equivalent Width Upper Limits 171
Table 7.1 The absorption lines in Gaia J0006+2858. If two lines lie within ∼ 10 Å, equivalent
widths and abundances were fitted simultaneously.
Line λ air (Å) λ obs (Å) EW (Å) RV (km/s) Spec Abundance Phot Abundance
HIRES X-sh HIRES X-sh
Ca II 3179.3315 3179.66 0.013 (0.003) 31.3 −6.21 −6.33
Ca II† 3933.6631 3934.02* 0.041 (0.006) 27.3 −6.13 −6.32
Ca Average: −6.17 - −6.33 -
Mg II 4481.1250 4481.59 0.208 (0.007) 31.2 −5.00 −4.90 −5.10 −4.97
Si II 3856.0184 3856.37 0.029 (0.003) 27.5 −4.79 −4.89
Si II 3862.5947 3862.94 0.015 (0.002) 26.8 −4.78 −4.90
Si II 4128.0542 4128.40 0.024 (0.003) 24.8 −4.99 −5.10
Si II 4130.8934 4131.26 0.024 (0.003) 26.3 −4.99 −5.10
Si II 5041.0230 5041.59 0.036 (0.006) 33.8 −5.10 −4.97 −5.20 −5.05
Si II 5055.9830 5056.53 0.055 (0.006) 32.3 −5.14 −4.97 −5.24 −5.05
Si II 6347.1062 6347.68 0.083 (0.008) 27.0 −4.95 −4.86 −5.04 −4.94
Si II 6371.3676 6371.99 0.046 (0.008) 29.2 −4.93 −5.03
Si Average: −4.95 −4.92 −5.06 −4.99
† Gaseous emission at this wavelength, additional 12 percent error added in quadrature.
* Ca II 3933 has extra absorption at rest wavelength of line, this was fitted simultaneously and
subtracted to derive the equivalent width. This could be the core of the double peaked
circumstellar emission feature.
Table 7.2 The absorption lines measured in the HIRES spectrum of Gaia J0347+1624. There
are also Na D lines at both 5890 Angstrom and 5896 Angstrom. However, in checking the
ISM model, this line of sight intercepts LIC (RV of 22.36 km/s) and Hyades (RV of 14.16
km/s). This is close to the measured RV of 15 km/s so it is deduced that these lines are not
photospheric.
Line λ air (Å) λ obs (Å) EW (Å) RV (km/s) Spec Abundance Phot Abundance
Ca II 3933.6631 3933.90 0.062 (0.006) 18.1 −5.79 −6.29
Ca II 3968.4690 3968.71 0.022 (0.004) 18.2 −5.60 −5.72
Ca Average: −5.69 −6.01
Mg II 4481.1250∗ 4481.36 0.040 (0.012) 16.0 −5.78 −6.05
∗ This is a merged Mg II doublet with 4481.3249. RV is calculated with respect to the line listed.
172 Appendix 2: Additional tables and figures from Chapter 4
Table 7.3 The absorption lines in the HIRES spectra of Gaia J0510+2315. If two lines lie
within ∼ 10 Å, equivalent widths and abundances were fitted simultaneously.
Line λ air (Å) λ obs (Å) EW (Å) RV (km/s) Spec Abundance Phot Abundance
Ca II 3933.6631 3934.03 0.032 (0.004) 27.6 −6.31 −7.10
Mg II∗ 4481.1250 4481.53 0.114 (0.011) 26.9 −5.23 −5.45
Mg II∗ 4481.3249 4481.74 0.037 (0.007) 27.8 −5.23 −5.45
Mg Average: −5.23 −5.45
O I† 7771.9377 7772.63 0.023 (0.005) 26.6 −4.23 −4.42
O I† 7774.1561 7774.88 0.020 (0.004) 27.8 −4.23 −4.42
O I† 7775.3858 7776.04 0.005 (0.002) 25.3 −4.23 −4.42
O Average: −4.23 −4.42
Si II 3856.0184 3856.35 0.019 (0.003) 26.0 −5.00 −4.99
Si II 4128.0542 4128.44 0.015 (0.005) 28.0 −4.90 −4.82
Si II 4130.8934 4131.25 0.030 (0.006) 25.8 −4.90 −4.82
Si II 5055.9830 5056.48 0.039 (0.003) 29.2 −5.36 −5.34
Si II 5041.0230 5041.52 0.014 (0.002) 29.8 −5.33 −5.31
Si II 6347.1062 6347.65 0.058 (0.004) 25.7 −5.19 −5.19
Si II 6371.3676 6371.92 0.031 (0.004) 26.1 −5.15 −5.14
Si Average: −5.15 −5.13
† Gaseous emission at this wavelength, additional 12 percent error added in quadrature.
∗ Both Mg II features resolved and fitted simultaneously for EW and RV.
An additional spectrum was obtained with HIRES and stacked for increased SNR to resolve the O
lines.
O line at 7775.3858 Å is marginal.
7.3 Equivalent Width Upper Limits 173
Table 7.4 The absorption lines in Gaia J0611−6931. If two lines lie within∼ 10 Å, equivalent
widths and abundances were fitted simultaneously.
Line λ air (Å) λ obs (Å) EW (Å) RV (km/s) Spec Abundance
X-sh MIKE
Ca II† 3933.6631 3934.51 0.118 (0.025) 64.5 −6.19 −5.92
Mg II 4481.1250 4482.14 0.546 (0.014) 67.6 −4.66 −4.53
Mg II 7896.0371 7898.08 0.080 (0.025) 77.6 −4.68 −4.50
Mg Average: −4.67 −4.52
O I† 7771.9377 7773.48 0.049 (0.014) 59.4 −3.67
O I† 7774.1561 7775.72 0.038 (0.014) 60.3 −3.67
O I† 7775.3858 7776.96 0.033 (0.017) 60.6 −3.67
O Average: - −3.67
Si II 5041.0230 5042.05∗ 0.007 (0.002) 61.3 −4.73
Si II 5055.9830 5057.13∗ 0.010 (0.003) 68.1 −4.73 −4.68
Si II 6347.1062 6348.40 0.117 (0.017) 60.9 −4.71 −4.79
Si II 6371.3676 6372.68 0.090 (0.0065) 61.8 −4.53
Si Average: −4.73 −4.67
Fe II† 5169.0318 5170.12 0.055 (0.023) 63.2 −4.24
† Gaseous emission at this wavelength, additional 12 percent error added in quadrature.
∗ Si II 5041 and 5055 measured line position and equivalent widths from X-shooter.
174 Appendix 2: Additional tables and figures from Chapter 4
Table 7.5 The absorption lines in Gaia J0644−0352. If two lines lie within∼ 10 Å, equivalent
widths and abundances were fitted simultaneously.
Line λ air (Å) λ obs (Å) EW (Å) RV (km/s) Spec Abundance Phot Abundance
HIRES X-sh HIRES X-sh
Al II 3586.5564 3587.63 0.030 (0.005) 89.9 −6.76 −7.05
Al II 3587.0723 3588.18 0.021 (0.006) 92.8 −6.76 −7.05
Al II 3587.4452 3588.53 0.011 (0.004) 90.5 −6.76 −7.05
Al Average: −6.76 − −7.05 −
Ca II 3158.8697 3159.86 0.092 (0.004) 93.5 −6.97 −6.91 −7.60 −7.52
Ca II 3179.3315 3180.34 0.094 (0.009) 95.1 −6.97 −6.72 −7.58 −7.32
Ca II 3181.2750 3182.27 0.025 (0.004) 93.4 −6.97 −6.72 −7.58 −7.32
Ca II 3706.0235 3707.19 0.020 (0.006) 94.2 −6.94 −6.57 −7.66 −7.44
Ca II 3736.9025 3738.07 0.061 (0.003) 93.5 −6.89 −6.86 −7.54 −7.50
Ca II 3933.6631 3934.87 0.333 (0.004) 91.7 −6.67 −6.70 −7.50 −7.52
Ca II 3968.4690 3969.69 0.181 (0.013) 92.4 −6.84 −6.84 −7.69 −7.68
Ca II† 8498.0177 8500.62 0.041 (0.015) 91.8 −6.60 −6.76 −7.21 −7.40
Ca II† 8542.0858 8544.76 0.157 (0.028) 93.8 −6.42 −6.56 −7.14 −7.26
Ca II† 8662.1352 8664.87 0.102 (0.022) 94.7 −6.63 −6.45 −7.30 −7.14
Ca Average: −6.77 −6.71 −7.47 −7.42
Cr II 3120.3584 3121.30 0.022 (0.006) 90.4 −7.65 −8.41
Cr II 3124.9732 3125.95 0.011 (0.004) 93.6 −7.93 −8.70
Cr II 3128.6923 3129.61 0.009 (0.003) 87.5 −7.77 −8.58
Cr II 3132.0534 3133.04 0.023 (0.005) 94.4 −7.77 −8.58
Cr II 3368.0416 3369.06 0.009 (0.002) 90.8 −7.90 −8.61
Cr Average: −7.81 − −8.58 −
Fe II 3154.1928 3155.19 0.011 (0.003) 94.5 −6.69 −7.32
Fe II * 3193.7988 3194.80 0.003 (0.001) 94.1 −6.49 −7.09
Fe II * 3193.8588 3194.88 0.002 (0.001) 95.9 −6.49 −7.09
Fe II 3213.3089 3214.31 0.014 (0.003) 93.0 −6.49 −7.14
Fe II 3227.7423 3228.74 0.013 (0.002) 92.3 −6.44 −7.18
Fe II 4583.8367 4585.27 0.005 (0.002) 93.9 −6.20 −6.78
Fe II 5169.0318 5170.64 0.018 (0.005) 93.1 −6.45 −7.02
Fe Average: −6.46 − −7.09 −
Mg I 3832.3036 3833.45 0.015 (0.004) 89.4 −5.71 −6.46
Mg I 3838.2921 3839.43 0.021 (0.003) 88.8 −5.71 −6.46
Mg II 4481.1250 4482.59 0.229 (0.013) 97.9 −5.52 −5.58 −6.35 −6.31
Mg II 7877.0502 7879.88 0.147 (0.045) 107.7 −5.85 −5.89 −6.30 −6.31
Mg II * (blended) 7896.04 7898.94 0.179 (0.027) 110.2 −5.87 −5.85 −6.32 −6.27
Mg Average: −5.74 −5.77 −6.36 −6.29
OI - 7771.9377 7774.41 0.102 (0.011) 95.2 −5.08 −5.10 −5.50 −5.55
OI - 7774.1561 7776.65 0.096 (0.016) 96.0 −5.08 −5.10 −5.50 −5.55
OI - 7775.3858 7777.89 0.050 (0.017) 96.6 −5.08 −5.10 −5.50 −5.55
OI 8446.3548 8448.87 0.050 (0.027) 89.1 −5.38 −5.20 −5.79 −5.62
O Average: −5.23 −5.15 −5.64 −5.58
Si II 3853.6650 3854.86 0.014 (0.003) 93.2 −5.80 −5.93 −6.31 −6.40
Si II 3856.0184 3857.21 0.099 (0.004) 92.3 −5.80 −5.93 −6.31 −6.40
Si II 3862.5947 3863.77 0.064 (0.003) 91.0 −5.80 −5.93 −6.31 −6.40
Si II * 4128.0542 4129.34 0.050 (0.005) 93.2 −6.01 −6.02 −6.51 −6.41
Si II * 4130.8934 4132.16 0.092 (0.005) 91.7 −6.01 −6.02 −6.51 −6.41
Si II 5055.9830 5057.73 0.092 (0.013) 103.7 −6.09 −6.47
Si II 6347.1062 6349.07 0.242 (0.011) 92.6 −6.00 −5.98 −6.06 −6.01
Si II 6371.3676 6373.34 0.145 (0.011) 92.6 −5.98 −6.24
Si Average: −5.98 −5.97 −6.32 −6.27
Ti II 3234.5145 3235.52 0.013 (0.002) 93.6 −8.25 −9.05
Ti II 3236.5720 3237.54 0.013 (0.003) 89.8 −8.25 −9.05
Ti II 3239.0364 3239.99 0.008 (0.002) 88.7 −8.25 −9.05
Ti II 3341.8742 3342.89 0.007 (0.002) 90.7 −8.37 −9.15
Ti II ** 3349.0334 3350.07 0.015 (0.003) 92.9 −8.22 −9.04
Ti II ** 3349.4023 3350.42 0.011 (0.002) 91.2 −8.22 −9.04
Ti II *** 3361.2123 3362.24 0.007 (0.002) 91.4 −8.49 −9.28
Ti II 3372.7923 3373.79 0.010 (0.002) 89.0 −8.34 −9.13
Ti II 3383.7585 3384.79 0.008 (0.002) 91.3 −8.37 −9.10
Ti II 3685.19/0.20 3686.31 0.004 (0.001) 90.1 −8.58 −9.29
Ti II 3759.2916 3760.45 0.007 (0.002) 92.5 −8.31 −9.04
Ti Average: −8.37 − −9.14 −
† Gaseous emission present at this wavelength. 12 percent error added in quadrature.
7.3 Equivalent Width Upper Limits 175
Table 7.6 The absorption lines measured in the WD 1622+587 HIRES spectra. If two lines
lie within ∼ 10 Å, equivalent widths and abundances were fitted simultaneously.
Line λ air (Å) λ obs (Å) EW (Å) RV (km/s) Spec Abundance Phot Abundance
Ca II 3179.3315 3179.11 0.031 (0.012) -21.2 −7.42 −6.94
Ca II 3933.6631 3933.40 0.111 (0.010) -20.3 −7.95 −7.48
Ca Average: −7.68 −7.21
Mg II (doublet) 4481.1250 4480.95 0.060 (0.009) -11.6 −6.60 −6.18
Mg II 7877.0502 7876.43 0.048 (0.016) -23.5 −5.97 −5.63
Mg II 7896.3620 7895.86 0.079 (0.018) -19.0 −6.17 −5.82
Mg Average: −6.25 −5.88
Si II 3856.0184 3855.79 0.062 (0.009) -17.9 −6.64 −6.29
Si II 3862.5947 3862.31 0.052 (0.010) -22.1 −6.38 −6.04
Si II* 4128.0542 4127.79 0.036 (0.008) -19.4 −6.44 −6.14
Si II* 4130.8934 4130.52 0.067 (0.009) -26.9 −6.44 −6.14
Si II 5055.9830 5055.77 0.087 (0.011) -12.8 −6.39 −6.11
Si II 6347.1062 6346.69 0.207 (0.017) -19.7 −6.15 −5.87
Si II 6371.3676 6370.90 0.152 (0.018) -22.4 −6.12 −5.85
Si Average: −6.35 −6.05
* Fitted together
Table 7.7 The absorption lines measured in Gaia J2100+2122. If two lines lie within ∼ 10 Å,
equivalent widths and abundances were fitted simultaneously.
Line λ air (Å) λ obs (Å) EW (Å) RV (km/s) Spec Abundance Phot Abundance
HIRES X-sh HIRES X-sh
Ca II 3179.3315 3179.35 0.009 (0.002) 2.1 −6.32 −6.66
Ca II* 3933.6631 3933.72 0.022 (0.001) 4.1 −6.13 −5.79 −6.65 −6.25
Ca Average: −6.23 −5.79 −6.65 −6.25
Fe II 3227.7423 3227.80 0.004 (0.001) 5.4 −4.96 −5.50
Mg II 4481.1250 4481.25 0.140 (0.005) 8.4 −5.12 −5.04 −5.40 −5.30
Si II 3856.0184 3856.07 0.015 (0.002) 3.9 −5.04 −5.32
Si II 3862.5947 3862.65 0.005 (0.001) 4.1 −5.10 −5.38
Si II * 4128.0542 4128.10 0.017 (0.002) 3.0 −4.96 −5.16
Si II * 4130.8934 4130.94 0.025 (0.002) 3.4 −5.12 −5.33
Si II 5055.9830 5056.15 0.027 (0.004) 9.7 −5.31 −5.32 −5.54 −5.53
Si II 6347.1062 6347.20 0.051 (0.003) 4.2 −5.14 −5.01 −5.41 −5.26
Si II 6371.3676 6371.44 0.019 (0.002) 3.6 −5.19 −5.46
Si Average: −5.12 −5.16 −5.4 −5.39
* Ca II has extra absorption bluewards. This is not resolved in X-shooter and is resolved in
HIRES. Therefore the abundance is higher in X-shooter and the average abundance only includes
the HIRES data.
176 Appendix 2: Additional tables and figures from Chapter 4
Table 7.8 The upper limit equivalent widths in mÅ of the material polluting the seven white
dwarfs in this study. ∗ denotes when gaseous emission is present at this wavelength. When
calculating abundance upper limit, add 12 percent onto the equivalent width quoted to be
conservative.
Element Line (Å) J0006 J0347 J0510 J0611 J0644 WD1622 J2100
O I 7771.9377 20.78∗ - - - - 31.4∗ 11.42∗
Na II 5889.9483 12.6 - 8.5 n/a∗ 25.1 16.5 8.7
Al II 3586.5564 7.0 16.6 14.3 92.1 - 13.0 3.4
Ti II 3349.0334 7.3 19.7 18.9 103.0 - 14.7 3.8
Cr II 3368.0416 7.2 19.1 18.4 121.8 - 14.8 3.8
Fe II 5169.0318 7.2∗ 20.3∗ 15.2∗ - - 8.0∗ -
Ni II 3513.9871 7.0 16.9 14.5 91.2 7.3 12.7 3.4
Fig. 7.2 Model fits (red lines) to the HIRES data using the average abundances for
Gaia J0006+2858. There is additional non-photospheric absorption bluewards of the Ca II K
line.
accurately normalise out the narrow gaseous emission features. Therefore, as there are no
sodium optical lines without gaseous emission, no upper limit is reported for this element.
7.4 Model fits to spectral lines
Figures 7.2 – 7.7 show the average model abundances fit to the strongest spectral line for
each element in six of the white dwarfs. The average abundance is plotted which is derived
from multiple spectral lines, so sometimes the fit to individual lines can be discrepant. Note
that for WD 1622+587 the abundance fits are shown in Fig. 4.3.
7.4 Model fits to spectral lines 177
Fig. 7.3 Model fits (red lines) to the HIRES data using the average abundances for
Gaia J0347+1624. Silicon is shown for reference, the absorption is not significant to 3σ and
is therefore taken as an upper limit.
Fig. 7.4 Model fits (red lines) to the HIRES data using the average abundances for
Gaia J0510+2315.
178 Appendix 2: Additional tables and figures from Chapter 4
Fig. 7.5 Model fits (red lines) to the MIKE data using the average abundances for
Gaia J0611−6931.
7.4 Model fits to spectral lines 179
Fig. 7.6 Model fits (red lines) to the HIRES data using the average abundances for
Gaia J0644−0352.
180 Appendix 2: Additional tables and figures from Chapter 4
Fig. 7.7 Model fits (red lines) to the HIRES data using the average abundances for
Gaia J2100−2122. There is an additional non-photospheric absorption bluewards of the Ca
II K line.
7.5 Bayesian output 181
7.5 Bayesian output
The resulting median parameters from the Bayesian models for the seven white dwarfs are
given in Table 7.9.
182 Appendix 2: Additional tables and figures from Chapter 4
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s}
-
-
-
0.
26
+
0.
06
−0
.0
5
{0
.5
2}
-
-
0.
30
+
0.
11
−0
.0
8
{0
.5
2}
D
iff
er
en
tia
tio
n
P
re
ss
ur
e
(G
pa
)
-
-
-
25
.3
+
2.
6
−2
.4
-
-
25
.6
+
19
.7
−1
5.
2
O
xy
ge
n
F
ug
ac
ity
-
-
-
-2
.4
+
0.
4
−0
.4
-
-
-2
.0
+
0.
6
−0
.6
B
ay
es
Fa
ct
or
n/
a
2.
1×
10
13
n/
a
4.
3×
10
4
5.
6×
10
4
17
4.
6×
10
2
N
σ
n/
a
8.
1
n/
a
5.
0
5.
1
2.
9
3.
9