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Draft version August 25, 2017
Preprint typeset using LATEX style emulateapj v. 01/23/15
THE BROADBAND AND SPECTRALLY-RESOLVED H-BAND ECLIPSE OF KELT-1B AND THE ROLE OF
SURFACE GRAVITY IN STRATOSPHERIC INVERSIONS IN HOT JUPITERS
Thomas G. Beatty1,2, Nikku Madhusudhan3, Richard Pogge4, Sun Mi Chung4, Allyson Bierlya5, B. Scott
Gaudi4,6, & David W. Latham5
Draft version August 25, 2017
ABSTRACT
We present a high precision H-band emission spectrum of the transiting brown dwarf KELT-1b,
which we spectrophotometrically observed during a single secondary eclipse using the LUCI1 multi-
object spectrograph on the Large Binocular Telescope. Using a Gaussian-process regression model,
we are able to clearly measure the broadband eclipse depth as ∆H = 1418± 94ppm. We are also able
to spectrally-resolve the H-band into five separate wavechannels and measure the eclipse spectrum
of KELT-1b at R ≈ 50 with an average precision of ±135ppm. We find that the day side has an
average brightness temperature of 3250± 50K, with significant variation as a function of wavelength.
Based on our observations, and previous measurements of KELT-1b’s eclipse at other wavelengths, we
find that KELT-1b’s day side appears identical to an isolated 3200K brown dwarf, and our modeling
of the atmospheric emission shows a monotonically decreasing temperature-pressure profile. This is
in contrast to hot Jupiters with similar day side brightness temperatures near 3000K, all of which
appear to be either isothermal or posses a stratospheric temperature inversion. We hypothesize that
the lack of an inversion in KELT-1b is due to its high surface gravity, which we argue could be caused
by the increased efficiency of cold-trap processes within its atmosphere.
1. INTRODUCTION
The atmospheres of hot Jupiters are intricate multi-
parameter systems. An exhaustive understanding of
their atmospheres would include the effects of exter-
nal irradiation, clouds, varying sedimentation efficiency,
surface gravity, internal heat, the bulk metallicity, spe-
cific abundances, and rotation (e.g., Burrows et al. 2006;
Fortney et al. 2008; Showman et al. 2009). Needless to
say, the complicated interplay between these cooperat-
ing and competing affects makes it difficult to isolate the
individual parameters setting hot Jupiters’ observed at-
mospheric properties.
As in stellar astronomy, we have two strong tools with
which to understand hot Jupiters’ complicated atmo-
spheres: differential comparisons between planets to iso-
late and vary one atmospheric parameter of interest, and
the detailed characterization of individual planets using
their atmospheric spectra.
As one particular example of a differential compar-
ison, consider the presence of a stratospheric temper-
ature inversion in a hot Jupiter’s atmosphere. Early
theoretical predictions indicated that most, or all,
hot Jupiters should have TiO- or VO-driven temper-
ature inversions as long as their day sides were hot-
1 Department of Astronomy & Astrophysics, The Pennsylva-
nia State University, 525 Davey Lab, University Park, PA 16802,
USA; tbeatty@psu.edu
2 Center for Exoplanets and Habitable Worlds, The Pennsylva-
nia State University, 525 Davey Lab, University Park, PA 16802,
USA
3 Institute of Astronomy, University of Cambridge, Madingley
Road, Cambridge CB3 0HA, UK
4 Department of Astronomy, The Ohio State University, 140
W. 18th Ave., Columbus, OH 43210, USA
5 Harvard-Smithsonian Center for Astrophysics, Cambridge,
MA 02138, USA
6 Jet Propulsion Laboratory, California Institute of Technol-
ogy, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
ter than the 1900K condensation point of TiO/VO gas
(Fortney et al. 2008). While early broadband measure-
ments of exoplanets’ emission spectra seemed to bear this
out (e.g., Knutson et al. 2008), reanalyses of these early
observations (Diamond-Lowe et al. 2014) and observa-
tions of other systems (e.g., Madhusudhan et al. 2014;
Crossfield 2015) have not yielded any significant detec-
tions of thermal inversions in hot Jupiters with day sides
cooler than around 2500K.
Recently, however, Haynes et al. (2015) reported the
detection of an inversion in the emission spectrum of
WASP-33b. The bulk properties of WASP-33b are pre-
sumably similar to other the hot Jupiters searched for
inversions, except that the day side brightness tempera-
ture of WASP-33b is on average 3300K. Based on this,
Haynes et al. (2015) suggested that stratospheric tem-
perature inversions may only be clearly present in hot
Jupiters with very hot, ∼3000K, day sides. If correct,
this indicates that there are additional aspects beyond
just the condensation point of TiO/VO that govern the
presence of inversion.
To make good differential comparisons, we also need
to make good observations of the planets themselves.
The atmospheric spectra of exoplanets are usually mea-
sured along the planetary terminator via transmission
spectroscopy, or integrated over the day side via eclipse
observations. Most ground-based exoplanet eclipse mea-
surements observe in one of the broadband near infrared
(NIR) filters. These broadband data have shown us the
diversity of albedos and recirculation regimes that exist
in hot Jupiters’ atmospheres (e.g., Cowan & Agol 2011).
However, the low-spectral resolution of these broadband
measurements (R ≈ 5) has made it difficult to use them
to draw strong conclusions about composition or the ver-
tical temperature-pressure structure in individual atmo-
spheres. In large part this is a reflection of the intrinsic
complexity of hot Jupiters’ atmospheres, and the diffi-
2 Beatty et al.
culty in constraining multi-parameter models using rela-
tively sparse datasets.
So far, almost all of spectrally-resolved (R ≈ 50)
exoplanet eclipse observations have been made using
space-based observatories. Based purely on photon-
noise expectations, large ground-based telescopes should
be able to easily exceed the performance of the space
telescopes, but atmospheric affects have proven to be
a large road-block in attempts to collect spectrally-
resolved data from the ground. This has limited
the clear detection of a ground-based eclipse spectrum
to just two systems, HD 189733b (Swain et al. 2010;
Mandell et al. 2011; Waldmann et al. 2012) and WASP-
19b (Bean et al. 2013), with another tentative detection
of an eclipse spectrum from WASP-12b (Crossfield et al.
2012).
After some early non-detections (Richardson et al.
2003), the first clear measurement of an exoplanet’s emis-
sion spectrum from the ground was accomplished by
Swain et al. (2010), using SpeX on the NASA Infrared
Telescope Facility (IRTF) to observe HD 189733b in K
and L at R ≈ 80 in single-slit mode. Nevertheless,
as an example of the difficulty of ground based eclipse
spectroscopy, Mandell et al. (2011) observed an L-band
eclipse of HD 189733b using Keck/NIRSPEC at very
high resolution (R = 27, 000) with a single slit to confirm
Swain et al. (2010)’s measurements, but were unable to
reproduce their results. Mandell et al. (2011) cautioned
that telluric water emission in the L-band could be the
cause of Swain et al. (2010)’s signal. Waldmann et al.
(2012) later collected new SpeX observations of the sys-
tem that showed an L-band eclipse spectrum stronger
than expected from telluric features. Notably, while
Waldmann et al. (2012) observed using a single spec-
trosopic slit, they used one large enough to include a
nearby star that they used as a simultaneous reference.
This improved the quality of their results compared to
Swain et al. (2010).
Crossfield et al. (2012) also used a single slit in their
measurements of WASP-12b’s eclipse, which they also
observed using SpeX. The lack of a reference star unfor-
tunately limited the absolute precision of their measured
eclipse depths, though they were able to make a tenta-
tive (∼ 1σ) detection of WASP-12b’s eclipse spectrum by
differencing the individual spectral wavechannels against
the broadband eclipse light curve. Crossfield et al.
(2012) also includes a detailed and illuminating discus-
sion of their reduction and analysis techniques, which
clearly elucidates the difficulties facing these types of ob-
servations from the ground.
The first ground-based eclipse observations using a
multi-object spectrograph were conducted by Bean et al.
(2013) using the MMIRS instrument on one of the Magel-
lan telescopes. By placing spectral slits over other nearby
stars, Bean et al. (2013) were able to use the other stars
as differential comparisons, and thus remove much of the
systematic noise in their light curve. Using two com-
bined eclipse observations, this allowed them to measure
the H and K emission spectrum from WASP-19b with a
average precision of 380ppm at R ≈ 15.
In an attempt to expand the number of exoplanets for
which we have ground-based eclipse spectra, we spec-
trophotometrically observed an eclipse of the transit-
ing brown dwarf KELT-1b (Siverd et al. 2012). Of the
twelve known transiting brown dwarfs, KELT-1b is the
most irradiated and around the brightest host star, a
combination which allows for high signal-to-noise ra-
tio atmospheric characterization observations. KELT-
1b is a 27MJ brown dwarf on a short, 1.217 day, or-
bit around a 6500K F5V host star. The system has a
model-dependent age of 1.75 ± 0.25Gyr, which would
make KELT-1b a T2 dwarf with an effective tempera-
ture of 1200K if it were an isolated field object. Previous
observations of KELT-1b’s eclipses in z′ (Beatty et al.
2014), Ks (Croll et al. 2014), and at 3.6µm and 4.5µm
(Beatty et al. 2014) have measured day side brightness
temperatures considerably hotter than this, at approxi-
mately 3200K.
We were particularly interested in observing KELT-1b
due to its extremely high surface gravity of 22 times that
of Jupiter. We wished to make a differential comparison
of KELT-1b’s eclipse spectrum against other very hot
Jupiters such as WASP-33b, to observationally investi-
gate the role surface gravity plays in setting the atmo-
spheric properties of hot Jupiters and irradiated brown
dwarfs. Additionally, we were able to use the LUCI1
multi-object spectrograph on the Large Binocular Tele-
scope for our observations. Similar to the Bean et al.
(2013) observations, this allowed us to use multiple spec-
tral slits over multiple stars in the instrument’s field of
view. Using these stars as simultaneous spectrophoto-
metric references allowed us to eliminate much of the
systematic trends in our time series, and allowed us to
approach the typical precision and spectral resolution of
space-based observations in our spectrally-resolved data.
2. OBSERVATIONS AND DATA REDUCTION
We observed a single H secondary eclipse of KELT-
1 (H = 9.534) on the night of UT 2013 October 26
using the LUCI1 near-infrared (NIR) multi-object spec-
trograph on the Large Binocular Telescope (LBT). The
observations began at UT 2013 October 26 0153 and
ran without interruption until UT 0704. This end time
was 45 minutes earlier then scheduled, because the tele-
scope guider failed. The predicted eclipse time was UT
0448, and the predicted eclipse duration was 2.70 hours
(Beatty et al. 2014). Our observations thus covered the
entire duration of the predicted eclipse, plus 1.57 hours
before the predicted ingress and another 0.92 hours af-
ter the predicted egress. At the start of the observations
KELT-1 had an airmass of z = 1.24, crossed through
the meridian at UT 0503 with an airmass of z = 1.007
and ended the observations at z = 1.10. Conditions were
photometric throughout.
For our observations we used a custom slit mask with
LUCI1’s N1.8 camera, the 210 zJHK grating, anH filter,
and a central wavelength of 1.65µm. A the time of our
observations LUCI1 used a Hawaii-2 2048× 2048 pixel
HgCdTe detector, which has since been replaced with an
H2RG detector. The slit mask (Figure 1) used three large
(10”× 30”) slits to image KELT-1 and two nearby com-
parison stars, 2MASSJ00011914+3924347 (“Comp-1”)
and 2MASSJ00011438+3924016 (“Comp-2”). These are
the two brightest stars near KELT-1 that would simulta-
neously fall within LUCI1’s 4’× 4’ field-of-view. The two
comparison stars have H magnitudes fainter, but rela-
tively close, to KELT-1’s (∆H = 0.568 and ∆H = 0.817,
respectively) and similar NIR colors (∆[J −K] = 0.057
KELT-1b H-band Eclipse Observations 3
Fig. 1.— The LUCI1 field of view, showing the positions of
KELT-1, the two comparison stars, and their associated slits. We
used large 10”× 30” slits to avoid slit losses. Note the smaller
narrow slits above and below the stars: these provided a telluric
wavelength reference for each star’s spectrum.
and ∆[J −K] = 0.006, respectively). Comp-1 is located
2’.16 away from KELT-1, and Comp-2 is 2’.62 away. The
orientation of the slit mask placed KELT-1 in the top
half of our images, and the two comparison stars close
together in the bottom half. In addition to the three slits
for the stars, the mask had four smaller slits (2”× 10”)
to observe sky lines and provide a wavelength reference.
We used an observing script that took groups of ten 60
second exposures. We read out using the o2dcr mode,
which has a read time of four seconds. Including other
overhead time, each full repeat of the script took ap-
proximately 13 minutes to complete. This length of time
was driven by the recommendation of the LBT staff to
refresh the guiding once every ten minutes. At the begin-
ning of each script we therefore included a “micro-offset”
of 0”.001 in the telescope guiding to trigger a reset of the
guiding program.
We calculated the BJDTDB time of each image from the
JDUTC mid-exposure time given in each of the fits image
headers. Within each batch of ten images observed by a
single run of our observing script, the images were evenly
spaced every 68.5 seconds. Every tenth image the time
between exposures increased to 85 seconds as the observ-
ing script and guider restarted. In total we acquired 267
images from JD 2456591.57875 to JD 2456591.79486.
In addition to our science images, we took five spectral
flats the afternoon after the night of the eclipse. We used
LUCI1’s “halo3” flat lamp for these exposures, and the
minimum exposure time of 4 seconds. All calibrations
for the LUCI1 spectra were obtained using the onboard
calibration system. Flat field spectra were taken using
the slit mask and the quartz-tungsten halogen (QTH)
continuum lamp, and dark frames were acquired using
the same exposure times as the individual target and
flat-field images. We stacked multiple darks to create
a median dark frame for the science and flat-field spec-
tral images, and subtracted this median dark image from
each frame. This removed most of the artifacts due to
persistent hot pixels on the LUCI1 HgCdTe detector ar-
ray.
Spectral flat fields required special handling because
of the customs slit mask and the need to preserve the
pixel-to-pixel noise characteristics as much as possible.
The individual spectral flats were combined into a me-
dian ‘super flat’. For each slit (exoplanet host and com-
parison stars), we extracted the two-dimensional spectral
flat trace and removed the wavelength-dependent color
term due to a combination of the spectral response of
the system and the spectrum of the QTH continuum cal-
ibration lamp. This produced a zero-color spectral flat
that preserved the pixel-to-pixel gain variations within
the spectral trace plus any residual non-color structure
in the flat. This was done separately for each slit. The
individual two-dimensional zero-color spectral flats for
each slit were then merged back into a single master two-
dimensional spectral flat field image.
There is a small amount of residual flexure in the
LUCI1 spectrograph that is not compensated for by the
internal flexure compensation system. This is because
of the very long visit time (5.2 hours), causing the spec-
trograph to swing through a wide range of orientations
relative to gravity, which stresses the fidelity of the in-
ternal lookup tables used by the open-loop LUCI flexure
compensation system. By comparing all of the science
spectra from the entire run, we created a mask that iso-
lated only those parts of the spectral traces that are com-
mon to all images. This mask was applied to the merged
zero-color spectral flat image, and used to perform the
flat field correction for each of the science images. These
final dark- and flat-corrected science images were used in
the subsequent analysis of the secondary eclipse.
We did not attempt to correct cosmic ray hits in our
images. This was motivated by a desire to remain as close
to the actual observations as possible, and we accepted
that images with cosmic rays in the spectral extraction
region would appear as outliers. We did generate a bad-
pixel mask from the median dark image, which we used to
mask out the effected pixels from our spectrophotometric
extraction process.
We used wide 10” slits on KELT-1 and the comparison
stars so as to avoid slit losses during the observations, but
this had the additional affect of creating broad telluric
features in our science images (e.g., the top panel of Fig-
ure 2). To perform precise photometry on all three stars,
we needed to remove these broad telluric “plateaus” from
our spectra without modifying the flux received from the
stars.
2.1. Telluric Background Subtraction
To remove the telluric features from our data, we first
determined the median sky background in regions away
from the stellar light. We began by taking smaller strips
of each science image around each of the stellar images,
and worked with these individual sub-images. For each
of our three stellar slits, the strip sub-images were 110
pixels tall, and the width of the detector along the dis-
persion axis. We centered the strips on their respective
stellar traces from the first image of the night. Since the
4 Beatty et al.
1220
1240
1260
1280
1300
y
 p
ix
e
l
0
1000
2000
3000
1100 1150 1200 1250 1300 1350
x pixel
0
20
40
60
80
100
(y
 p
ix
e
l)
-1
2
1
0
0
10
20
30
Fig. 2.— An example portion of a science image with (top) tel-
luric background, and after subtraction (bottom). Note that the
scale in the bottom panel is 100 times smaller than the top panel.
The median subtracted background was about 1.5 DN/pixel, on av-
erage, compared to peak counts of approximately 8000 DN/pixel
from the target stars.
images of the three slits drifted by approximately 2 pixels
on the detector over the course of our observations, this
means that the fixed image strips include slightly differ-
ent portions of the slit images as a function of time. As
the telluric background appeared to be constant along
the spatial direction of our slits, we did not consider the
affect of this small slit movement on our results.
We defined the background portions of each 110-pixel
strip to be from row 0 to 20 and then from row 65 to
95. Due to the tilt of the telluric background in each
strip (Figure 2), a straight median of these two back-
ground regions in each strip would smear out many of
the features of interest. We therefore needed to rectify
the background regions of each strip. To do so, we used
the bottom row in each strip as a reference row, and lin-
early shifted each subsequent row in a strip’s background
regions such that it lined up with this reference row. We
used a cubic interpolation to allow for sub-pixel shifts.
The red crosses in the top panel of Figure 2 demonstrate
the shift values for the KELT-1 strip in the first image
of the night. We then took the interpolated-and-shifted
background rows and median combined them to deter-
mine the median telluric background in each strip.
We next subtracted the median background from the
area of each strip around the stellar light. To do so, we
constructed an appropriately tilted median background
estimate near the stars by, first, fitting a quadratic poly-
nomial to the shift values we determined in the back-
ground regions. We used these predicted shifts for each
row near the star light to interpolate-and-shift our pre-
viously determined median background to match. This
allowed us to construct a model of the tilted background,
by extrapolating from both the level of background and
its tilt, in regions of our 2D spectra away from the stellar
light and use it subtract the background near the stars.
The bottom panel of Figure 2 shows an example result
of this subtraction process on a portion of the KELT-1
strip in the first image of the night. In the regions of the
strip away from the star, the median of the subtracted
background is 3.2 DN/pixel for this example image, and
was on average 1.3 DN/pixel for the KELT-1 strips, 1.5
DN/pixel for Comp-1, and 1.9 DN/pixel for Comp-2.
In addition to the interpolate-and-shift method that
we have just described, we also experimented with
the upsample-rectify-downsample telluric subtraction
method described in Stevenson et al. (2014a). We found
the photometry from the two sets of differently re-
duced images to be qualitatively the same. Though
there were small differences between individual measure-
ments, the photometry from both reduction methods
were consistent within 1σ of each other. We do note that
Stevenson et al. (2014a)’s method completed in about
one day, while our subtraction method took a little under
a week to finish.
2.2. Wavelength Calibration
Our primary concern regarding the wavelength cali-
bration of our spectra was to match wavelength ranges
between KELT-1 and the two comparison stars during
the spectrophotometric extraction, and to maintain this
specific wavelength range over the course of the observa-
tions as the stars moved within their slits. To do so, we
first used the telluric lines imaged by each of the narrow
sky slits to determine an initial calibration, and then lin-
early offset this to match the positions of the stars, which
were not centered in their wide slits, by identifying lines
in the stellar spectra.
To perform the telluric wavelength calibration, we used
the four 2”× 10” sky slits positioned immediately above
and below the slits for KELT-1 and the two comparison
stars. All four of these slits showed strong OH emission
lines across their entire spectral range. As shown in Fig-
ure 1, we had two slits above and below KELT-1, one slit
above Comp-1, and one slit below Comp-2. In all of the
sky slits the telluric lines were narrow plateaus approx-
0 500 1000 1500 2000
x-pixel
0
50000
100000
150000
200000
250000
300000
D
N
17450.2Å
17123.9Å
16840.1Å
16079.9Å
15972.4Å
15597.5Å
Fig. 3.— An example of the 1D telluric spectrum we used for
our initial wavelength and dispersion calibration. Nearly all of the
lines present are from atmospheric OH, and we have labeled the
six lines we used in determining our 3rd-order polynomial fit for
pixel as a function of wavelength for each image.
KELT-1b H-band Eclipse Observations 5
imately seven pixels wide. For each slit we extracted a
rectangular region 20 pixels tall centered on the middle
of the spatial axis of the sky slits, and that spanned the
entire width of each image along the dispersion direc-
tion. We created 1D spectra of these extraction regions
by simply summing along the detector columns. We did
not attempt to rectify the telluric lines, as we judged the
uncertainty introduced by their slope (a shift of approx-
imately 0.2 pixels from the top of the extraction range
to bottom) to be small relative to the flat-topped 7 pixel
width of the lines themselves.
For each of the four 1D sky spectra that came from
each science image, we identified the same 6 isolated
OH emission lines (Figure 3) and tracked their posi-
tion for each slit for all of our images. To determine
the center of the lines along the dispersion direction we
used the center-of-light centering method described by
Howell et al. (2006). We fit the measured line centers
by a third-order polynomial that gave x-pixel as a func-
tion of wavelength. The average standard deviation of
these fits was 0.12 pixels, with variation from 0.2 pixels
to 0.05 pixels over the course of the observations. These
polynomial wavelength solutions allowed us to track the
central wavelength and dispersion at the center of the
stellar slits.
Due to small inaccuracies LBT’s guiding, all three of
our observed stars were neither in the center of their slits,
nor did they remain stationary over the course of our ob-
servations. All three stars moved around in the disper-
sion and spatial axes, but for the purposes of wavelength
calibration, we focus here on the movement of the stars
along the dispersion direction.
The total movement along the dispersion axis is rel-
atively small, no more than 3 pixels from the start lo-
cations, but trends from this movement were present in
the initially uncorrected spectrophotometry. To trans-
late the telluric wavelength calibration onto the sky slits,
we treated the offset and motion of the stars along the
dispersion direction of the detector as a linear offset to
the telluric calibration; we did not attempt to correct for
any variations in dispersion. To track the motion of the
stars, we identified and centroided the Brackett 15-4 line
in the spectra of KELT-1 and the two comparison stars.
We created the 1D spectra we used for this line tracking
by doing a simple spectral extraction in a rectangular
area 30 pixels tall that was centered on the position of
the stars in the first image of the night, and spanned
the width of the detector. Figure 4 shows the resulting
1D spectra for KELT-1 stacked vertically and zoomed on
the line we identified. The overplotted red line shows the
line centroid locations, which we determined by fitting a
Gaussian profile of variable width to the 1D spectra. The
motion of the line over the course of the observations is
clearly visible. Of particular note is the sudden move-
ment of the line to the right around image number 150.
We discuss this event in more detail in Section 3 and 3.5,
as it introduced significant systematics into our photom-
etry. For now, knowing the true wavelength of this line,
we calculated an offset from the previously determined
telluric wavelength solution, to transfer this solution to
the true positions of the stars.
With the initial wavelength and dispersion calibration
provided by the telluric emission imaged by the sky slits,
and the offset provided by the stellar line tracking, we
1800 1805 1810 1815 1820 1825 1830 1835 1840
x-pixel
50
100
150
200
Im
a
g
e
 N
u
m
b
e
r
Fig. 4.— Motion of the Brackett 15-4 line in KELT-1’s spectrum
over image number. The red line is the fitted line centroid position.
The sharp feature at about image no. 150 leads to a “bump” in our
photometry halfway through the eclipse (Figure 6). We believe it
was caused by a shift in the telescope or instrument optics shortly
after crossing the meridian.
were able to define a constant wavelength region along
the dispersion axis on the detector for each star in each
image for the following spectrophotometric extraction.
Recall from Figure 1 that to fit all three target stars
within LUCI1’s field of view, we were not able to align
the stars along the dispersion direction. This means that
the spectra for each covered slightly different wavelength
ranges. Due to the motion of the stars on detector the
exact range changed with each image, but was gener-
ally 1.55µm to 1.75µm for KELT-1, 1.52µm to 1.72µm
for Comp-1, and 1.55µm to 1.75µm for Comp-2. We
found that including Comp-1 in the detrending offered
no improvement to the results, and so used only Comp-
2. The total overlapping wavelength region available be-
tween KELT-1 and Comp-2 was therefore from 1.55µm
to 1.75µm. This is slightly narrower thanH-band, which
is generally from 1.50µm to 1.80µm.
3. LIGHT CURVE EXTRACTION AND FITTING
We wished to measure both the broadband, H , eclipse
depth of KELT-1b, and to spectrally resolve the eclipse
to measure depth changes as a function of wavelength
within the H-band. This led us to use slightly different
spectrophotometric extraction techniques, and different
fitting parameters, for the broadband and the spectrally-
resolved light curves. Our fitting technique remained the
same between the two types of measurements.
An initial examination of both the broadband and
spectrally-resolved spectrophotometry showed strong
correlated variability in our measured time series. First,
we noticed a clear bump in the spectrophotometry
around JD 2456591.70, or image number 150. As shown
in Figure 4, this corresponds to a sudden shift to the
right in the position of KELT-1 within the spectral slit.
This event also occurred at the same time that the entire
spectral trace for KELT-1 deformed towards the right
6 Beatty et al.
of our images, which we consider to be the root cause
of the KELT-1’s apparent motion within its slit. The
change in the shape of the trace points towards an event
within the optics of LUCI1, but we have no direct infor-
mation about the optics during the observations. Our
best theory, since the shift happened approximately 15
minutes after the telescope passed through the meridian,
is that shortly after the meridian crossing some portion
of LUCI1’s optics shifted position slightly, causing the
deformation of the trace, the shift of KELT-1’s apparent
position, and the bump in the spectrophotometry.
Second, we presume that the Hawaii-2 detector in use
with LUCI1 at the time of our observations showed the
same sort of linearity (and flux-dependent non-linearity)
effects that are common to all NIR detectors. Unfortu-
nately, no characterization of the linearity of the detec-
tor was done before it was replaced in the spring of 2015,
and since the exact linearity corrections vary between
NIR detectors, we did not consider it appropriate to use
the linearity corrections derived for another chip. We
therefore did not attempt any linearity correction to our
science images. Since the peak counts in our images was
about 8,000 adu pix−1, which is about 12% of the full-
well depth in the LUCI detectors, presumably the actual
linearity correction would have been relatively low.
Another possible source of systematic uncertainty in
our observations is the possible stellar companion to
KELT-1 discovered by Siverd et al. (2012). The com-
panion is located 558 mas to the southeast of KELT-1,
and has ∆H = 5.90± 0.10 and ∆K ′ = 5.59± 0.12. The
companion is unresolved in our observations. Based on
the the ∆H measurement of the companion to KELT-
1, it contributes approximately 0.4% of the system light
in the wavelength range we observed. This is substan-
tially below the fractional uncertainty we calculate for
the broadband eclipse depth (about 7%). We therefore
chose to ignore its contribution to our observations.
3.1. Fitting via Non-parametric Gaussian Processes
To deal with the correlated noise in our spectropho-
tometric time series, we choose to fit the eclipse data
via a non-parametric Gaussian process (GP) regression.
We initially attempted to fit the eclipse using a more
traditional polynomial decorrelation against the major
systematic noise variables (e.g., telescope focus and air-
mass). This polynomial detrending gave a fit to the
eclipse that looked reasonable and had a formal uncer-
tainty on the eclipse depth that was on the order of 5%.
Unfortunately,a closer investigation showed that the final
measured properties of the eclipse changed significantly
depending upon the choice of decorrelation function we
made (i.e., linear, quadratic, etc.), and upon what spe-
cific variables we were decorrelating against (time vs. air-
mass, for example). The changes in our measurements of
the eclipse properties were typically two to three times
larger than the formal uncertainty we determined for any
specific set of decorrelation choices. We therefore con-
cluded that the correlated noise in our data was causing
a measurement uncertainty that was not being correctly
captured or dealt with by the polynomial decorrelation
techniques.
This conclusion prompted us to investigate using a GP
to fit our eclipse data, since one way to conceptualize
a GP is as a marginalization over many possible sys-
tematic noise models. More specifically, a GP models
the observed data points as random draws from a multi-
variate Gaussian distribution about some mean function.
This is in contrast, for example, to a χ2 fitting process,
which models the data as random draws from a univari-
ate Gaussian distribution. As a result, GPs are able to
model the possible covariances between data points while
remaining relatively agnostic about the precise functional
form of the systematic noise model.
GP methods were first used in the context of time se-
ries observations of exoplanets by Gibson et al. (2012),
though they have a longer history in the general astro-
nomical community (e.g., Way & Srivastava 2006). For
a detailed mathematical introduction to GPs, we refer
the reader to Rasmussen & Williams (2006), and to Ap-
pendix A of Gibson et al. (2012).
We will define our GP model using the notation from
Gibson et al. (2012). Let us describe our observed
N data points as a vector of observed fluxes, f =
(f1, ..., fN)
T , with a vector of corresponding observed
times, t = (t1, ..., tN )
T . Additionally, we will keep track
of K state parameters (e.g., airmass and telescope focus)
at each time t with the state vector x = (xt,1, ..., xt,K)
T .
For compactness, we will combine these state parame-
ter vectors for each of our N observations in the N ×K
matrix, X . Our GP model will use an eclipse model
E(t, φ) as its mean function, where φ is the set of phys-
ical parameters describing the eclipse. Finally, let us
define the multivariate Gaussian distribution underlying
the GP model with the N × N × K covariance matrix
Σ(X, θ), where θ is the set of “hyperparameters” used
to generate the covariance matrix from the X state pa-
rameters. This allows us to write the joint probability
distribution of our observed data f as
p(f |X, θ, φ) = N [E(t, φ),Σ(X, θ)], (1)
where N represents the multivariate Gaussian distribu-
tion. Our GP model will therefore depend upon on an
eclipse model E(t, φ), and a generating function – re-
ferred to as the covariance kernel – for the covariance
matrix Σ(X, θ). We generated our GP covariance matri-
ces and calculated the GP likelihoods using the George
python package (Ambikasaran et al. 2014).
While we used the same eclipse model to fit both the
broadband and spectrally-resolved datasets, we needed
to choose different covariance kernels for each set of ob-
servations. We describe our exact choice of covariance
kernels in Sections 3.3 and 3.4.
3.2. The Eclipse Model, Parameters, and Priors
For the mean function of our GP model, we use a
Mandel & Agol (2002) eclipse light curve. To generate
our eclipse light curves we used the batman (Kreidberg
2015) implementation of Mandel & Agol (2002) algo-
rithm. We modeled the eclipse by assuming KELT-1b
was a uniformly bright disk, with no limb-darkening, be-
ing occulted by the much larger KELT-1.
We parameterized the broadband eclipse model using
the quantities
φbroad=(TS,pred, logP,
√
e cosω,
√
e sinω, (2)
cos i, RP /R∗, log a/R∗, δ).
These eight parameters are the predicted time of the
KELT-1b H-band Eclipse Observations 7
secondary eclipse (TS,pred), the orbital period (log(P )),√
e cosω,
√
e sinω, the cosine of the orbital inclina-
tion (cos i), the radius of the planet in stellar radii
(RP /R∗), the semi-major axis in units of the stellar radii
(log[a/R∗]), and the eclipse depth (δ).
For seven of these parameters (TS,pred, log(P ),√
e cosω,
√
e sinω, cos i, RP /R∗, and a/R∗), we had
strong prior expectations for their values from the KELT-
1b discovery paper (Siverd et al. 2012) and the pre-
viously observed eclipses of the system (Beatty et al.
2014). We did not have a prior expectation for the eclipse
depth, δ.
We assumed Gaussian priors on the eclipse parame-
ters for which we have previous information, which we
note does not consider any possible covariances between
the parameters. We used the average central values
and 1σ uncertainties for log(P ),
√
e cosω,
√
e sinω, cos i,
RP /R∗, and log(a/R∗) from the two eclipses observed by
Beatty et al. (2014), which were themselves based on the
results of the free-eccentricity fit in Siverd et al. (2012).
For the predicted time of secondary eclipse, we took
the straight average of the two eclipse times measured by
Beatty et al. (2014) to determine an epoch-zero eclipse
time, and then used the period and associated period
uncertainty of KELT-1b to predict the eclipse for the
time of the our observations.
Regarding the period of KELT-1b, observations of the
transits of the system over the past several years by the
KELT follow-up network have demonstrated to us that
the period given in the discovery paper is slightly too
long: the discovery ephemeris currently gives predicted
transit times that are approximately 30 minutes late. To
refine the ephemeris for our eclipse observations, we ob-
served a full transit of KELT-1b using the 1.2m tele-
scope at the Fred L. Whipple Observatory (FLWO) on
the night of UT October 18 2013.
We observed the transit using KeplerCam on the 1.2m
telescope. KeplerCam has a single 4K×4K Fairchild
CCD with a pixel scale of 0”.366 pixel−1, for a total
FOV of 23’.1×23’.1. We observed the complete transit
of KELT-1b on the night of UT October 18 2013 in the
SDSS i′ filter with 30 second exposures. We reduced
the data using a light curve reduction pipeline outlined
in Carter et al. (2011), which uses standard idl tech-
niques. We fit the reduced light curve using exofast
(Eastman et al. 2013) using priors on the transit param-
eters from Siverd et al. (2012).
The measured transit center time from these obser-
vations of BJDUTC = 2456583.78435 ± 0.0006 allowed
us to considerably refine the orbital period of KELT-
1b. Using the transit center time given in Siverd et al.
(2012), we determined a new orbital period of P =
1.217494± 0.000004 days. This is approximately 1.6 sec-
onds, and 1.2σ, shorter than the discovery’s paper period
of P = 1.217513± 0.000015 days.
As we have no prior expectation for the value of δ,
we do not include a probability penalty for this term,
and therefore implicitly assume a uniform prior. We al-
lowed for negative values of δ in both the broadband and
spectrally-resolved fits.
For the spectrally-resolved eclipse observations, due
to the relatively low signal-to-noise of the spectrally-
resolved data we used an eclipse model with depth and
secondary eclipse time as the free parameters:
φspec = (δ, TS). (3)
We fixed the other parameters of the spectrally-resolved
eclipse model (logP,
√
e cosω,
√
e sinω, cos i, RP /R∗,
log a/R∗) to the values which we determined from our
broadband eclipse measurements. For TS , the secondary
eclipse time, we imposed a Gaussian prior from the time
and uncertainty we measured in the broadband data.
3.3. Broadband Spectrophotometric Extraction and GP
Parameters
Using our previously determined wavelength calibra-
tion for KELT-1 and the comparison star Comp-2, we
defined a constant region in wavelength space where both
stars overlapped, from 1.55µm to 1.75µm, on our tel-
luric subtracted images to extract our spectrophotom-
etry. To create our final summed spectrophotometry,
we first summed along a limited range of the detectors’
columns within this constant wavelength region. We de-
fined the vertical limits of the extraction area relative to
the stellar trace in each column of the detector. That is,
for a given column x, the vertical extraction limits were
from T (x) − H(M1Z) to T (x) + H(M1Z), where T (x)
is the vertical position of the stellar trace in column x,
and H(M1Z) is the vertical half-height of the extraction
area. Note that the height of the extraction area de-
pended upon the m1z value in the fits headers for our
images. We explain this in more detail below.
To determine T (x) for each of our three stars, we fit a
9th-order polynomial to the spectral traces in each im-
age. We determined the positions of the traces by fit-
ting variable-width Gaussian profiles along the detector
columns once every 20 columns. This gave us 101 (x, y)
positions, which we used to determine the polynomial fit
to the trace.
In both the horizontal and vertical directions on the
detector the borders of our extraction areas did not fall
along integer pixel values, but partially included these
edge pixels. We determined the flux contribution from
these partially covered edge pixels via linear interpola-
tion.
To determine the appropriate value forH , the height of
the extraction area, we initially trialled several constant
values ofH , but found that the resulting broadband time
series was strongly anti-correlated with the m1z fits
header values. m1z roughly captures the value of the
telescope’s focus, and visual inspection of our telluric-
subtracted images showed that the vertical width of all
three stars’ spectra decreased with increasing m1z, and
vice versa.
To account for the slightly varying focus of the tele-
scope and the slightly varying width of our spectra, we
therefore choose to use a variable value of H that de-
pended upon the value of m1z for each image. Specifi-
cally, we set H to be
H(M1Z) = H0 + C
(
M1Z
M1Z
− 1
)
, (4)
whereH0 is some baseline value, M1Z is the average value
of m1z over all our observations, and C is some scaling
constant.
8 Beatty et al.
10 12 14 16 18
H0
10
12
14
16
18
20
C
10 12 14 16 18
H0
10 12 14 16 18
H0
1200 1350 1500 1650 1800 550 600 650 900 100011001200
Depth (ppm) RMS (ppm) Ln(p)
Fig. 5.— We scaled the spectrophotometric extraction aperture to the m1z value for each image, which roughly corresponds to the
telescope’s focus (Equation [4]). H0 = 13 and C = 15 gave the combination of the lowest RMS and the highest ln(p), and we use these
values for our extraction. Note that in the far left panel the plotted contours correspond to multiples of our final 1σ uncertainty on the
eclipse depth. The upper left area on all three panels gave extremely poor fitting results, and we excluded these from the plots.
To determine appropriate values for both H0 and C,
we tested values of H0 from 10 to 20 pixels, in integer
steps, and values of C from 10 to 20 in steps of 0.5. For
each combination of values, we extracted and summed
the spectrophotometry for all three stars, and then per-
formed the initial maximization stage of our fitting pro-
cedure, which we describe in Section 3.5. This gave us
an initial fit to the eclipse light curve, and we recorded
the root-mean-squared (RMS) scatter of the residuals,
the ln(p) value of the fit, and the depth of the eclipse.
As shown in Figure 5, we found optimal values of
H0 = 13 and C = 15, which makes the angular half-
height of the extraction box roughly 3.′′25. This gave the
combination of the lowest RMS and the highest ln(p)
(Equation [10]). Note in the right-most panel of Figure
5 that the broadband eclipse depths from these trial fits
remained relatively constant near our choice for the op-
timum aperture: the fitted depths have a scatter of 90
ppm, while our final broadband eclipse depth has an un-
certainty of 94 ppm. We therefore do not consider that
our final results are affected above our errors by the pre-
cise choice of H0 and C.
3.3.1. Broadband Covariance Kernel and Hyperparameter
Priors
Recall that we are defining the multivariate Guassian
distribution underlying our GP model by its covariance
matrix, Σ(X, θ), and the covariance matrix’s associated
generating covariance kernel.
For our broadband spectrophotometry, we adopted a
relatively simple “squared-exponential” kernel using time
as the sole input state parameter. This allowed us to
generate a squareN×N covariance matrix for each point-
wise combination of observation times ti and tj as:
Σ(t, θ) = At exp
[
−
(
ti − tj
Lt
)2]
, (5)
where θ = {At, Lt} are the hyperparameters setting the
amplitude and the length-scale of the point-wise covari-
ance.
A squared-exponential kernel is generally used in GP
modeling to account for variations in the data that occur
smoothly as a function of the input state parameter. This
makes it a good general choice for a covariance kernel, as
a squared-exponential is usually regarded as the simplest
choice for a kernel.
In our fitting, we do not impose any prior on the kernel
amplitude or the length-scale, other than requiring that
the length-scale cannot be less than or equal to the pre-
dicted eclipse ingress and egress durations of 0.09 days.
This lower limit on the allowable length-scale values en-
sures that the GP model does not treat the eclipse itself
as correlated noise.
3.4. Spectrally-resolved Spectrophotometric Extraction
and GP Parameters
We extracted the spectrally-resolved spectrophotome-
try for KELT-1 and the comparison stars in the same
way as we did for the broadband eclipse measurement,
except that we divided the spectrum of each star into
five evenly-spaced wavelength bins using our wavelength
calibration. We used the same scaling relation with m1z
to vary the extraction width as we did for the broad-
band extraction, and we set H0 = 13 and C = 15: the
optimum values we found using the broadband results.
As with our broadband photometry, we detrended each
individual wavechannel against the corresponding sec-
KELT-1b H-band Eclipse Observations 9
0.996
0.998
0.999
1.000
1.002
1.004
In
te
n
si
ty
1.60 1.65 1.70 1.75
BJD - 2456590
−0.00150
−0.00075
0.00000
0.00075
0.00150
O
-C
1.60 1.65 1.70 1.75
1.60 1.65 1.70 1.75
BJD - 2456590
Fig. 6.— Raw (left) and detrended (right) broadband photometry. The solid red line in the left panel shows the predictive mean of our
Gaussian Process regression, which is a combination of the eclipse model and the noise model. The dashed red line in the left panel shows
only the noise model. In the right panel, the red line is just the fitted eclipse model. The lower panels both show the residuals to our best
fit model.
tions of the comparison stars’ spectrophotometry. Again,
we found that including the star Comp-1 in the detrend-
ing ensemble provide no improvement in the resulting
light curves, and so we only used Comp-2 for detrending.
This allowed the data to cover from 1.55µm to 1.75µm
(i.e., Section 2.2).
3.4.1. Spectrally-resolved Covariance Kernel and
Hyperparameter Priors
Since our spectrally-resolved light curves showed no-
ticeably more correlated noise than the broadband spec-
trophotometry, we used a higher dimensional covariance
matrix to model these additional noise sources. Visual
examination of the spectrally-resolved data showed cor-
relations between the measured flux and airmass (X).
Again, in an attempt to keep our GP model as simple as
possible, we used squared-exponential kernels to describe
all of these covariances.
First, we included the same temporal covariance as in
the broadband GP model with
Σt(t, θ) = exp
[
−
(
ti − tj
Lt
)2]
. (6)
Next, we modeled the affect of changing airmass with the
kernel
Σair(X, θ) = exp
[
−
(
Xi −Xj
Lair
)2]
. (7)
We multiplicatively combined these two individual ker-
nels together into one total kernel that we used for our
spectrally-resolved GP model,
Σtotal(t,X, θ) = Atotal ΣtΣair, (8)
where θ = {Atotal, Lt, Lair} are the four hyperparameters
setting the properties of the covariance kernel.
We combined the kernels via multiplication to effect
the equivalent of a Boolean “AND” operation in the
generation of our GP covariance kernel, in contrast to
combining the kernels via addition, the method used
in Gibson et al. (2012), which gives the equivalent of a
Boolean “OR.”
During the fitting of the spectrally-resolved light
curves we did not impose a prior on any of the am-
plitude terms, and only imposed hard lower limits on
all of the coavariance length scales, to prevent the GP
model from fitting out the eclipse, or attempting to fit
the white noise. Specifically, we required Lt > 0.09 and
Lair > 0.01.
3.5. Fitting Process and Results
For both the broadband and spectrally-resolved data
we used the same general fitting procedure to find the
model parameters with the maximum likelihood and to
estimate our parameter uncertainties. Specifically, we
optimized the combined likelihood of our GP model and
our priors. The natural logarithm of our GP model like-
lihood was
ln pGP(r|X, θ, φ) = −1
2
r
TΣ−1r − 1
2
ln |Σ| − N
2
ln(2pi),
(9)
where r = f −E(t, φ) is the vector of the residuals of our
observed data (f) from our eclipse model (E) defined in
Section 3.2. This log-likelihood follows directly from our
definition of the GP model in Equation (1).
Our combined log-likelihhod function combined the
GP log-likelihood with our priors, as
ln ptot(φ, θ|f,X) = ln pGP(r|X, θ, φ) +
∑
ln pprior. (10)
10 Beatty et al.
Fig. 7.— Covariance plot for the broadband fitting process. We
find that there is little covariance between our model parameters.
We assigned Gaussian priors to all of the eclipse parame-
ters, except the eclipse depth, as described at the end of
Section 3.2 and Table 1. Recall that we fit for all of the
eclipse parameters with the broadband data, and only
the eclipse time and depth for the spectrally-resolved
data. For the hyperparameters, we imposed no priors,
other than to impose a lower limit on the covariance
length scales as described in Sections 3.3.1 and 3.4.1.
Our fitting process began by using a Nelder-Mead max-
imization to find an initial log-likelihood maximum to use
as an estimate of the best fit. We then used MCMC to ex-
plore the parameter space around the log-likelihood max-
imum to determine uncertainties and to verify that we
had correctly identified the global likelihood maximum.
To perform the MCMC computations we used the emcee
Python package. Our MCMC runs began with a 500 step
burn-in, followed by 3000 production steps. At the end
of the production run we verified that the MCMC chains
had converged by calculating the Gelamn-Rubin statis-
tic for each free parameters, and we judged the chains
to have successfully converged if all the Gelman-Rubin
statistics were smaller than 1.1.
The results of our fit to the broadband data are shown
in Figures 6, 7, and listed in Table 2. Our best fit gave
δ = 1418± 94ppm, This depth uncertainty is about four
times what one would expect from photon noise noise
alone. An Anderson-Darling test of the residuals gave
a test statistic of 0.177, indicating that the distribution
of the residuals was consistent with a Gaussian distribu-
tion. One feature to note in Figure 6 is the “bump” that
occurs around mid-eclipse. The timing of this event cor-
responded exactly with the jump in KELT-1’s measured
position shown about half-way up Figure 4. This nicely
demonstrates the necessity of keeping the target stars
stationary – or at least moving slowly – on the detector
during these types of observations.
Figures 8 and Table 3 show the results of our fits to
1.60 1.65 1.70 1.75
BJD-2456590
0.965
0.970
0.975
0.980
0.985
0.990
0.995
1.000
1.005
In
te
n
si
ty
1.55-1.59µm
1.59-1.63µm
1.63-1.67µm
1.67-1.71µm
1.71-1.75µm
Fig. 8.— The detrended sepctrally-resolved eclipse light curves.
The flux in each individual wavechannel is plotted with an increas-
ing offset from unity, for visual clarity.
the spectrally-resolved eclipses. We clearly detected the
eclipse in each wavechannel, but did not see a shift in
the eclipse timing above the measurement uncertainties.
We computed an Anderson-Darling test statistic for the
residuals in each wave channel of the spectrally-resolved
eclipse measurements, and found that all five were consis-
tent with a Gaussian distribution. The uncertainties in
the depth measurements were four times what one would
expect from photon noise alone.
The average brightness temperatures of the spectrally-
resolved eclipses corresponds to 3420 ± 70K, which is
2.3 σ higher than the average day side brightness tem-
perature of 3220 ± 50K one calculates using all of the
available eclipse measurements.
4. MODELING AND DISCUSSION
KELT-1b is a relatively unique object, in that it is one
of the twelve known brown dwarfs in a close orbit around
a single main sequence star. This makes the external
atmospheric forcing from the incoming stellar irradiation
of KELT-1 similar to hot Jupiters, while the mass of
KELT-1b and its implied internal energy are similar to
field brown dwarfs. We therefore approached the analysis
KELT-1b H-band Eclipse Observations 11
1 2 3 4 5
Wavelength (µm)
0
500
1000
1500
2000
2500
3000
F
P
/F
S
 (
p
p
m
)
Decreasing
Inverted
Isothermal
This Work
Prev. Obs.
1.55 1.60 1.65 1.70 1.75 1.80
Wavelength (µm)
1000
1200
1400
1600
1800
F
P
/F
S
 (
p
p
m
)
2000 2500 3000 3500 4000
Temperature (K)
10-5
10-4
10-3
10-2
10-1
100
101
P
re
ss
u
re
 (
b
a
r)
Fig. 9.— Our modeling of KELT-1b’s H emission spectrum and previous the broadband eclipses measured by Beatty et al. (2014) and
Croll et al. (2014) using Madhusudhan & Seager (2009)’s planetary atmosphere models favors a monotonically decreasing temperature-
pressure (TP) profile. We exclude an 3250K isothermal TP profile at 3.3σ and an inverted TP profile at 8σ.
of KELT-1b’s measured eclipse depths from two different
directions.
4.1. Atmospheric Modeling Results
First, we modeled our spectrally-resolved eclipse
depths, together with the previous eclipse measurements
at other wavelengths, using the hot Jupiter atmospheric
model described in Madhusudhan & Seager (2009) and
Madhusudhan (2012). This model is comprised of a 1D
plane parallel atmosphere in hydrostatic equilibrium and
local thermodynamic equilibrium (LTE). The emergent
spectrum is computed using a 1D line-by-line radiative
transfer solver in the planetary atmosphere. The atmo-
spheric temperature-pressure (TP) profile and chemical
composition are free parameters of the model, with 6
parameters for the TP profile and a parameter each for
each chemical species included in the model. The range
of molecules considered and the sources of opacity are
discussed in Madhusudhan (2012).
In the present work, our goal was to obtain a general
understanding of the model parameter space consistent
with the data rather than finding a unique best fit. We
therefore assumed three different cases for the TP pro-
file, and then fit for the best models that generally rep-
resented these three cases. The three TP profiles we
considered were one that was monotonically decreasing,
a profile with a thermal inversion, and an isothermal TP
profile. We fixed the composition to be that predicted for
chemical equilibrium with Solar elemental abundances
for all three TP profiles, since we found that letting the
abundances vary did not affect our conclusions regarding
the temperature profile of KELT-1b’s atmosphere.
Of the three TP profiles we considered, our model-
ing preferred a monotonically decreasing TP profile in
KELT-1b’s upper atmosphere using Solar values for the
bulk atmospheric metallicity (Figure 9), with a best fit of
χ2 = 12.97 for eight degrees of freedom (χ2/dof = 1.62).
We exclude an 3250K isothermal TP profile at 3.9σ
(χ2/dof = 3.94) and an inverted TP profile at 8.2σ
(χ2/dof = 11.50) at Solar metallicities.
Visually, the lack of a thermal inversion is evident even
without considering the model spectra. The H-band
typically probes the continuum in a planetary spectrum
due to lack of strong molecular absorption features in
this spectral range (Madhusudhan 2012). As such, the
brightness temperature in the H-band is representative
of the deepest layers of the observable atmosphere, below
which a combination of several factors, such as increased
density and collision-induced absorption, makes the at-
mosphere inaccessible in the visible and infrared. On the
other hand, the Spitzer IRAC bands at 3.6µm and 4.5µm
contain strong molecular bands due to all the prominent
molecules expected in H2-rich atmospheres.
7 In particu-
lar, at the approximately 3200K temperatures of KELT-
1b’s day side, H2O and CO provide strong absorption
in the 3.6µm and 4.5µm bands, respectively. When the
atmospheric TP profile is monotonically decreasing, ab-
sorption absorption from these two molecules leads to
lower brightness temperatures in these two bands than
that observed in the H-band. This is indeed what the
observations show. Conversely, if the TP profile were in-
verted with the temperature increasing outward, or if it
were isothermal, the brightness temperatures at 3.6µm
and 4.5µm would be greater than or equal to that in the
H-band. Both these scenarios are ruled out by the data.
7 H2O, CO, CH4, and CO2 depending on the elemental abun-
dances and temperature.
12 Beatty et al.
1 2 3 4 5
Wavelength (µm)
0
500
1000
1500
2000
2500
3000
F
P
/F
S
 (
p
p
m
)
Field M5
Low Grav. M6
Isothermal
This Work
Prev. Obs.
1.55 1.60 1.65 1.70 1.75 1.80
Wavelength (µm)
1000
1200
1400
1600
1800
F
P
/F
S
 (
p
p
m
)
Fig. 10.— Measured thermal emission from KELT-1b from this paper, Beatty et al. (2014), and Croll et al. (2014). Also plotted are the
best fit 3250K blackbody curve and template spectra for a high gravity field brown dwarf and low gravity brown dwarf. The normalization
of the template spectra are computed using model predictions for the H brightness of these objects, and is not a free parameter. The
striking agreement between the observed emission spectrum of KELT-1b’s day side and the field templates is another indication that the
TP profile in KELT-1b’s upper atmosphere is monotonically decreasing.
4.2. Brown Dwarf Spectral Typing and Surface Gravity
Indicators
Second, we compared the day side atmosphere of
KELT-1b to high-gravity field brown dwarfs, and low-
gravity young brown dwarfs, by comparing the measured
eclipse depths to spectral templates. To do so, we used
field object templates from the SpeX Library covering
spectral types from M4 to T9 and young, low-gravity,
templates from Allers & Liu (2013) covering spectral
types from M5 to T9. Using a 6500K blackbody for the
emission from the star KELT-1, we transformed these
template spectra from normalized flux vs. wavelength
to expected eclipse depth vs. wavelength. We normal-
ized the resulting eclipse spectra using the absolute H
magnitudes for these objects predicted by the BT-Settl
models (Allard et al. 2011) using the Caffau et al. (2011)
values for Solar abundances. There were therefore no
free parameters in our spectral typing process: the rel-
ative luminosities of KELT-1 and the field spectra were
set by the BT-Settl predictions. We used the observed
z′ (Beatty et al. 2014) and Ks (Croll et al. 2014) eclipse
depths in addition to our spectrally-resolved depths to
evaluate the fit to the spectral templates.
We find that the day side of KELT-1b appears to have
a field spectral type of M5+1
−2, and a low-gravity spectral
type of M6+1
−3 (Figure 10). This is almost entirely due to
the spectral slope of the eclipse depths from 1.55µm to
1.65µm, which drives the template fitting towards rel-
atively broad wings for the H2O absorption feature at
1.4µm. Both the field and low-gravity templates fit the
measured eclipse depths extremely well, with χ2 = 1.34
(χ2/dof = 0.19) for the field template and χ2 = 4.39
(χ2/dof = 0.63) for the low-gravity template, both with
seven degrees of freedom.
The goodness of fits for both spectral templates is quite
striking considering that we allowed for no free param-
eters in the comparison process. Both spectral types
correspond to effective temperatures of approximately
3200K, which approximately the same as our average
measured brightness temperatures for KELT-1b at these
wavelengths. More generally, the exquisite agreement be-
tween the observed emission spectrum of KELT-1b’s day
side and the field templates is also indicative that the TP
profile in KELT-1b’s upper atmosphere is monotonically
decreasing, since both the field and low-gravity brown
dwarfs are expected to steady cool going towards lower
pressures in the outer portions of their atmospheres.
While our spectrally-resolved results appear to show
the “peaky H-band” feature typically used to identify
low-gravity objects at later spectral types, by M5 this
feature and its associated H-cont spectral index have
largely lost their power to distinguish between field and
low-gravity brown dwarfs (Allers & Liu 2013). As a
result, as illustrated by the inset in Figure 10, our
spectrally-resolved results are not sufficient to give a clear
preference to a field or a low-gravity spectral template.
The broadband H − K colors of KELT-1b’s day side
are similarly non-discriminatory. Using the measured
H and Ks eclipse depths for KELT-1b from this work
and from Croll et al. (2014), and the distance for KELT-
1 determined by Siverd et al. (2012), we compared the
day side NIR colors of KELT-1b’s atmosphere to the
field (Dupuy & Liu 2012) and young (Gagne´ et al. 2015)
brown dwarf color-magnitude sequences (Figure 11).
Young isolated brown dwarfs are typically slightly redder
than older, field objects at the same absolute magnitude
KELT-1b H-band Eclipse Observations 13
(Liu et al. 2013). Physically, this redward offset occurs
due to the lower surface gravity and higher internal heat
of the younger objects. Given the apparent inflation of
KELT-1b’s atmosphere (Siverd et al. 2012), we might ex-
pect that it would appear more similar to these younger
objects than the higher surface gravity field brown dwarfs
While our measured H −K color for KELT-1b’s day
side is consistent with it laying along the general color
sequence for brown dwarfs, the uncertainties on make it
difficult to distinguish if the broadband properties of the
atmosphere are more similar to a young or a field brown
dwarf. We do find it more likely that the day side colors
of KELT-1b are that of a field brown dwarf, but this is
at a low (1.6 σ) significance.
4.3. The Lack of a Stratopsheric Temperature
Inversion
As mentioned in the introduction, early expectations
were that hot Jupiters with day sides hotter than ap-
proximately 1900K should show a stratospheric temper-
ature inversion in their TP profiles due to the presence
of gaseous TiO or VO (Fortney et al. 2008). However,
subsequent eclipse observations of several giant planets
with day side temperatures of 2000K to 2500K showed
no convincing evidence for an inversion in their day side
emission spectra (Madhusudhan et al. 2014; Crossfield
2015). Given the theoretical expectation that TiO/VO
should be generically present in the atmospheres of gi-
ant planets, Spiegel et al. (2009) posited that a vertical
“cold-trap” might strongly deplete the TiO/VO abun-
dance in the upper atmosphere of hot Jupiters. Given the
strong day-night contrast observed on hot Jupiters with
day sides hotter than 2000K (e.g., Komacek & Showman
2016, and references therein), Parmentier et al. (2013)
later suggested that a day-night cold-trap would also be
able to deplete the TiO/VO abundance in the upper at-
mospheres of these hot giant planets.
Both a vertical and day-night cold-trap envision TiO
and VO raining-out of a hot Jupiter’s upper atmosphere,
by condensing from the gas phase and then gravitation-
ally settling into the planetary interior. In the case of
a vertical cold trap, the day side TP profile is assumed
to cross below the TiO or VO condensation curves at
some point relatively high in the atmosphere. Gas-phase
TiO/VO molecules that happen to fall below this height
will then begin to condense and fall further into the at-
mosphere. Without some vigorous mechanism to loft the
TiO/VO condensates back into regions hot enough for
TiO/VO gas, Spiegel et al. (2009) found that this process
would rapidly deplete an upper atmosphere’s gas-phase
TiO/VO.
A day-night cold-trap is broadly similar, but is instead
caused by TiO/VO condensing on the cooler night side of
a hot Jupiter. Briefly, if TiO/VO molecules can condense
and fall far enough while they cross the cold night side
of a planet, they will not be able to diffuse back into
the upper atmosphere when they revaporize on the day
side. Parmentier et al. (2013) found that if TiO/VOwere
to condense into particles larger than a few microns on
the night sides of hot Jupiters, then a day-night cold-
trap would efficiently deplete TiO/VO gas in the upper
atmosphere.
Interestingly, recent observations of giant planets with
day sides closer to 3000K using Wide Field Camera 3
−1.0 −0.5 0.0 0.5 1.0 1.5
H−K
8
9
10
11
12
13
14
15
16
M
H
Field BDs
Young BDs
KELT-1b
Fig. 11.— KELT-1b’s day side has an H −K color and and H-
band brightness consistent with the brown dwarf color sequence.
While KELT-1b’s day side appears more similar to higher grav-
ity field objects than the low gravity sequence, this is at a low
(1.6σ) significance. The field brown dwarf magnitudes are from
Dupuy & Liu (2012) and the young brown dwarfs magnitudes are
from Gagne´ et al. (2015).
(WFC3) on the Hubble Space Telescope are best fit by
inverted or isothermal TP profiles. These planets are
WASP-12b (2930K, Stevenson et al. 2014b), WASP-33b
(3300K, Haynes et al. 2015) and WASP-103b (2900K
Cartier et al. 2017). In discussing the emission spectrum
of WASP-33b, Haynes et al. (2015) suggested that it may
be that only the very hot giant planets, with day side
brightness temperatures near 3000K, avoid the cold-trap
processes and posses a stratospheric temperature inver-
sion.
Since our observations strongly indicate that no in-
version (and presumably TiO or VO) is present in
the upper atmosphere of KELT-1b, it provides a in-
teresting contrast to the observations of the three hot
Jupiters. While all four objects (KELT-1b, WASP-12b,
WASP-33b, WASP-103b) show roughly the same day
side brightness temperatures, KELT-1b possess a surface
gravity approximately 20 times greater than the giant
planets. If we accept Haynes et al. (2015)’s supposition
that inversions may only be present on very high tem-
perature planets, KELT-1b’s atmosphere indicates that
there may also be a surface gravity dependence.
In both the vertical and day-night cold-traps, the con-
densate particles gravitationally settle into the planetary
interior. For simplicity, let us assume that the region of
an atmosphere where the condensates begin to form has
a low Knudsen number, so that the terminal velocity of
the condensate particles is equal to the Stokes velocity
Vterm =
2a2g(ρp − ρ)
9η
, (11)
where a is the particle radius, g is the gravitational accel-
eration, ρp is the particle density, ρ is the atmospheric
density, and η is the viscosity of the gas. Let us also
assume that the atmospheric compositions of hot giant
planets and brown dwarfs are roughly similar, such that
14 Beatty et al.
the atmospheric scale height on both the day and night
side of a hot Jupiter increases with increasing day side
temperature, and that the night side crossing and the
vertical mixing time are roughly independent of both
temperature and surface gravity in the regimes we are
interested in. Then the time for a particle to free fall
one atmospheric scale height, H = kBT/µmg, will be
proportional to
τff =
H
Vterm
∝ Ta−2g−2. (12)
Note that since the typical hydrodynamical relaxation
time for a giant planet (∼20 minutes) is much shorter
than the expected hemisphere crossing time (∼10s
hours), the scale height of the atmosphere, and hence
T above, on the day and night side will be different.
Under these assumptions, the free-fall timescale will
scale linearly with temperature and inversely as the
square of the surface gravity. Since both cold-trap pro-
cesses rely upon condensates free-falling out of the up-
per atmosphere, to first order the efficiency of the cold-
trap processes should go as the inverse of the free-fall
time. This possible functional dependence would explain
why only hot Jupiters with day side temperatures near
3000K have shown evidence for inversions, while KELT-
1b – with its much higher gravity – does not. Indeed, if
free-fall driven cold-traps are the primary inhibitor of in-
versions within hot giant planet atmospheres, we would
not expect to see an inversion in a hot brown dwarf at-
mosphere unless it was extremely (perhaps prohibitively)
hot. On the other hand, stratospheric inversions could be
possible in giant planets with day sides closer to 2000K
if their surface gravities were low.
Based on our observations of KELT-1b’s atmosphere,
surface gravity appears to play a noticeable role in set-
ting the observable properties of a hot Jupiter’s atmo-
sphere. While we have focused on the presence of a
stratospheric temperature inversion in the upper atmo-
sphere, we note that Stevenson (2016) recently showed
that the cloudiness of hot Jupiters near their termina-
tors appears to depend upon both temperature and sur-
face gravity. Stevenson (2016) found that hot, high grav-
ity giant planets show little to no evidence for clouds in
transmission spectroscopy, which he suggests is a result
of a varying efficiency of vertical diffusion. If this is cor-
rect, the different functional dependence that Stevenson
(2016) finds for clouds compared to our Equation 12 sug-
gests that the mechanisms underlying cloud formation
and stratospheric inversion in hot Jupiter atmospheres
– while both possibly dependent upon surface gravity –
could be fundamentally different.
5. SUMMARY
Using the LUCI1 NIR spectrograph on LBT, we spec-
trophotometrically observed a single secondary eclipse of
KELT-1b on the night of UT 2013 October 26 in the H-
band. After subtracting the telluric background emission
and accounting slight changes in the wavelength solution
over the course of the observations, we extracted a set of
broadband and spectrally-resolved light curves.
We fit an eclipse model to the broadband data using
a Gaussian Process regression analysis, which gave us a
clear measurement of the eclipse at ∆H = 1418±94ppm.
For the spectrally-resolved data, we divided the time se-
ries in each spectral wavechannel by the broadband time
series, and measured a set of spectrally-resolved eclipse
depths. Using a similar Gaussian Process regression
model to the broadband analysis, we are able to divide
the H-band into five spectral channels and measure the
eclipse depth in each to an average precision of approx-
imately 135ppm (Table 3). We find that the average
brightness temperature of the day side is approximately
3420 ± 70K in the H-band, which is hotter than the
3220 ± 50K average brightness temperature calculated
using all the measured eclipses.
Based on these measurements, and previous broad-
band eclipse observations at other wavelengths, we find
that the day side atmosphere of KELT-1b appears iden-
tical to an isolated M5 star or brown dwarf (Figure
10). Our modeling of KELT-1b’s atmosphere using hot
Jupiter atmospheric models yields a qualitatively similar
result (Figure 9). We therefore conclude that the day
side of KELT-1b possesses a monotonically decreasing
temperature-pressure profile, and is neither isothermal,
nor does it posses a stratospheric temperature inversion.
This is in contrast to the hot Jupiters WASP-
12b (Stevenson et al. 2014b), WASP-33b (Haynes et al.
2015) and WASP-103b (Cartier et al. 2017), all three of
which have similar dayside brightness temperatures as
KELT-1b, but all show evidence for either an isothermal
or inverted atmospheric TP profile. Our observations
of KELT-1b indicate an additional surface gravity de-
pendence on the processes governing the presence of an
inversion.
Spiegel et al. (2009) and Parmentier et al. (2013) have
previously suggested that vertical or day-night cold-traps
in hot Jupiters’ atmospheres may be responsible for de-
pleting the abundance of TiO and VO in these planets’
upper atmospheres, inhibiting inversions. To first order,
the efficiency of a cold-trap should scale as the inverse
of this free-fall timescale, and based on this we hypoth-
esize that KELT-1b’s very high surface gravity dramat-
ically shortens the free-fall timescale, thereby allowing
TiO/VO to be “cold-trapped” out of the atmosphere.
Our observations of KELT-1b are not sufficient to dis-
tinguish between a field brown dwarf spectral template
with high surface gravity, and a low gravity spectral
template. On an H − K color-magnitude diagram, the
day side of KELT-1b appears to lie directly on the field
brown dwarf color sequence. However, the uncertainties
on KELT-1b’s H and K eclipse depths mean that our
measurement of the day side’s H −K color is only 1.6 σ
off from the low-gravity color sequence.
In the coming year, observations of KELT-1b’s eclipse
using Wide Field Camera 3 on the Hubble Space Tele-
scope should allow us to differentiate between the field
and low-gravity spectral templates. Since KELT-1b tran-
sits its host star, we are able to independently measure
its mass and radius, and thus its surface gravity, without
relying on template matching or gravity indices. These
upcoming HST/WFC3 will therefore, hopefully, be the
first direct test of the spectral surface gravity indicators
used throughout the fields of brown dwarfs and directly-
imaged planets. We are also in the process of analyzing
Spitzer phase curve observations of KELT-1b at 3.6µm
and 4.5µm , which should allow us to see how the at-
mosphere changes from the day to night side. It will be
KELT-1b H-band Eclipse Observations 15
interesting to see if the striking similarity of the day side
to isolated field brown dwarfs also hold true on the night
side of KELT-1b.
We thank the anonymous referee for their comments
during the review process, and we wish to thank Leo Liu,
Jason Wright, and Ming Zhao for helpful discussions.
T.G.B. partially supported by funding from the Cen-
ter for Exoplanets and Habitable Worlds. The Center
for Exoplanets and Habitable Worlds is supported by
the Pennsylvania State University, the Eberly College of
Science, and the Pennsylvania Space Grant Consortium.
Work by T.G.B and B.S.G. was partially supported by
NSF CAREER Grant AST-1056524.
The LBT is an international collaboration among insti-
tutions in the United States, Italy and Germany. LBT
Corporation partners are: The Ohio State University,
The University of Arizona on behalf of the Arizona uni-
versity system; Istituto Nazionale di Astrofisica, Italy;
LBT Beteiligungsgesellschaft, Germany, representing the
Max-Planck Society, the Astrophysical Institute Pots-
dam, and Heidelberg University; The Research Corpo-
ration, on behalf of The University of Notre Dame, Uni-
versity of Minnesota and University of Virginia.
This publication makes use of data products from the
Two Micron All Sky Survey, which is a joint project of
the University of Massachusetts and the Infrared Pro-
cessing and Analysis Center/California Institute of Tech-
nology, funded by the National Aeronautics and Space
Administration and the National Science Foundation.
This work has made use of NASA’s Astrophysics
Data System, the Extrasolar Planet Encyclopedia
at exoplanet.eu (Schneider et al. 2011), the SIMBAD
database operated at CDS, Strasbourg, France, and the
VizieR catalog access tool, CDS, Strasbourg, France
(Ochsenbein et al. 2000).
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TABLE 1
Prior Values for the Broadband Eclipse Parameters
Parameter Units Value
TS . . . . . . . . . Predicted Eclipse Time (BJDTDB) 2456591.69888 ± 0.00075
log(P ) . . . . . . Log orbital period (days) . . . . . . . . . 0.0854668 ± 0.0000014√
e cos ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.005± 0.03√
e sinω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.001± 0.075
cos i . . . . . . . . Cosine of inclination . . . . . . . . . . . . . . 0.052± 0.023
RP /R∗ . . . . . Radius of planet in stellar radii . . . 0.077590 ± 0.00058
log(a/R∗) . . Log semi-major axis in stellar radii 0.559± 0.006
Note. — These values are the average of the parameters from the dual-channel
Spitzer eclipse measurements in Beatty et al. (2014), except for the period mea-
surement, which we updated using transit measurements described in Section
3.2.
TABLE 2
Median Values and 68% Confidence Intervals for the Broadband
Eclipse
Parameter Units Value
GP Hyperparameters:
At . . . . . . . . . Covariance Amplitude . . . . . . . . . . . . 0.0012
+0.0397
−0.0011
Lt . . . . . . . . . . Covariance Length-scale . . . . . . . . . . 0.257
+0.376
−0.123
Eclipse Model Parameters:
TS . . . . . . . . . Eclipse Time (BJDTDB) . . . . . . . . . . 2456591.6958 ± 0.0005
log(P ) . . . . . . Log orbital period (days) . . . . . . . . . 0.0854668 ± 0.0000014√
e cosω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.005± 0.03√
e sinω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.004± 0.073
cos i . . . . . . . . Cosine of inclination . . . . . . . . . . . . . . 0.064± 0.019
RP /R∗ . . . . . Radius of planet in stellar radii . . . 0.07742 ± 0.00056
log(a/R∗) . . Log semi-major axis in stellar radii 0.557± 0.005
δ . . . . . . . . . . . Eclipse depth (ppm) . . . . . . . . . . . . . . 1418 ± 94
Derived Parameters:
P . . . . . . . . . . Orbital period (days) . . . . . . . . . . . . . 1.217494 ± 0.000004
a/R∗ . . . . . . . Semi-major axis in stellar radii . . . . 3.60± 0.04
i . . . . . . . . . . . Inclination (degrees) . . . . . . . . . . . . . . 86.3± 1.1
b . . . . . . . . . . . Impact Parameter . . . . . . . . . . . . . . . . 0.232+0.063
−0.072
TFWHM . . . FWHM duration (days) . . . . . . . . . . . 0.1061
+0.0014
−0.0019
τ . . . . . . . . . . . Ingress/egress duration (days) . . . . 0.00894 ± 0.00024
T14 . . . . . . . . . Total duration (days) . . . . . . . . . . . . . 0.1151 ± 0.0016
e cosω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.0002 ± 0.002
e sinω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.000006 ± 0.0058
e . . . . . . . . . . . Orbital Eccentricity . . . . . . . . . . . . . . . 0.0037+0.0080
−0.0028
ω . . . . . . . . . . . Argument of periastron (degrees) . 3+32
−39
TABLE 3
Median Values and 68% Confidence Intervals for the Spectrally-Resolved Eclipses
Parameter 1.55µm–1.59µm 1.59µm–1.63µm 1.63µm–1.67µm 1.67µm–1.71µm 1.71µm–1.75µm
Spectrally-Resolved Eclipse Model Parameters:
δ (ppm) . . . . . . . . . . . . . . . 1285 ± 131 1461 ± 128 1587 ± 130 1532 ± 137 1623 ± 158
TS (BJDTDB−2456590) 1.6957 ± 0.0005 1.6959 ± 0.0005 1.6957 ± 0.0005 1.6958± 0.0005 1.6959 ± 0.0005
GP Hyperparameters:
Atotal (×10−5) . . . . . . . . 1.6± 1.5 5.9± 3.7 7.8± 4.3 1.5± 1.2 2.7± 1.5
Lt . . . . . . . . . . . . . . . . . . . . . 0.23± 0.02 0.19± 0.03 0.18± 0.025 0.15± 0.03 0.429 ± 0.05
Lair . . . . . . . . . . . . . . . . . . . 2.06± 0.59 1.39± 0.35 1.48 ± 0.23 1.78± 0.85 1.56± 1.05