Draft version May 14, 2020
Typeset using LATEX twocolumn style in AASTeX63
A pair of TESS planets spanning the radius valley around the nearby mid-M dwarf LTT 3780
Ryan Cloutier,1 Jason D. Eastman,1 Joseph E. Rodriguez,1 Nicola Astudillo-Defru,2 Xavier Bonfils,3
Annelies Mortier,4 Christopher A. Watson,5 Manu Stalport,6 Matteo Pinamonti,7 Florian Lienhard,4
Avet Harutyunyan,8 Mario Damasso,7 David W. Latham,1 Karen A. Collins,1 Robert Massey,9
Jonathan Irwin,1 Jennifer G. Winters,1 David Charbonneau,1 Carl Ziegler,10 Elisabeth Matthews,11
Ian J. M. Crossfield,12 Laura Kreidberg,1 Samuel N. Quinn,1 George Ricker,11 Roland Vanderspek,11
Sara Seager,13, 14, 15 Joshua Winn,16 Jon M. Jenkins,17 Michael Vezie,11 Ste´phane Udry,6 Joseph D. Twicken,17, 18
Peter Tenenbaum,17 Alessandro Sozzetti,7 Damien Se´gransan,6 Joshua E. Schlieder,19 Dimitar Sasselov,1
Nuno C. Santos,20, 21 Ken Rice,22 Benjamin V. Rackham,11, 23 Ennio Poretti,8, 24 Giampaolo Piotto,25
David Phillips,1 Francesco Pepe,6 Emilio Molinari,26 Lucile Mignon,3 Giuseppina Micela,27 Claudio Melo,28
Jose´ R. de Medeiros,29 Michel Mayor,6 Rachel A. Matson,30 Aldo F. Martinez Fiorenzano,8
Andrew W. Mann,31 Antonio Magazzu´,8 Christophe Lovis,6 Mercedes Lo´pez-Morales,1 Eric Lopez,19
Jack J. Lissauer,17 Se´bastien Le´pine,32 Nicholas Law,31 John F. Kielkopf,33 John A. Johnson,1
Eric L. N. Jensen,34 Steve B. Howell,17 Erica Gonzales,35 Adriano Ghedina,8 Thierry Forveille,3
Pedro Figueira,36, 20 Xavier Dumusque,6 Courtney D. Dressing,37 Rene´ Doyon,38 Rodrigo F. D´ıaz,39
Luca Di Fabrizio,8 Xavier Delfosse,3 Rosario Cosentino,8 Dennis M. Conti,40 Kevin I. Collins,41
Andrew Collier Cameron,42 David Ciardi,43 Douglas A. Caldwell,17 Christopher Burke,11 Lars Buchhave,44
Ce´sar Bricen˜o,45 Patricia Boyd,19 Franc¸ois Bouchy,6 Charles Beichman,46 E´tienne Artigau,38 and
Jose M. Almenara3
ABSTRACT
We present the confirmation of two new planets transiting the nearby mid-M dwarf LTT 3780 (TIC
36724087, TOI-732, V = 13.07, Ks = 8.204, Rs=0.374 R, Ms=0.401 M, d=22 pc). The two planet
candidates are identified in a single TESS sector and are validated with reconnaissance spectroscopy,
ground-based photometric follow-up, and high-resolution imaging. With measured orbital periods
of Pb = 0.77 days, Pc = 12.25 days and sizes rp,b = 1.33 ± 0.07 R⊕, rp,c = 2.30 ± 0.16 R⊕, the
two planets span the radius valley in period-radius space around low mass stars thus making the
system a laboratory to test competing theories of the emergence of the radius valley in that stellar
mass regime. By combining 63 precise radial-velocity measurements from HARPS and HARPS-N,
we measure planet masses of mp,b = 2.62
+0.48
−0.46 M⊕ and mp,c = 8.6
+1.6
−1.3 M⊕, which indicates that
LTT 3780b has a bulk composition consistent with being Earth-like, while LTT 3780c likely hosts an
extended H/He envelope. We show that the recovered planetary masses are consistent with predictions
from both photoevaporation and from core-powered mass loss models. The brightness and small size
of LTT 3780, along with the measured planetary parameters, render LTT 3780b and c as accessible
targets for atmospheric characterization of planets within the same planetary system and spanning the
radius valley.
1. INTRODUCTION
Since the commencement of its prime mission in July
2018, NASA’s Transiting Exoplanet Survey Satellite
(TESS ; Ricker et al. 2015) has unveiled many of the
closest transiting exoplanetary systems to our solar sys-
tem. The proximity of many of these systems make their
planets ideal targets for the detailed characterization
of their bulk compositions and atmospheric properties.
Systems of multiple transiting planets are of particular
Corresponding author: Ryan Cloutier
ryan.cloutier@cfa.harvard.edu
interest as they afford the unique opportunity for di-
rect comparative planetology, having formed within the
same protoplanetary disk and evolved around the same
host star.
The occurrence rate of close-in planets features a
dearth of planets between 1.7 − 2.0 R⊕ around Sun-
like stars and between 1.5 − 1.7 around low mass stars
(Fulton et al. 2017; Mayo et al. 2018; Cloutier & Menou
2020; Hardegree-Ullman et al. 2020). The so-called ra-
dius valley is likely a result of the existence of an or-
bital separation-dependent transition between primar-
ily rocky planets and non-rocky planets that host ex-
tended H/He envelopes. A number of physical pro-
cesses have been proposed to explain the existence of
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2 Cloutier et al.
this rocky/non-rocky transition, including photoevapo-
ration, wherein XUV heating from the host star drives
thermal atmospheric escape preferentially on smaller,
low surface gravity planets during the first 100 Myrs
(Owen & Wu 2013; Jin et al. 2014; Lopez & Fortney
2014; Chen & Rogers 2016; Owen & Wu 2017; Jin &
Mordasini 2018; Lopez & Rice 2018; Wu 2019). Alterna-
tively, the core-powered mass loss mechanism, wherein
the dissipation of the planetary core’s primordial energy
from formation drives atmospheric mass loss over Gyr
timescales (Ginzburg et al. 2018; Gupta & Schlichting
2019, 2020). Rather than resulting from the dissipation
of primordial planetary atmospheres, the radius valley
may instead arise from the superposition of rocky and
non-rocky planet populations, with the former forming
in a gas-poor environment after the dissipation of the
gaseous protoplanetary disk (Lee et al. 2014; Lee & Chi-
ang 2016; Lopez & Rice 2018).
Each of the aforementioned mechanisms make explicit
predictions for the location of the rocky/non-rocky tran-
sition in the orbital period-radius space. Measurements
of planetary bulk compositions in systems of multi-
ple planets that span the radius valley therefore offer
an opportunities to resolve the precise location of the
rocky/non-rocky transition (Owen & Campos Estrada
2020) and distinguish between the model predictions.
Precise planetary bulk composition measurements for
systems around a range of host stellar masses will en-
able the dependence of the radius valley on stellar mass
to be resolved and consequently used to test competing
models of the emergence of the radius valley (Cloutier
& Menou 2020, hereafter CM20).
Here we present the discovery and confirmation of the
two-planet system around the nearby (d=22 pc) mid-M
dwarf LTT 3780 from the TESS mission. The plan-
ets LTT 3780b and c span the rocky/non-rocky transi-
tion such that the characterization of their bulk com-
positions can be used to constrain emergence models of
the radius valley by marginalizing over unknown sys-
tem parameters such as the star’s XUV luminosity his-
tory. The brightness of LTT 3780 (Ks = 8.204) and
the architecture of its planetary system also make it an
attractive target for the atmospheric characterization
of multiple planets within the same planetary system.
In Sect. 2 we present the properties of LTT 3780. In
Sect. 3 we present the TESS light curve along with our
suite of follow-up observations, including reconnaissance
spectroscopy, ground-based photometry, high-resolution
imaging, and precise radial-velocity measurements. In
Sect. 4 we present our two independent analyses of our
data, to ensure the robustness of our results, before con-
cluding with a discussion and summary of our results in
Sects. 5 and 6.
2. STELLAR CHARACTERIZATION
LTT 3780 (LP 729-54, TIC 36724087, TOI-732) is a
mid-M dwarf at a distance of 22 pc (Gaia Collaboration
et al. 2018; Lindegren et al. 2018). Astrometry, photom-
etry, and the LTT 3780 stellar parameters are reported
in Table 1. The stellar Teff = 3331 ± 157 K is taken
from the TESS Input Catalog (TIC v8; Stassun et al.
2019) and is consistent with the value derived from the
Stefan-Boltzmann equation (3343± 150 K). The stellar
metallicity is weakly constrained by its SED and MIST
isochrones (Dotter 2016). The LTT 3780 mass and ra-
dius are derived from the stellar parallax and Ks-band
magnitude, used to compute the absolute Ks-band mag-
nitude MKs , and the empirically-derived M dwarf mass-
luminosity and radius-luminosity relations from Bene-
dict et al. (2016) and Mann et al. (2015) respectively.
LTT 3780’s surface gravity is computed from its mass
and radius. No photometric rotation period is appar-
ent in either the TESS or ground-based photometry.
However, the low value of logR′HK = −5.59 is indica-
tive of a chromospherically inactive star with likely a
long rotation period (estimated Prot = 104 ± 15 days;
Astudillo-Defru et al. 2017).
LTT 3780 is the primary component of a visual bi-
nary system with an angular separation of 16.1′′ from
the Gaia DR2 positions (Gaia Collaboration et al. 2018;
Lindegren et al. 2018). The binary was previously iden-
tified to be co-moving from measures of each stellar
component’s proper motion and spectroscopic distance
(Luyten 1979; Scholz et al. 2005). The common par-
allaxes and proper motions of LTT 3780 (alias LP 729-
54) and its stellar companion LP 729-55 (TIC 36724086)
were verified in Gaia DR2. Their angular separation of
16.1′′ implies a projected physical separation of 354 AU.
The fainter companion star has Ks = 10.223±0.021 (i.e.
∆Ks = 2.019 mag) which corresponds to a mass and ra-
dius of 0.136± 0.004 M and 0.173± 0.005 R. Given
the stellar mass ratio of q = 0.340 ± 0.014, the orbital
period of the stellar binary at their projected physical
separation is about 9100 years. Assuming a circular or-
bit, this corresponds to a negligible maximum radial ve-
locity (RV) variation of . 15 cm s−1 over the timescale
of our RV observations presented in Sect. 3.5. We also
calculated the secular acceleration of the binary system
given its large proper motion (Table 1) to be < 10 cm
s−1 year−1. This RV variation is also well below the
noise limit of our observations over our RV baseline.
The LTT 3780 planetary system may be an interesting
test case of planet formation models in a binary systems.
Two planets spanning the radius valley around LTT 3780 3
Table 1. LTT 3780 stellar parameters.
Parameter Value Refs
LTT 3780, LP 729-54, TIC 36724087, TOI-732
Astrometry
Right ascension (J2000.0), α 10:18:34.78 1,2
Declination (J2000.0), δ -11:43:04.08 1,2
RA proper motion, µα [mas yr
−1] −341.41± 0.11 1,2
Dec proper motion, µδ [mas yr
−1] −247.87± 0.11 1,2
Parallax, $ [mas] 45.493± 0.083 1,2
Distance, d [pc] 21.981± 0.040 1,2
Photometry
V 13.07± 0.015 3
GBP 13.352± 0.004 1,4
G 11.8465± 0.0005 1,4
GRP 10.658± 0.002 1,4
T 10.585± 0.007 5
J 9.007± 0.030 6
H 8.439± 0.065 6
Ks 8.204± 0.021 6
W1 8.037± 0.022 7
W2 7.880± 0.019 7
W3 7.771± 0.019 7
W4 7.577± 0.166 7
Stellar parameters
Spectral type M4V 8
MV 11.36± 0.02 9
MKs 6.49± 0.02 9
Effective temperature, Teff [K] 3331± 157 5
Surface gravity, log g [dex] 4.896± 0.029 9
Metallicity, [Fe/H] [dex] 0.28+0.11−0.13 9
Stellar radius, Rs [R] 0.374± 0.011 9
Stellar mass, Ms [M] 0.401± 0.012 9
Projected rotation velocity,
< 1.3 9
v sin i [km s−1]
logR′HK −5.59± 0.09 9
Estimated rotation period,
104± 15 9
Prot [days]
Note—References: 1) Gaia Collaboration et al. 2018 2) Lin-
degren et al. 2018 3) Reid et al. 2002 4) Evans et al. 2018 5)
Stassun et al. 2019 6) Cutri et al. 2003 7) Cutri & et al. 2014
8) Scholz et al. 2005 9) this work.
Although, the large physical separation of the stellar
components likely resulted in isolated planet formation
around LTT 3780.
3. OBSERVATIONS
3.1. TESS photometry
LTT 3780 was observed in TESS sector nine (i.e. or-
bits 25 and 26) for 27.26 days from UT February 28 to
March 26, 2019 with CCD 1 on Camera 1. As a member
of the Cool Dwarf target list (Muirhead et al. 2018), LTT
3780 was included in the TIC and in the Candidate Tar-
get List (CTL; Stassun et al. 2017) such that its light
curve was sampled at 2-minute cadence. These data
were processed by the NASA Ames Science Processing
Operations Center (SPOC; Jenkins et al. 2016). The
resulting Presearch Data Conditioning Simple Aperture
Photometry (PDCSAP; Smith et al. 2012; Stumpe et al.
2012, 2014) light curve of LTT 3780 was corrected for di-
lution by known contaminating sources within the pho-
tometric aperture with a dilution factor of 0.713. Ac-
cording to the sector nine data release notes1, the level
of scattered light from the Earth in Camera 1 CCD 1
at the start of each orbit was high and resulted in no
photometry or centroid positions being calculated dur-
ing the first 1.22 days of orbit 25 nor in the first 1.12
days of orbit 26. Data collection was also paused for
1.18 days for data downloading close to the spacecraft’s
time of perigee passage. Overall, a total of 24.08 days
of science data collection was performed in TESS sector
nine.
A sample image of the field surrounding LTT 3780
from the TESS target pixel files is shown in Figure 1.
The TESS photometric aperture used to produce the
PDCSAP light curve was selected to maximize photo-
metric signal-to-noise (Bryson et al. 2010) and is over-
laid in Figure 1. Blending in the TESS photometry
by nearby sources is unsurprising given the large (21′′)
TESS pixels and the 1′ FWHM of its point spread func-
tion, coupled with the large number density of 37 sources
within 2.5′ (Gaia Collaboration et al. 2018; Lindegren
et al. 2018). In Figure 1, the low-resolution TESS im-
age is compared with an example ground-based image
taken with the 1m telescope at the Cerro Tololo Inter-
American Observatory (CTIO) location of the Las Cum-
bres Observatory Global Telescope network (LCOGT).
The LCOGT zs-band image features a pixel scale of
0.39′′ which is equivalent to a spatial resolution that is 54
times higher than in the TESS images. The LCOGT im-
age clearly depicts the position of LTT 3780 within the
TESS aperture and the positions of 24 nearby sources
from the Gaia DR2. The relative positions of the neigh-
boring sources to the TESS photometric aperture re-
veals how the aperture was optimized to minimize con-
1 https://archive.stsci.edu/missions/tess/doc/tess drn/
tess sector 09 drn11 v04.pdf
4 Cloutier et al.
Figure 1. Upper panel : an example TESS target pixel file
image of LTT 3780 and the surrounding field. The TESS
pixel scale is 21′′. The position of LTT 3780 in Gaia DR2
is circled in black while the remaining Gaia sources out to
2.5′ are circled in yellow. The pixels highlighted in white
demarcate the TESS photometric aperture used to derive
the PDCSAP light curve of LTT 3780. Lower panel : an
example zs image of the same field taken with the LCOGT
1m telescope at CTIO with a much finer pixel scale of 0.39′′
pixel−1 enabling LTT 3780 and nearby sources to be spatially
resolved.
tamination by the nearby bright sources including the
binary companion star LP 729-55 at 16.1′′ east of LTT
3780’s position.
In the subsequent transit search conducted by the
SPOC using the Transiting Planet Search (TPS)
Pipeline Module (Jenkins 2002; Jenkins et al. 2010), two
transiting planet candidate signals were flagged and sub-
sequently passed a set of internal data validation tests
(Twicken et al. 2018; Li et al. 2019). The planet candi-
dates TOI-732.01 and 02 had reported periods of 0.768
days and 12.254 days, corresponding to 28 and 2 ob-
served transits respectively. However, focusing solely on
TESS measurements wherein the quality flag QUALITY
equals zero, indicating the reliability of those measure-
ments, the second transit of TOI-732.02 is only partially
resolved as its ingress is largely contaminated. Although
the SPOC does not make an identical cut based on the
QUALITY flag, the SPOC-reported orbital period of TOI-
732.02 is found to be underestimated by about three
minutes as we will learn from our follow-up transit light
curve analysis (Sect. 3.3).
The initially reported depth for each planet candidate
was 1253 ± 106 and 3417 ± 283 ppm corresponding to
preliminary planetary radii of 1.44±0.07 and 2.38±0.12
R⊕ using the stellar radius reported in Table 1. Note
that these planet parameters are preliminary and will
be refined in our analysis of the TESS light curve in
Sect. 4.1.
3.2. Reconnaissance spectroscopy
3.2.1. TRES spectroscopy
We obtained a single reconnaissance spectrum of LTT
3780 with the Tillinghast Reflector E´chelle Spectrograph
(TRES), mounted on the 1.5m Tillinghast Reflector
telescope at Fred L. Whipple Observatory (FLWO) on
Mount Hopkins, AZ on UT January 30, 2020. TRES is a
fiber-fed, R = 44, 000 optical e´chelle spectrograph (310-
910 nm) whose typical limiting RV precision on slowly
rotating M dwarfs of 50 m s−1 is insufficient to measure
the masses of the LTT 3780 planet candidates. We ob-
tained the spectrum to assess the star’s level of chromo-
spheric activity, to potentially measure rotational broad-
ening, and to search for a double-lined spectrum that
could indicate the presence of a close-in stellar com-
panion to LTT 3780. We median-combined three 600
second exposures that were wavelength calibrated using
a ThAr lamp exposure. The resulting signal-to-noise
(S/N) per resolution element at 715 nm was 16. We
then cross-correlated the spectrum order-by-order with
an empirical template spectrum of Barnard’s star.
The reduced data revealed a single-lined spectrum.
We see Hα in absorption and do not resolve any rota-
tional broadening. With these data we place an upper
limit on v sin i at half the spectral resolution of TRES;
v sin i ≤ 3.4 km s−1. Note that this value will be re-
fined in Sect. 3.5 with our high resolution spectra from
HARPS. The lack of Hα in emission and lack of any sig-
nificant stellar rotation, combined with the low level of
stellar photometric variability in the TESS light curve
and the absence of flares, emphasizes the low levels of
Two planets spanning the radius valley around LTT 3780 5
magnetic activity produced by LTT 3780. This fact will
have important implications for the precise RV char-
acterization of the TOI-732 planetary system and for
future atmospheric characterization efforts in which at-
mospheric feature detections may be degenerate with
signatures from magnetically active regions if not prop-
erly modeled in transmission spectra (Rackham et al.
2018).
3.3. Ground-based transit photometry
TESS ’s large pixels (21′′) result in significant blend-
ing of the LTT 3780 light curve with nearby sources,
including with its visual binary companion at 16.1′′ to
the east (with a TESS magnitude difference ∆T = 2.42,
see Figure 1). We obtained seeing-limited photometric
follow-up observations of the LTT 3780 field close to the
expected transit times of each planet candidate as part
of the TESS Follow-up Observing Program (TFOP).
The example image from this follow-up campaign in Fig-
ure 1 reveals how individual sources are resolved, which
enabled the confirmation of the transit events on-target,
and the scrutiny of nearby sources for nearby eclipsing
binaries (EBs). Follow-up efforts were scheduled using
the TESS Transit Finder, which is a customized version
of the Tapir software package (Jensen 2013). Unless
otherwise noted, the photometric data were extracted
and detrended using the AstroImageJ software package
(AIJ; Collins et al. 2017). The resulting light curves
were detrended with any combination of time (i.e. a
linear trend), airmass, and total background counts as
necessary in attempts to flatten the out-of-transit por-
tion of each light curve. Furthermore, the differential
light curves were derived using an optimal photometric
aperture and a set of comparison stars chosen by the
observer.
Numerous ground-based facilities conducted photo-
metric follow-up of the TOI-732 system. Their respec-
tive data acquisition and reduction strategies are de-
scribed in the following sections while their detrended
light curves are plotted in Figure 2. Differences in the
instrumental setups and nightly observing conditions
produce varying levels of photometric precision among
the light curves. Each detrended light curve, available
through TFOP, is fit with a Mandel & Agol (2002) tran-
sit model that we calculate using the batman software
package (Kreidberg 2015). The shallow transit depths
of both planet candidates produce low S/N transit light
curves that may only marginally improve the measure-
ment precision on most model parameters compared to
the values measured from the TESS light curve with
the exception being the planets’ orbital periods when
all light curves are fit simultaneously. As such, we fix
the orbital periods and impact parameters in the indi-
vidual light curve fits to the values obtained from the
SPOC Data Validation module (Pb = 0.76842 days,
Pc = 12.25422 days, bb = 0.69, bc = 0.35). We also de-
rive the scaled semimajor axes using the stellar param-
eters given in Table 1 (ab/Rs = 6.96, ac/Rs = 44.09).
Each planet’s orbit is also fixed to circular and the
quadratic limb darkening parameters in the correspond-
ing passband are interpolated from the Claret & Bloe-
men (2011) tables using the EXOFAST software (Eastman
et al. 2013) given LTT 3780’s Teff, log g, and [Fe/H]. We
fit the following parameters via non-linear least squares
optimization using scipy.curve fit: the baseline flux
f0, the time of mid-transit T0, and the planet-to-star
radius ratio rp/Rs. Measuring T0 relative to the ex-
pected transit time is used to refine the planet’s orbital
ephemeris while rp/Rs measurements in each passband
are required to investigate transit depth chromaticity as
a chromatically varying transit depth could be indicative
of a blended EB.
3.3.1. LCOGT photometry
We used three observatories as part of the Las Cum-
bres Observatory Global Telescope network (LCOGT;
Brown et al. 2013) to follow-up transits of both TOI-
732.01 and 02. Each 1m telescope is equipped with a
4096 × 4096 LCOGT SINISTRO camera whose pixel
scale is 389 mas pixel−1, resulting in a 26′ × 26′ field-
of-view (FOV). We calibrated all image sequences using
the standard LCOGT BANZAI pipeline (McCully et al.
2018). An example of one such image from the LCOGT
was shown in Figure 1.
We observed three full transits of TOI-732.01 between
UT June 9-17, 2019 from various LCOGT observatories.
These data include two zs-band light curves taken at
the LCOGT-Cerro Tololo Inter-American Observatory
(CTIO) on UT June 9 and 16 2019, and a third tran-
sit light curve obtained on UT June 17, 2019 in the zs
and g′-bands by the LCOGT-South African Astronom-
ical Observatory (SAAO). These four light curves are
shown in Figure 2. We searched for transit-like events
from nearby EBs (NEB) around 37 sources identified by
Gaia DR2 to be within 2.5′. The field was consequently
cleared of NEBs down to ∆zs = 7.686 as no transit-like
signals were detected on any off-target source. All three
expected transit events were shown to occur on-target
and arrived within 4 minutes of their expected transit
times.
We observed one full transit of TOI-732.02 on UT Jan-
uary 4, 2020 with the LCOGT-Siding Springs Observa-
tory (SSO) in the B-band. The light curve is included
in Figure 2. Similarly to our TOI-732.01 transit analy-
6 Cloutier et al.
Figure 2. Ground-based transit light curves of TOI-732.01
(upper panel) and 02 (lower panel) taken as part of TFOP.
Solid curves depict the optimized transit model fit with all
model parameters fixed other than the baseline flux, the mid-
transit time, and the planet-to-star radius ratio. Annotated
next to each light curve is the telescope facility, the passband,
and the UT observation date.
sis, the field was cleared of NEBs during the TOI-732.02
transit window. The expected transit event was shown
to occur on-target with a transit depth of 2.4 parts per
thousand (ppt). However, the transit arrived 60 min-
utes early indicating that the preliminary orbital period
of Pc = 12.254 days, derived from the TESS light curve
alone, is slightly underestimated if the period is con-
stant. The orbital period of LTT 3780c will be refined
in our global analysis in Sect. 4, which will include the
ground-based light curves.
3.3.2. OSN photometry
We observed one additional transit of TOI-732.02 on
UT December 10, 2019 with the Observatorio de Sierra
Nevada (OSN) 1.5m telescope near Granada, Spain.
The OSN 1.5m telescope is equipped with an Andor
ikon-L 2048 × 2048 CCD camera whose pixel scale is
232 mas pixel−1, resulting in a 7.9′ × 7.9′ FOV. We
observed the full transit simultaneously in both the V
and R-bands to check for chromaticity. Similarly to the
LCOGT-SSO transit observation of TOI-732.02, the ex-
pected transit event arrived 60 minutes early. The mea-
sured transit depths of 2.9 ppt and 3.2 ppt in the V and
R-bands respectively are consistent with each other and
with the LCO-SSO B-band transit at 1σ. TOI-732.02
therefore does not show any strong chromaticity. The
two transit light curves are included in Figure 2.
3.3.3. TRAPPIST-North photometry
The UT December 10, 2019 transit of TOI-732.02 ob-
served by OSN was also observed by the 60cm TRAn-
siting Planets and PlanetesImals Small Telescope-North
(TRAPPIST-North) located at the Ouka¨ımden Obser-
vatory in Morocco (Jehin et al. 2011; Gillon et al. 2013;
Barkaoui et al. 2019). TRAPPIST-North employs a
2048×2048 pixel Andor IKONL BEX2 DD camera with
a pixel scale of 600 mas pixel−1 resulting in a 20.5′×20.5′
FOV. The photometry was analyzed using custom soft-
ware for TRAPPIST-North. We observed the full tran-
sit in the z-band, thus contributing to the four transit
light curves of TOI-732.02 from TFOP in the B, V , R,
and z-bands. The measured transit depth in the z-band
is 3.2 ppt, which is consistent with the measured tran-
sit depths in the aforementioned passbands thus con-
firming that no strong chromaticity is detected. The
TRAPPIST-North light curve is included in Figure 2.
3.3.4. MEarth-North photometry
We observed a partial transit of TOI-732.02 on UT
February 9, 2020 using seven of eight telescopes from
the MEarth-North telescope array located at FLWO
on Mount Hopkins, AZ. The MEarth-North array con-
sists of eight 40cm Ritchey-Chre´tien telescopes, each
Two planets spanning the radius valley around LTT 3780 7
equipped with a 2048× 2048 pixel Apogee U42 camera.
The 750 mas pixel scale results in a 25.6′ × 25.6′ FOV.
The light curve was obtained in the custom MEarth
passband centered in the red optical and is shown in
Figure 2. The observations include a three hour out-of-
transit baseline plus the transit ingress and 37 minutes
in-transit, equal to nearly half of the full transit dura-
tion. The measured transit depth of 3.3 ppt is consistent
with all other TFOP transits again confirming the lack
of transit depth chromaticity.
The collective photometric data from TFOP have ver-
ified the periodic nature of the transits of TOI-732.01
and 02 and that both of these planet candidates orbit
the target star LTT 3780. We do not detect any signifi-
cant depth discrepancies, indicating that the transits are
likely achromatic and thus consistent with being plan-
etary in origin. Furthermore, the early arrival of the
TOI-732.02 transits on December 10, 2019 and on Jan-
uary 4, 2020 allow us to estimate the true orbital period
of LTT 3780c, which shrinks from its SPOC-reported
value of 12.254 to 12.2519 days, assuming a constant pe-
riod. This refined period prior is used in our up-coming
analysis of the TESS light curve in Sect. 4.1.
3.4. High-resolution imaging
Very nearby stars that are not detected in Gaia DR2,
nor in any of the seeing-limited image sequences, and
that fall within the same 21′′ TESS pixel as the target
star, will result in photometric contamination that is
unaccounted for in the TESS light curve. This effect re-
duces the depth of the observed transits and can produce
a false positive transit signal from another astrophysical
source, such as a blended EB (Ciardi et al. 2015). We
used two independent sets of high-resolution follow-up
imaging sequences to search for any such close-in sources
as described in the following sections.
3.4.1. SOAR speckle imaging
We obtained SOAR speckle imaging (Tokovinin 2018)
of LTT 3780 on UT December 12, 2019 in the I-band, a
visible bandpass similar to that of TESS. Details of the
observations from the SOAR TESS survey are provided
in Ziegler et al. (2020). No bright nearby stars are de-
tected within 3′′ of LTT 3780 within the 5σ detection
sensitivity of the observations. The resulting 5σ con-
trast curve is plotted in Figure 3 along with the speckle
auto-correlation function.
3.4.2. NIRI AO imaging
We obtained adaptive-optics (AO) images with Gem-
ini/NIRI (Hodapp et al. 2003) on UT November 25,
2019 in the Brγ filter (2.17 µm). We collected nine
dithered images with integration times of 2.2 seconds.
Figure 3. Upper panel : I-band 5σ contrast curve from
SOAR speckle imaging of LTT 3780 (TIC 36724087). The
inset depicts the corresponding speckle auto-correlation func-
tion. Lower panel : Brγ 5σ contrast curve from Gemini/NIRI
AO imaging. A few bad pixels persist at 2′′ from the target
(blue diamond), but these have a minimal effect on the con-
trast. The inset depicts the central coadded image centered
on LTT 3780. No visual companions are detected in either
dataset at ≥ 5σ.
We followed a standard data reduction procedure in-
cluding corrections for bad pixels, flat-fielding, sky back-
ground subtraction, and image coaddition. No visual
companions are identified within 5′′ of LTT 3780 within
the 5σ sensitivity of the observations. These high qual-
ity data are sensitive to companions five magnitudes
fainter than the target at just 270 mas and 7.4 mag-
nitudes fainter at separations & 1′′. The 5σ contrast
curve and the coadded image centered on LTT 3780 are
included in Figure 3.
Due to the single-lined spectrum of LTT 3780, the ver-
ification of the expected transit events on-target from
ground-based photometry, and the lack of nearby con-
8 Cloutier et al.
taminating sources from high-resolution imaging, we
conclude that the planet candidates TOI-732.01 and 02
are verified planets. We will refer to these planets as
LTT 3780b and c for the remainder of this study.
3.5. Precise radial-velocities
3.5.1. HARPS radial velocities
We obtained 33 spectra of LTT 3780 with the High Ac-
curacy Radial velocity Planet Searcher (HARPS; Mayor
et al. 2003) e´chelle spectrograph mounted at the ESO
3.6m telescope at La Silla Observatory, Chile. The
HARPS optical spectrograph at R = 115, 000 is sta-
bilized in pressure and temperature, which enable it
to achieve sub-m s−1 accuracy. The observations were
taken between UT June 21, 2019 and February 24, 2020
as part of the ESO program 1102.C-0339. The exposure
time was set to 2400 seconds, which resulted in a median
S/N over all orders of 26 and a median measurement
uncertainty of 1.31 m s−1 following the RV extraction
described below. Similarly to the TRES reconnaissance
spectra at R = 44, 000, LTT 3780 does not exhibit any
rotational broadening in the HARPS spectra. The cor-
responding upper limit on stellar rotation is v sin i ≤ 1.3
km s−1.
We extracted the HARPS RV measurements using
the TERRA pipeline (Anglada-Escude´ & Butler 2012).
TERRA employs a template-matching scheme that has
been shown to outperform the cross-correlation function
(CCF) technique on M dwarfs (Anglada-Escude´ & But-
ler 2012). M dwarfs are particularly well-suited to RV
extraction via template-matching because the line lists
used to define the binary mask for the CCF technique
are incomplete. The resulting CCF template is often a
poor match for cool M dwarfs.
TERRA constructs a master template spectrum by
first shifting the individual spectra to the barycentric
frame using the barycentric corrections calculated by the
HARPS Data Reduction Software (DRS; Lovis & Pepe
2007). We masked portions of the wavelength-calibrated
spectra in which telluric absorption exceeds 1%. The
spectra are then coadded to build a high S/N spectral
template. We computed the RV of each spectrum by
least-squares matching the individual spectrum to the
master template. Throughout the extraction process, we
only consider orders redward of order 18 (428-689 nm)
such that the bluest orders at low S/N are ignored. Be-
cause the master spectrum is derived from the observed
spectra, template construction does not require any ad-
ditional assumptions about the stellar properties. Using
this method, we found that the median LTT 3780 RV
measurement precision was improved by a factor of two
compared to the standard CCF method utilized within
Table 2. Radial velocity time series of LTT 3780 from
HARPS & HARPS-N
Time RV σRV Instrument
[BJD - 2,457,000] [m s−1] [m s−1]
1821.837965 -0.959 1.310 HARPS
1831.760260 -10.056 1.330 HARPS-N
1836.858657 -5.946 1.403 HARPS
the HARPS DRS. The resulting RV time series is re-
ported in Table 2.
3.5.2. HARPS-N radial velocities
We obtained 30 spectra of LTT 3780 with the HARPS-
N optical e´chelle spectrograph at the TNG on La Palma
in the Canary Islands. The observations were taken as
part of the HARPS-N Collaboration Guaranteed Time
Observations program between UT December 14, 2019
and March 15, 2020. The exposure time was set to 1800
seconds, which resulted in a median S/N over all orders
of 20 and a median measurement uncertainty of 1.43 m
s−1.
Identically to the HARPS RVs, we extracted the
HARPS-N RVs using the TERRA template-matching al-
gorithm. The resulting RV time series is included in
Table 2.
4. DATA ANALYSIS & RESULTS
Here we conduct two independent analyses of our data
to test the robustness of the recovered planetary pa-
rameters. In our fiducial analysis (Sects. 4.1 and 4.2),
the TESS light curve is modeled separately with the
resulting planet parameters being used as priors in the
subsequent RV analysis. In Sect. 4.3 we describe an al-
ternative, global analysis using the EXOFASTv2 software
(Eastman et al. 2019).
4.1. TESS transit analysis
We begin by analyzing the TESS PDCSAP light curve
wherein the planet candidates TOI-732.01 and 02 were
initially detected. The majority of apparent signals from
non-random noise sources in the light curve have al-
ready been removed by the SPOC processing. However,
low frequency and small amplitude signals that do not
resemble planetary transits are seen to persist in the
PDCSAP light curve shown in Figure 4. The nature
of these signals as residual systematics or photometric
stellar variability is unclear so we proceed with modeling
the aforementioned noise signals as an untrained semi-
parametric Gaussian process (GP) regression model,
Two planets spanning the radius valley around LTT 3780 9
simultaneously with the two transiting planet candi-
dates using the exoplanet software package (Foreman-
Mackey et al. 2019). exoplanet computes analytical
transit models using the STARRY package (Luger et al.
2019) and uses the celerite package (Foreman-Mackey
et al. 2017) to evaluate the marginalized likelihood un-
der a GP model. In this analysis, the covariance kernel
takes the form of a stochastically-driven, damped sim-
ple harmonic oscillator (SHO) whose Fourier transform
is known as the power spectral density (PSD) and is
given by
S(ω) =
√
2
pi
S0 ω
4
0
(ω2 − ω02)2 + ω02 ω2/Q2 . (1)
The PSD of the SHO is parameterized by the frequency
of the undamped oscillator ω0, S0, which is propor-
tional to the power at the frequency ω0, and the qual-
ity factor Q, which is fixed to
√
0.5. We selected this
covariance kernel and parameterization because work-
ing in Fourier space is much more computationally effi-
cient for large datasets, such as our TESS light curve
(N = 15, 210), and because the underlying cause of
the photometric variations being modeled remains un-
known. In practice, we also fit for the baseline flux
f0 and an additive scalar jitter sTESS. We fit the
GP hyperparameters using the parameter combinations
{lnω0, lnS0ω40 , f0, log s2TESS} with uninformative priors.
The transit model within exoplanet fits the stel-
lar mass Ms, stellar radius Rs, and quadratic limb
darkening parameters {u1, u2} along with the following
planetary parameters: logarithmic orbital periods lnP ,
times of mid-transit T0, logarithmic planet radii ln rp,
impact parameters b, and the eccentricity and argument
of periastron of LTT 3780c only; {ec, ωc}. We assume
a circular orbit for the inner planet LTT 3780b be-
cause its ultra-short period of 0.77 days implies a very
short circularization timescale of 1 Myr (Goldreich &
Soter 1966). Jointly fitting for the physical stellar and
planetary parameters enables us to derive the transit
observables a/Rs, rp/Rs, and inclination i. The joint
GP plus two-planet transit model therefore includes 18
model parameters: {f0, lnω0, lnS0ω40 , ln s2TESS,Ms, Rs,
u1, u2, lnPb, T0,b, ln rp,b, bb, lnPc, T0,c, ln rp,c, bc, ec, ωc}.
Table 3 summarizes the TESS transit model parameter
priors used in this, our fiducial analysis.
Our full model is fit to the TESS PDCSAP light curve
using the PyMC3 Markov Chain Monte-Carlo (MCMC)
package (Salvatier et al. 2016) implemented within
exoplanet. We ran four simultaneous chains with 4000
tuning steps and 3000 draws in the final sample. PyMC3
produces the 18-dimensional joint posterior probability
density function (PDF) of the model parameters. Me-
dian point estimates from the marginalized posterior
PDFs of the GP hyperparameters are used to construct
the GP predictive distribution whose mean function is
shown in Figure 4 and is used to detrend the TESS
light curve for visualization purposes. Similarly, the
median point estimates of the transit model parame-
ters are used to compute the ‘best-fit’ transit models
shown in Figure 4. Table 6 reports the median values of
all model parameters from their marginalized posterior
PDFs along with their uncertainties from the 16th and
84th percentiles.
4.2. Precise radial-velocity analysis
In our fiducial analysis, we elected to fit the RVs
independently of the transit data but exploiting the
strong priors on the orbital periods and mid-transit
times established by our TESS light curve analysis
(Sect. 4.1). We note that the information content
within the TESS light curve and the RV measurements
with regards to their shared model parameters (i.e.
{Pb, T0,b, Pc, T0,c, ec, ωc}) is dominated by one dataset
or the other. In other words, the strongest constraints
on each planet’s orbital period and mid-transit time
are derived from the TESS and ground-based transit
light curves. Conversely, most of the information re-
garding the eccentricity and argument of periastron of
LTT 3780c is derived from the RVs since the planet’s
secondary eclipse is unresolved in the TESS light curve
and the eccentricity’s effect on the transit duration is
degenerate with a/Rs, rp/Rs, and b. Note that this is
only an approximation as global transit plus RV mod-
eling can help to mitigate the eccentricity degeneracy
(Eastman et al. 2019). We will also consider a global
model in Sect. 4.3.
Although LTT 3780 is known to be relatively inac-
tive, we do not expect its surface to be completely
static and homogeneous. As such, we expect some
temporally-correlated residual RV signals from magnetic
activity that we model with a quasi-periodic GP regres-
sion model for each spectrograph. The quasi-periodic
covariance kernel is
kij = a
2 exp
[
− (ti − tj)
2
2λ2
− Γ2 sin2
(
pi|ti − tj |
PGP
)]
(2)
and features four hyperparameters: the covariance am-
plitude a, the exponential timescale λ, the coherence Γ,
and the periodic timescale PGP. We also fit an additive
scalar jitter sRV for each spectrograph to absorb any ex-
cess white noise. Due to the unique systematic noise
properties of each spectrograph, we fit a unique covari-
ance amplitude and scalar jitter to the data from each
10 Cloutier et al.
Table 3. TESS light curve and RV model parameter priors
Parameter Fiducial Model Priors EXOFASTv2 Model Priors
Stellar parameters
Teff, [K] N (3331, 157) N (3351, 150)
Ms, [M] N (0.401, 0.012) N (0.401, 0.012)
Rs, [R] N (0.374, 0.011) N (0.374, 0.011)
Light curve hyperparameters
f0 N (0, 10) U(− inf, inf)
lnω0, [days
−1] N (0, 10) -
lnS0ω
4
0 N (ln var(fTESS), 10) -
ln s2TESS N (ln var(fTESS), 10) -
u1 U(0, 1) U(0.225, 0.425)
u2 U(0, 1) U(0.232, 0.432)
Dilution - N (0, 0.1 δ)a
RV parameters
lnλ, [days] U(ln 1, ln 1000) -
ln Γ U(−3, 3) -
lnPGP, [days] N (ln 104, ln 30)b -
ln aHARPS, [m s
−1] U(−5, 5) -
ln aHARPS-N, [m s
−1] U(−5, 5) -
ln sHARPS, [m s
−1] U(−5, 5) U(− inf, inf)
ln sHARPS-N, [m s
−1] U(−5, 5) U(− inf, inf)
γHARPS, [m s
−1] U(−185, 205) U(− inf, inf)
γHARPS-N, [m s
−1] U(−185, 205) U(− inf, inf)
LTT 3780b parameters
lnPb, [days] N (ln 0.768, 0.5) -
Pb, [days] - U(− inf, inf)
T0,b, [BJD-2,457,000] N (1543.911, 0.5) U(1543.7, 1544.2)
ln rp,b, [R⊕] N (0.5 · ln(Zb) + lnRs, 1)c -
rp,b/Rs - U(− inf, inf)
bb U(0, 1 + rp,b/Rs) -
lnKb, [m s
−1] U(−5, 5) -
Kb, [m s
−1] - U(− inf, inf)
LTT 3780c parameters
lnPc, [days] N (ln 12.254, 0.5) -
Pc, [days] - U(− inf, inf)
T0,c, [BJD-2,457,000] N (1546.848, 0.5) U(1542.8, 1550.9)
ln rp,c, [R⊕] N (0.5 · ln(Zc) + lnRs, 1)d
rp,c/Rs - U(− inf, inf)
bc U(0, 1 + rp,c/Rs)
lnKc, [m s
−1] U(−5, 5) -
Kc, [m s
−1] - U(− inf, inf)
ec B(0.867, 3.03)e
ωc, [rad] U(−pi, pi)
Note—Gaussian distributions are denoted by N and are parameterized by mean
and standard deviation values. Uniform distributions are denoted by U and
bounded by the specified lower and upper limits. Beta distributions are denoted
by B and are parameterized by the shape parameters α and β.
adelta is the SPOC-derived dilution factor applied to the TESS light curve.
b PGP is constrained by the estimate of the stellar rotation period from logR
′
HK
whose uncertainty is artificially inflated.
cThe transit depth of TOI-732.01 reported by the SPOC: Zb = 1253 ppm.
dThe transit depth of TOI-732.02 reported by the SPOC: Zb = 3417 ppm.
eKipping 2013.
Two planets spanning the radius valley around LTT 3780 11
Figure 4. Upper panel : the TESS PDCSAP light curve of LTT 3780 (black curve) along with the mean GP detrending model
(green curve) and its 3σ confidence interval in the surrounding shaded region which is narrow and hence difficult to discern.
The vertical red and blue ticks along the x-axis highlight the mid-transit times of the planets LTT 3780b and c respectively.
Middle panel : the detrended TESS light curve. Lower panels: phase-folded light curves of LTT 3780b (left) and c (right) along
with their best-fit transit models. White markers depict the temporally-binned phase-folded light curves to help visualize the
transit events.
12 Cloutier et al.
of the HARPS and HARPS-N spectrographs. Through-
out, the covariance parameters {λ,Γ, PGP}, which only
depend on signals originating from the star, are kept
fixed between the two spectrographs.
Our full RV model consists of a GP activity
model for each spectrograph plus independent Ke-
plerian orbital solutions for each planet with RV
semi-amplitudes Kb and Kc. We also fit for each
spectrograph’s systemic velocity γ to account for
any RV offset between the two instruments. Our
full RV model therefore features 17 model pa-
rameters: {ln aHARPS, ln aHARPS-N, lnλ, ln Γ, lnPGP,
ln sHARPS, ln sHARPS-N, γHARPS, γHARPS-N, Pb, T0,b, lnKb,
Pc, T0,c, lnKc, hc, kc} where hc = √ec cosωc and
kc =
√
ec sinωc. Note that the GP hyperparameters,
scalar jitter parameters, and planetary semi-amplitudes
are fit in logarithmic units. Table 3 includes each of the
RV model parameter priors.
Figure 5 shows the raw RVs and the individual model
components including the RV activity along with LTT
3780b and c. The Bayesian generalized Lomb-Scargle
periodogram (BGLS; Mortier et al. 2015) of each RV com-
ponent is also included in Figure 5. The BGLS of the
raw RVs exhibits a small number of significant peaks
(e.g. 3.1 days) that are not strictly at either planet’s
orbital period. We will see that the subtraction of the
individual Keplerian orbits effectively removes these pe-
riodicities such that they can be attributed to harmonics
of the planetary orbital periods. The median RV model
parameters from their marginalized posterior PDFs are
used to produce the models shown in Figure 5 and are
reported in Table 6 along with their 16th and 84th per-
centiles. The RV semi-amplitudes of LTT 3780b and c
are found to be 3.41+0.63−0.63 and 4.44
+0.82
−0.68 m s
−1 and thus
are clearly detected at 5.4σ and 5.9σ respectively. The
resulting Keplerian RV signals are clearly discernible in
their phase-folded RV time series. The rms of the RV
residuals are found to be 1.55 and 1.74 m s−1 for HARPS
and HARPS-N respectively.
M dwarfs are known to commonly host 2-3 planets
per star out to 200 days (e.g. Dressing & Charbonneau
2015; Ballard & Johnson 2016; Cloutier & Menou 2020;
Hardegree-Ullman et al. 2019) such that the probabil-
ity that a third planet exists around LTT 3780 is non-
negligible. However, the BGLS of the RV residuals in
Figure 5 does not exhibit any strong periodic signals
that are statistically significant. This indicates that a
hypothetical third planet is unlikely to have been de-
tected. To confirm this robustly, we considered a three-
planet RV model, with fixed Keplerian parameters for
LTT 3780b and c, plus a third Keplerian component
‘d’ on a circular orbit. We separately tested two three-
planet models with differing priors on the orbital period
Pd: U(1.3, 2.1) and U(50, 150) days. The chosen period
limits approximately span the two highest peaks in the
BGLS of the RV residuals. We then ran two separate
MCMCs to sample the posteriors of the hypothetical
planet’s period, time of inferior conjunction (analogous
to the mid-transit time), and semi-amplitude. We find
that neither model settles onto a preferred period or
phase and each marginalized Pd posterior simply recov-
ers its uninformative prior. The lack of a well-defined
maximum a-posteriori Pd and T0,d prevents us from
searching the TESS light curve for any missed transit
signals from the hypothetical planet ‘d’ and from placing
a meaningful upper limit on the planet’s mass. We note
that the only threshold crossing events identified by the
TPS in the TESS light curve were those corresponding
to the confirmed planets LTT 3780b and c. Addition-
ally, the recovered semi-amplitudes Kd in both MCMCs
favored zero m s−1 with an upper limit of Kd ≤ 2.4
m s−1 at 95% confidence. Taken together, these find-
ings emphasize that the fiducial two-planet model for
the current dataset is likely complete as no third planet
is detected in our data.
4.3. An alternative global transit + RV analysis
To evaluate the robustness of the results derived in
our fiducial analysis (Sects. 4.1 and 4.2), we conducted
an independent analysis using the EXOFASTv2 exoplanet
transit plus RV fitting package (Eastman et al. 2019).
The methods of the EXOFASTv2 fitting routine are de-
tailed in Eastman et al. (2019) although we provide a
brief summary here.
To constrain the stellar-dependent parameters during
the transit fit, we feed EXOFASTv2 the Ms and Rs pa-
rameter priors as in our fiducial model. The routine also
takes as input the pre-detrended light curves from TESS
and from ground-based facilities, and performs a differ-
ential MCMC to evaluate the two-planet transit model
whose parameter priors are included in Table 3.
There are a few notable differences between our fidu-
cial analysis (Sects. 4.1 and 4.2) and the EXOFASTv2 ap-
proach. The exoplanet model simultaneously fits the
hyperparameters of the GP detrending model plus the
transiting planet parameters to achieve self-consistent
detrending and transit models wherein the uncertain-
ties in the recovered planet parameters are marginalized
over uncertainties in the detrending model. Conversely,
EXOFASTv2 uses pre-detrended light curves and so the
aforementioned marginalization of the planet parameter
uncertainties over the GP hyperparameters does not oc-
cur. Furthermore, the RV model in our fiducial analysis
includes the treatment of residual RV signals as a quasi-
Two planets spanning the radius valley around LTT 3780 13
Figure 5. The RV data and individual model components from our analysis of the HARPS (gray circles) and HARPS-N (green
triangles) RV measurements. The data and models are depicted in the left column of the first five rows while their corresponding
Bayesian generalized Lomb-Scargle periodograms are depicted in the right column. The marginalized posteriors of the LTT
3780b and c orbital periods are depicted as vertical lines along with the estimated stellar rotation period using the M dwarf
activity-rotation relation from Astudillo-Defru et al. (2017) (Prot = 104 ± 15 days). First row : the raw RV measurements.
Second row : the RV activity signal modeled with a quasi-periodic GP for each spectrograph. Third row : the RV signal from
LTT 3780b at 0.77 days. Fourth row : the RV signal from LTT 3780c at 12.25 days. Fifth row : the RV residuals. Bottom row :
the phase-folded RV signals of LTT 3780b and c.
14 Cloutier et al.
periodic GP whereas, EXOFASTv2 assumes the RV resid-
uals to be well-represented by a Gaussian noise term
characterized by an additive jitter factor.
Our EXOFASTv2 modeling has the important advan-
tage of evaluating a global model that includes the TESS
light curve, ground-based transit light curves, and RV
measurements. The resulting planet parameters, in-
cluding the orbital periods, mid-transit times, eccen-
tricities, and argument of periastron, will therefore be
self-consistent between all input datasets. In particu-
lar, each planet’s ephemeris will be more precisely con-
strained by the inclusion of the ground-based transit
light curves and the eccentricity of LTT 3780c will be
jointly constrained by its transit duration, Keplerian RV
model, and the stellar density. EXOFASTv2 also fits a free
dilution parameter to model any discrepancies between
the dilution applied to the PDCSAP light curve and the
true dilution.
The results from our fiducial model in Table 6 are ac-
companied by the results from our alternative analysis
using EXOFASTv2. We find consistency between the two
models at < 1σ for nearly all model parameters. This
speaks to the robustness of the planetary model param-
eters inferred from our data. The only exceptions are
the 2σ and 2.8σ discrepant RV jitter parameters sHARPS
and sHARPS-N. However, this is not alarming as the RV
residuals, following the removal of the two Keplerian so-
lutions, are modeled with a GP in our fiducial model
whereas the EXOFASTv2 model treats the residuals with
a scalar jitter. Crucially, these approaches yield consis-
tent RV semi-amplitudes for LTT 3780b and c whose
agreement between the two models is 0.2σ and 0.7σ re-
spectively.
5. DISCUSSION
5.1. Fundamental planet parameters
From our analysis of the TESS transit light curve we
measure the planetary radii of LTT 3780b and c to be
rp,b = 1.332
+0.072
−0.075 R⊕ and rp,c = 2.30
+0.16
−0.15 R⊕. By com-
bining the TESS analysis with the mid-transit times
measured from transit follow-up observations, we mea-
sure orbital periods for LTT 3780b and c to be Pb =
0.7683881+0.0000084−0.0000083 days and Pc = 12.252048
+0.000060
−0.000059
days. This places LTT 3780b at 0.012 AU where it
receives 106 times Earth’s insolation. Assuming uni-
form heat redistribution and a Bond albedo of zero, LTT
3780b has an equilibrium temperature of Teq,b = 892 K.
Similarly, the orbital period of LTT 3780c places it at
0.077 AU where it receives 2.6 times Earth’s insolation
with a zero-albedo equilibrium temperature of 353 K.
From our RV analysis we measure planet masses of
mp,b = 2.62
+0.48
−0.46 M⊕ and mp,c = 8.6
+1.6
−1.3 M⊕, which rep-
resent 5.6σ and 5.9σ mass detections respectively. By
combining the planetary mass and radius measurements,
we derive bulk densities of ρp,b = 6.1
+1.8
−1.5 g cm
−3 and
ρp,c = 3.9
+1.0
−0.9 g cm
−3. Figure 6 details the mass-radius
diagram of exoplanets around M dwarfs with masses
measured at the level of ≥ 3σ, including the LTT 3780
planets. The LTT 3780 planet masses and radii are com-
pared to theoretical models of fully-differentiated plan-
etary interiors consisting of combinations of water, sili-
cate rock, and iron (Zeng & Sasselov 2013). In Figure 6
we see that LTT 3780b is consistent with an Earth-like
bulk composition of 33% iron plus 67% magnesium sil-
icate by mass. This composition is shared by the ma-
jority of planets in the . 1.5 R⊕ size regime. We also
consider models of Earth-like solid cores that include
1% H2 envelopes by mass, over a range of equilibrium
temperatures from 300-1000 K (Zeng et al. 2019). The
mass and radius of LTT 3780c appear consistent with a
water-dominated bulk composition but also with a pre-
dominantly Earth-like body that hosts an extended low
mean molecular weight atmosphere. Distinguishing be-
tween these two degenerate structure models will require
the extent of LTT 3780c’s atmosphere to be investigated
through transmission spectroscopy. Due to the depen-
dence of the atmospheric scale height on the planet’s
surface gravity, the accurate interpretation of forthcom-
ing transmission spectroscopy observations will be facil-
itated by the planetary mass measurements presented in
this study. The feasibility of targeting LTT 3780c with
transmission spectroscopy is discussed in Sect. 5.4.
The LTT 3780 two-planet system adds to the grow-
ing number of confirmed multi-planet systems around
nearby M dwarfs with at least one transiting planet
(e.g. GJ 1132; Berta-Thompson et al. 2015; Bonfils
et al. 2018, K2-3; Crossfield et al. 2015; Damasso et al.
2018, K2-18; Montet et al. 2015; Cloutier et al. 2019b,
L 98-59; Kostov et al. 2019; Cloutier et al. 2019a, LHS
1140; Dittmann et al. 2017; Ment et al. 2019, LP 791-
18; Crossfield et al. 2019, TOI-270; Gu¨nther et al.
2019, TOI-700; Gilbert et al. 2020; Rodriguez et al.
2020, TRAPPIST-1; Gillon et al. 2017). With their
sub-Neptune-sized radii and measured masses presented
herein, both LTT 3780b and c contribute directly to the
completion of the TESS level one science requirement
to obtain masses for fifty planets smaller than 4 R⊕.
5.2. Implications for the origin of the radius valley
around mid-M dwarfs
The occurrence rate distribution of close-in planet
radii around Sun-like stars features a bimodality with
a dearth of planets at 1.7 − 2.0 R⊕ known as the ra-
dius valley (Fulton et al. 2017; Mayo et al. 2018). This
Two planets spanning the radius valley around LTT 3780 15
Figure 6. Planetary mass-radius diagram for small planets
orbiting M dwarfs including LTT 3780b and c (bold symbols).
The solid curves represent planetary internal structure mod-
els for bodies composed of 100% water, 100% silicate rock,
67% rock plus 33% iron (i.e. Earth-like), and 100% iron by
mass. The dashed curves represent models of planets with
Earth-like solid cores plus a 1% by mass gaseous H2 envelope
at 1 mbar surface pressure and with the equilibrium temper-
ature annotated next to each curve. Marker colors indicate
the planet’s insolation.
feature likely results from the existence of a transition
between predominantly rocky planets and larger plan-
ets that host significant H/He envelopes, as a function
of planet radius and orbital separation. The slope of the
radius valley in P − rp space marks the critical radius
separating rocky and non-rocky planets as a function of
orbital period. The empirical slope of the radius val-
ley around Sun-like stars is consistent with models of
thermally-driven atmospheric mass loss such as photoe-
vaporation and core-powered mass loss (Van Eylen et al.
2018; Martinez et al. 2019; Wu 2019). However for mid-
K to mid-M dwarfs, the radius valley slope flattens and
becomes increasingly favored by models of an alternative
formation pathway for terrestrial planets in a gas-poor
environment (CM20).
Figure 7 depicts the LTT 3780 planets in P−rp space,
along with the subset of M dwarf planets from Figure 6
with RV-derived masses. The planets in Figure 7 are
classified as having a bulk composition that is either
rocky, gaseous, or intermediate based on their mass and
radius. Rocky planets are defined as planets that are
consistent with having a bulk density greater than that
of 100% MgSiO3 given their size. Similarly, unambigu-
ously gaseous planets are defined as planets that are con-
sistent with having a bulk density less than that of 100%
H2O given their size. The remaining planets are flagged
as having bulk compositions that are intermediate be-
tween rocky and gaseous. LTT 3780b and c have rocky
and intermediate dispositions respectively (Figure 6).
In Figure 7, LTT 3780b and c are shown to span the
empirically-derived location of the radius valley around
low mass stars under the gas-poor formation and pho-
toevaporation models (CM20). The slope of the ra-
dius valley around low mass stars is considerably flat-
ter than around Sun-like stars, with the former slope
being consistent with gas-poor formation while the lat-
ter is more consistent with a thermally-driven atmo-
spheric mass loss process. To compare the compositions
of planets around low mass stars to the rocky/non-rocky
transition locations in Figure 7, we scale the transi-
tion measured around Sun-like stars down to the low
stellar mass regime under the photoevaporation model
(rp ∝ (Ms/M)1/4; Wu 2019)2. The slope measured
around low mass stars is plotted verbatim in Figure 7.
Both models predict that LTT 3780b should have a
rocky bulk composition in which any residual gaseous
envelope only contributes marginally to the planet’s
mass and radius. Indeed these predictions are consis-
tent with our finding that LTT 3780b has an Earth-like
composition. Similarly, both models predict that LTT
3780c should be non-rocky in that it should have re-
tained a substantial gaseous envelope and therefore be
inconsistent with having a bulk rocky composition. Al-
though we cannot definitively identify the bulk compo-
sition of LTT 3780c with our data, due to internal struc-
ture model degeneracies, we confirm that LTT 3780c is
consistent with both model predictions. In other words,
the models correctly identify LTT 3780c as being incon-
sistent with an Earth-like composition and requires a
significant amount of volatile material or H/He gas to
explain its mass and radius.
5.2.1. Planetary mass limits from photoevaporation models
Stars such as LTT 3780 with multi-transiting planets
that span the radius valley provide valuable test cases
of radius valley emergence models. The virtue of these
systems is that limits on the planetary masses can be
derived by scaling the properties of one planet to the
other (Owen & Campos Estrada 2020). For example,
assuming that the initial H/He envelope of the rocky
2 The median stellar mass in the sample of Sun-like stars from
Martinez et al. (2019) is 1.01 M. The median stellar mass
in the sample of low mass stars from CM20 is 0.65 M. The
resulting scaling of the rocky/non-rocky transition from Sun-like
stars to the low stellar mass regime under photoevaporation is
(0.65/1.01)1/4 = 0.896 (Wu 2019).
16 Cloutier et al.
Figure 7. Period, radii, and bulk densities of M dwarf
planets with precise RV masses compared to the empirical
location of the radius valley around low mass stars versus
orbital period and planet radius. LTT 3780b and c are de-
picted with the bold symbols. Contours represent the plane-
tary occurrence rates around low mass stars (CM20). Planet
marker shapes depict the planet’s compositional disposition
as either rocky (circles), gaseous (triangles), or intermediate
(squares). Marker colors indicate the planet’s bulk density.
The dashed and solid lines depict the locations of the ra-
dius valley around low mass stars from model predictions of
thermally-driven atmospheric mass loss and from gas-poor
terrestrial planet formation respectively. The shaded regions
highlight where the model predictions of planetary bulk com-
positions are discrepant between the two models.
planet below the valley has been completely stripped by
some physical process, the theoretical minimum mass of
the non-rocky planet above the valley can be calculated
by scaling its properties to those of the rocky planet. An
equivalent principle can be used to derive the maximum
mass of the rocky planet. The power of this comparative
scaling of planets within the same planetary system is
that certain unobservable quantities that directly affect
final planet masses are scaled out. An example of this
is the host star’s XUV luminosity history in the photo-
evaporation scenario (Owen & Campos Estrada 2020).
A full derivation is presented in Appendix A but here
we simply state the condition for the consistency of the
gaseous (i.e. non-rocky) and rocky planet parameters
with the photoevaporation model. This requires that
the gaseous planet’s mass loss timescale exceeds the
maximum mass loss timescale of the rocky planet (Owen
& Campos Estrada 2020). This condition leads to
1 ≤ m
0.64
core,gas
mcore,rock
(
agas
arock
)2/3
r
4/3
core,rock. (3)
where each planet’s core mass and radius are given in
units of the Earth. In the LTT 3780 system we define
LTT 3780b to be the rocky planet below the valley whose
H/He envelope has been photoevaporated away leaving
behind a solid core whose mass and radius are equal to
the planet’s total mass and radius: mcore,rock = mp,b =
2.62± 0.47 M⊕ and rcore,rock = rp,b = 1.332± 0.074 R⊕.
The gaseous planet above the valley is then LTT 3780c,
whose mass is assumed to be dominated by an Earth-
like core such that mcore,gas = mp,c = 8.6± 1.5 M⊕ and
whose core radius is approximated by the mass-radius
relation for Earth-like bodies (rp ∝ m1/3.7p ; Zeng et al.
2016). Lastly, the semimajor axes arock and agas are
ab = 0.01211± 0.00012 AU and ac = 0.07673± 0.00076
AU respectively.
Using Equation 3 and sampling the planetary parame-
ters Θ = {mp,b, ab, rp,b, ac} from their marginalized pos-
terior PDFs, we find that the mass of LTT 3780c must
be ≥ 0.49± 0.15 M⊕ in order to be consistent with the
photoevaporation model. In the same way, but by re-
placing mp,b with mp,c in the set Θ, we calculate that
the mass of LTT 3780b must be ≤ 19.6± 2.8 M⊕ to be
consistent with photoevaporation. Clearly the measured
masses mp,c = 8.6± 1.5 M⊕ and mp,b = 2.62± 0.47 M⊕
are both consistent with predictions from the photoe-
vaporation model, implying that photoevaporation is a
feasible process for sculpting the observed architecture
of the LTT 3780 system.
A few notable caveats exist with the planetary mass
limits imposed by the photoevaporation model in Equa-
tion 3 (Owen & Campos Estrada 2020). These are dis-
cussed in Appendix A.
5.2.2. Planetary mass limits from core-powered mass loss
models
Similarly to the photoevaporation model, we can com-
pare the mass loss timescales of the LTT 3780 planets
under the core-powered mass loss scenario (Ginzburg
et al. 2018; Gupta & Schlichting 2019, 2020) to constrain
their permissible planet masses under that model. In the
core-powered mass loss scenario, the lower atmosphere
is in thermal contact with the planetary core which con-
ducts energy from its formation into the atmosphere.
This heat flux drives convective heat transport radially
outwards to the radiative-convective boundary (RCB) of
the atmosphere, above which the atmosphere is isother-
mal at Teq and atmospheric cooling is radiative. The
Two planets spanning the radius valley around LTT 3780 17
physical limit to the atmospheric mass loss rate is given
by the thermal velocity of the gas at the Bondi radius;
the radial distance at which the escape velocity equals
the thermal sound speed cs =
√
kBTeq/µ where kB is
the Boltzmann constant and µ is the atmospheric mean
molecular weight which we fix to 2 amu for H2.
The derivation of the mass loss timescale in the core-
powered mass loss model is presented in Appendix B.
As in the photoevaporation scenario, we require that
the mass loss timescale for the gaseous planet exceeds
that of the rocky planet which leads to the following
condition for consistency of the planetary parameters
with the core-powered mass loss model:
1 ≤
(
mcore,gas
mcore,rock
)(
Teq,gas
Teq,rock
)−3/2
exp
[
c′
(
mcore,gas
Teq,gas rp,gas
− mcore,rock
Teq,rock rp,rock
)]
, (4)
where the constant c′ = Gµ/kB ≈ 104 R⊕ K
M⊕−1, Teq,gas = Teq,c = 323 ± 16 K, Teq,rock =
Teq,b = 816 ± 40 K, rp,gas = rp,c = 2.30 ± 0.16
R⊕, and rp,rock = rp,b = 1.332 ± 0.074 R⊕. The
inequality in Equation 4 has no analytic solution
so we solve for the limiting masses of mcore,gas and
mcore,rock by again sampling the planetary parameters
{mcore,rock, Teq,rock, rp,rock,mcore,gas, Teq,gas, rp,gas} from
their marginalized posterior PDFs and numerically solv-
ing for the limiting core masses. Recall that both planets
are assumed to have small envelope mass fractions such
that mcore ≈ mp.
Under the core-powered mass loss mechanism, we find
that the mass of LTT 3780c must be ≥ 2.1 ± 0.5 M⊕
to be consistent with the model. Similarly, by solving
for mcore,rock we calculate that the mass of LTT 3780b
must be ≤ 12.6 ± 2.9 M⊕. As with the photoevapora-
tion mass limits from Sect. 5.2.1, the measured masses
mp,c = 8.6 ± 1.5 M⊕ and mp,b = 2.62 ± 0.47 M⊕ are
both consistent with predictions from the core-powered
mass loss model.
The masses of LTT 3780b and c recovered in this study
from HARPS and HARPS-N RV measurements are both
consistent with radius valley emergence model predic-
tions from photoevaporation and core-powered mass
loss, two physical processes that thermally drive atmo-
spheric escape on close-in planets. Thus, the recov-
ered masses of LTT 3780b and c are unable to provide
strong evidence for the inapplicability of either mecha-
nism. However, the photoevaporation and core-powered
mass loss models do make distinct predictions for the
maximum mass of the rocky planet and the minimum
mass of the non-rocky in systems like LTT 3780 that
feature such planet pairs. Therefore, other systems with
multi-transiting planets that span the radius valley may
exist for which either photoevaporation or core-powered
mass loss may be ruled out by the planets’ masses. This
prospect is especially viable for increasingly compact
systems wherein the ratios agas/arock and Teq,gas/Teq,rock
approach unity.
5.2.3. Planetary mass limits from gas-poor terrestrial
planet formation models
Unlike the photoevaporation and core-powered mass
loss scenarios, it is not clear that analogous arguments
can be made within the gas-poor formation framework
to scale out unknown system parameters and place lim-
its on the permissible planet masses. This is because the
model invokes the formation of two planet populations
with distinct rocky and non-rocky bulk compositions
(Lee et al. 2014; Lee & Chiang 2016; Lopez & Rice 2018).
Both populations are thought to form cores of rock and
ice but only the non-rocky population subsequently ac-
cretes a gaseous envelope prior to disk dispersal after a
few Myrs (Haisch et al. 2001; Cloutier et al. 2014). Be-
cause the gas accretion term only impacts the non-rocky
planet population, unobservable quantities for the LTT
3780 system when it was just a few Myrs old, such as
the local density of the gaseous disk, the disk structure,
and the disk dynamics, cannot be scaled out by com-
paring the rocky and non-rocky planet parameters. As
such, we are not in a position to compare the LTT 3780
planet masses to constraints imposed by the gas-poor
terrestrial planet formation model.
5.3. TTV analysis
We used the TTV2Fast2Furious python package
(Hadden 2019) to predict the amplitudes of transit tim-
ing variations (TTVs) of the planets LTT 3780b and c.
We ran 103 realizations with the planetary masses being
sampled from their marginalized posterior PDFs from
our RV analysis (Sect. 4.2). The stellar mass, planet or-
bital periods, and times of mid-transit are drawn from
their respective priors used in our RV analysis. Recall
that the free eccentricity of LTT 3780b is assumed to be
zero because of its short circularization timescale. Fur-
thermore, due to their large period ratio (Pb = 0.768388
days, Pc = 12.252048 days, Pc/Pb = 15.945130), im-
posing a non-zero free eccentricity on either planet will
have a negligible effect on their TTV amplitudes so we
fix the input free eccentricities to zero. The forced ec-
centricities induced by the planets’ mutual interactions
are calculated within TTV2Fast2Furious. Arguments of
periastron are drawn from U(0, 2pi).
In each realization, with its unique set of parameters,
we compute each planet’s maximum deviation from a
18 Cloutier et al.
linear ephemeris over a 2-year baseline beginning with
the commencement of the TESS sector 9 observations.
Over the 103 realizations we find maximum TTV am-
plitudes of 0.02 and 1 second for LTT 3780b and c re-
spectively. The small amplitude of the expected TTV
signals make the LTT 3780 system a poor candidate for
intensive transit follow-up to derive TTV masses of the
two known planets. However, ongoing transit observa-
tions of LTT 3780c may reveal TTVs induced by an
insofar unseen outer planet. For this purpose, we note
that LTT 3780 is scheduled to be observed in sector 35
of the TESS extended mission between UT February 9
and March 7, 2021.
5.4. Prospects for atmospheric characterization
The stellar and planetary parameters of the LTT 3780
system make the planets LTT 3780b and c accessible tar-
gets for atmospheric characterization via emission and
transmission spectroscopy respectively. Assuming uni-
form heat redistribution and a Bond albedo of zero, the
equilibrium temperature of LTT 3780c is Teq,c = 353 K.
The expected depth of its transmission features up to
two atmospheric scale heights (Stevenson 2016; Fu et al.
2017), in a cloud-free low mean molecular weight atmo-
sphere (µ = 2), is 79 ppm. Alternatively, it is expected
that some mini-Neptune atmospheres are metal enriched
(Fortney et al. 2013) which will partially suppress trans-
mission feature depths to 32 ppm in a 100x solar metal-
licity atmosphere (µ ≈ 5). Simulated transit observa-
tions with PandExo (Batalha et al. 2017) confirm that
molecular features in a clear, low mean molecular weight
atmosphere will be detectable at ≥ 5σ confidence from
a single transit observation with JWST/NIRISS slit-
less spectroscopy3 (Kreidberg et al. 2015). Four transits
would be required to reach a similar precision for a 100x
solar metallicity atmosphere. We also note the caveat
that if high altitude clouds are present on LTT 3780c,
as seen for many other planets in its size regime (Cross-
field & Kreidberg 2017), additional observing time will
be required.
For LTT 3780c, we can also consider the transmis-
sion spectroscopy metric (TSM; Kempton et al. 2018)
which is proportional to the expected S/N of trans-
mission features in a cloud-free atmosphere. Based on
the TSM, LTT 3780c is among the best warm mini-
Neptunes (P ∈ [10, 40] days, rp ∈ [2, 3] R⊕) for atmo-
spheric characterization via transmission spectroscopy
observations. To date, the best such planets are the
3 Note that LTT 3780’s J-band magnitude of 9.007 does not exceed
any imposed brightness limit in the NIRISS Single Object Slitless
Spectroscopy (SOSS) mode.
TESS -discovered planets TOI-700c (Gilbert et al. 2020;
Rodriguez et al. 2020), TOI-270d (Gu¨nther et al. 2019),
and LTT 3780c, whose TSM values are all within 17% of
each other and are at minimum 17% greater than that of
the next best potential target: HD 15337c (Dumusque
et al. 2019). The TSM values of favorable warm mini-
Neptunes are reported in Table 4 and are compared in
Figure 8.
The ultra-short period planet LTT 3780b has a zero-
albedo equilibrium temperature of Teq,b = 892 K. The
hot dayside of LTT 3780b makes it a very attractive tar-
get for atmospheric characterization via emission spec-
troscopy observations. In particular, eclipse observa-
tions can help to discern whether the planet has retained
a substantial atmosphere or if its emitting temperature
is consistent with that of pure rock. The distinction be-
tween a 1 bar atmosphere and a bare rocky surface on
LTT 3780b will be accessible with a single JWST/MIRI
eclipse observation (Koll et al. 2019).
Similarly to the TSM, the expected S/N of thermal
emission signatures at 7.5 µm is proportional to the
emission spectroscopy metric (ESM; Kempton et al.
2018). Computing the ESM for hot planets with likely
terrestrial compositions (rp < 1.5 R⊕), that are favor-
able targets for emission spectroscopy measurements, re-
veals that LTT 3780b is among the best such planets
(Table 5, Figure 8). The ESM for LTT 3780b is the third
highest among these planets and closely matches that of
GJ 1252b (Shporer et al. 2019). Both of these targets
have ESM values that are nearly half that of LHS 3844b
(Vanderspek et al. 2019), a rocky planet whose ther-
mal phase curve has been characterized by the Spitzer
Space Telescope and found to be consistent with a dark
basaltic surface that lacks any substantial atmosphere
(Kreidberg et al. 2019).
The favorable ESM and TSM values of LTT 3780b
and c respectively make them both accessible targets for
atmospheric characterization. Together they present a
unique opportunity to conduct direct comparative stud-
ies of exoplanet atmospheres among planets within the
same planetary system which is critical for informing our
understanding of the formation and evolution of close-in
planets at a range of sizes and equilibrium temperatures.
5.5. An independent analysis of the LTT 3780 system
by CARMENES
Following the announcement of the planet candidates
TOI-732.01 and 02 in May 2019, multiple PRV instru-
ment teams began working towards the mass charac-
terization of these potential planets. This study has
presented the subset of those efforts from HARPS and
HARPS-N but we acknowledge that the CARMENES
Two planets spanning the radius valley around LTT 3780 19
Figure 8. Normalized atmospheric characterization metrics (Kempton et al. 2018) versus equilibrium temperature and host
star apparent magnitude. Left panel : the transmission spectroscopy metric (TSM) for warm mini-Neptunes around bright host
stars (J < 10) with P ∈ [10, 40] days and rp ∈ [2, 3] R⊕, including LTT 3780c. Marker colors depict the host star’s J-band
magnitude. Right panel : the emission spectroscopy metric (ESM) for favorable close-in rocky planets (rp < 1.5 R⊕) including
LTT 3780b. Marker colors depict the host star’s Ks-band magnitude. In both panels the marker sizes depict the primary transit
depths.
Table 4. Transmission spectroscopy metric values for warm mini-Neptunesa
Planet P rp mp Z Teq
b J Teff Rs Ms TSM TSM- Refs
name [days] [R⊕] [M⊕] [ppt] [K] mag [K] [R] [M] normalized
TOI-270d 11.38 2.13 5.48c 2.6 372 9.099 3386 0.38 0.40 86.8 1.00 1
TOI-700c 16.05 2.63 7.64c 3.3 356 9.469 3480 0.42 0.42 77.5 0.89 2,3
LTT 3780c 12.25 2.30 8.59 3.3 353 9.007 3331 0.37 0.40 71.5 0.82 4
HD 15337c 17.17 2.52 8.79 0.6 648 7.553 5125 0.87 0.90 60.6 0.70 5
GJ 143b 35.61 2.61 22.70 1.2 427 6.081 4640 0.70 0.73 53.0 0.61 6
K2-266d 14.70 2.93 8.90 1.5 538 9.611 4285 0.70 0.69 47.1 0.54 7
K2-18b 32.94 2.71 8.63 2.8 290 9.763 3505 0.47 0.50 42.8 0.49 8
Kepler-96b 15.24 2.67 8.46 0.6 798 9.260 5690 1.02 1.00 30.6 0.35 9
K2-266e 19.48 2.73 14.30 1.3 490 9.611 4285 0.70 0.69 21.3 0.24 7
Kepler-102e 16.15 2.22 8.93 0.7 604 9.984 4909 0.76 0.81 16.3 0.19 9
HD 119130b 16.98 2.63 24.50 0.5 801 8.730 5725 1.09 1.00 11.3 0.13 10
K2-38c 10.56 2.42 9.90 0.3 928 9.911 5757 1.38 2.24 9.2 0.11 11
Note—References: 1) Gu¨nther et al. 2019 2) Gilbert et al. 2020 3) Rodriguez et al. 2020 4) this work 5)
Dumusque et al. 2019 6) Dragomir et al. 2019 7) Rodriguez et al. 2018 8) Cloutier et al. 2019b 9) Marcy
et al. 2014 10) Luque et al. 2019 11) Sinukoff et al. 2016.
aHere we define warm mini-Neptunes as having P ∈ [10, 40] days and rp ∈ [2, 3] R⊕.
b Teq is calculated assuming zero albedo and full heat redistribution.
cPlanet masses are estimated using the mass-radius relation implemented in the forecaster code (Chen &
Kipping 2017).
20 Cloutier et al.
Table 5. Emission spectroscopy metric values for select close-in Earth-sized planetsa
Planet P rp Z Teq
b Tdayc Ks Teff Rs Ms ESM ESM- Refs
name [days] [R⊕] [ppt] [K] [K] mag [K] [R] [M] normalized
LHS 3844b 0.46 1.30 4.0 805 886 9.145 3036 0.19 0.15 29.0 1.00 1
GJ 1252b 0.52 1.19 0.8 1089 1198 7.915 3458 0.39 0.38 16.4 0.57 2
LTT 3780b 0.77 1.33 1.1 892 982 8.204 3331 0.37 0.40 13.4 0.46 3
L 168-9b 1.40 1.39 0.5 981 1079 7.082 3800 0.60 0.62 9.9 0.34 4
GJ 1132b 1.63 1.13 2.4 585 643 8.322 3270 0.21 0.18 9.5 0.33 5
L 98-59c 3.69 1.35 1.6 515 566 7.101 3412 0.31 0.31 6.9 0.24 6
LTT 1445Ab 5.36 1.38 2.0 435 478 6.500 3335 0.28 0.26 6.3 0.22 7
LP 791-18b 0.95 1.12 3.6 594 653 10.644 2949 0.17 0.14 5.9 0.20 8
L 98-59b 2.25 0.80 0.6 607 668 7.101 3412 0.31 0.31 4.1 0.14 6
TRAPPIST-1b 1.51 1.09 6.9 405 446 10.300 2559 0.12 0.08 4.0 0.14 9
LHS 1140c 3.78 1.28 3.1 434 477 8.821 3216 0.21 0.18 3.4 0.12 10
Note—References: 1) Vanderspek et al. 2019 2) Shporer et al. 2019 3) this work 4) Astudillo-Defru et al. 2020
5) Berta-Thompson et al. 2015 6) Kostov et al. 2019 7) Winters et al. 2019 8) Crossfield et al. 2019 9) Gillon
et al. 2017 10) Ment et al. 2019
aHere we define Earth-sized planets as those with rp < 1.5 R⊕.
b Teq is calulated assuming zero albedo and full heat redistribution.
cFor the purpose of calculating ESM values, we assume that Tday = 1.1Teq for all planets.
Two planets spanning the radius valley around LTT 3780 21
team has also submitted a paper presenting their own
RV time series and analysis (Nowak et al. 2020). Al-
though the submissions of these complementary studies
were coordinated between the two groups, their respec-
tive data, analyses, and writeups were intentionally con-
ducted independently.
6. SUMMARY
In this study, we present the LTT 3780 multi-
transiting system from the TESS mission. The newly
discovered planets LTT 3780b and c are confirmed with
intensive follow-up observations that includes ground-
based transit photometry, reconnaissance spectroscopy,
high-resolution imaging, and 63 precise RV measure-
ments from HARPS and HARPS-N. Our main findings
are summarized below.
• LTT 3780 is a bright (V = 13.07, Ks = 8.204)
mid-M dwarf with Ms = 0.401 ± 0.012 M and
Rs = 0.374± 0.011 R, located at 22 pc.
• LTT 3780b is a hot rocky exoplanet with Pb = 0.77
days, rp,b = 1.33± 0.07 R⊕, and mp,b = 2.62+0.48−0.46
M⊕, making its bulk composition consistent with
that of the Earth.
• LTT 3780c is a warm mini-Neptune with Pc =
12.25 days, rp,c = 2.30 ± 0.16 R⊕, and mp,c =
8.6+1.6−1.3 M⊕. Its bulk composition is inconsistent
with being Earth-like and requires a significant
amount of volatile material or H/He gas to explain
its mass and radius.
• The two planets span the radius valley around
low mass stars which enables the comparison of
their planetary parameters to predictions from
models of the emergence of the radius valley.
Both planets’ physical and orbital properties are
shown to be consistent with predictions of atmo-
spheric escape from photoevaporation and from
core-powered mass loss.
• The brightness and small size of LTT 3780 make
the planets LTT 3780b and c accessible targets for
atmospheric characterization of a hot rocky planet
and a warm mini-Neptune via emission and trans-
mission spectroscopy observations respectively.
ACKNOWLEDGMENTS
RC is supported by a grant from the National Aero-
nautics and Space Administration in support of the
TESS science mission. We thank Amber Medina for
assistance with detrending the TESS light curve. We
thank Sam Hadden for discussions regarding the TTV
analysis. We also thank the anonymous referee for their
comments that helped to improve the completeness of
our paper.
NAD acknowledges the support from FONDECYT
3180063.
AM acknowledges support from the senior Kavli In-
stitute Fellowships.
JGW is supported by a grant from the John Temple-
ton Foundation. The opinions expressed in this publi-
cation are those of the authors and do not necessarily
reflect the views of the John Templeton Foundation.
CZ is supported by a Dunlap Fellowship at the Dunlap
Institute for Astronomy & Astrophysics, funded through
an endowment established by the Dunlap family and the
University of Toronto.
IJMC acknowledges support from the NSF through
grant AST-1824644, and from NASA through Cal-
tech/JPL grant RSA-1610091.
FL gratefully acknowledges a scholarship from the
Fondation Zde˘nek et Michaela Bakala.
MS thanks the Swiss National Science Foundation
(SNSF) and the Geneva University for their continuous
support to our exoplanet researches. This work has been
in particular carried out in the frame of the National
Center for Competence in Research ‘PlanetS’ supported
by SNSF.
CAW acknowledges support from Science and Tech-
nology Facilities Council grant ST/P000312/1.
NCS acknowledges supported by FCT - Fundac¸a˜o
para a Cieˆncia e a Tecnologia through national
funds and by FEDER through COMPETE2020 -
Programa Operacional Competitividade e Interna-
cionalizao by these grants: UID/FIS/04434/2019;
UIDB/04434/2020; UIDP/04434/2020; PTDC/FIS-
AST/32113/2017 & POCI-01-0145-FEDER-032113;
PTDC/FIS-AST/28953/2017 & POCI-01-0145-
FEDER-028953.
MPi gratefully acknowledges the support from
the European Union Seventh Framework Programme
(FP7/2007-2013) under Grant Agreement No. 313014
(ETAEARTH).
JRM acknowledges the support by the CAPES,
CNPq, and FAPERN Brazilian agencies.
This work has been partially supported by the Na-
tional Aeronautics and Space Administration under
22 Cloutier et al.
grant No. NNX17AB59G issued through the Exoplanets
Research Program.
We acknowledge the use of public TESS Alert data
from the pipelines at the TESS Science Office and at
the TESS Science Processing Operations Center.
This work makes use of observations acquired with the
T150 telescope at Sierra Nevada Observatory, operated
by the Instituto de Astrof´ısica de Andaluca (IAA-CSIC).
The MEarth Team gratefully acknowledges funding
from the David and Lucile Packard Fellowship for Sci-
ence and Engineering (awarded to D.C.). This material
is based upon work supported by the National Science
Foundation under grants AST-0807690, AST-1109468,
AST-1004488 (Alan T. Waterman Award), and AST-
1616624. This work is made possible by a grant from the
John Templeton Foundation. The opinions expressed in
this publication are those of the authors and do not nec-
essarily reflect the views of the John Templeton Founda-
tion. This material is based upon work supported by the
National Aeronautics and Space Administration under
Grant No. 80NSSC18K0476 issued through the XRP
Program.
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
Processing and Analysis Center/California Institute of
Technology, funded by the National Aeronautics and
Space Administration and the National Science Foun-
dation.
This work has made use of data from the Euro-
pean Space Agency (ESA) mission Gaia (https://www.
cosmos.esa.int/gaia), processed by the Gaia Data Pro-
cessing and Analysis Consortium (DPAC, https://www.
cosmos.esa.int/web/gaia/dpac/consortium). Funding
for the DPAC has been provided by national institu-
tions, in particular the institutions participating in the
Gaia Multilateral Agreement.
This work makes use of observations from the LCOGT
network.
Resources supporting this work were provided by the
NASA High-End Computing (HEC) Program through
the NASA Advanced Supercomputing (NAS) Division
at Ames Research Center for the production of the
SPOC data products.
This work was supported by the French National
Research Agency in the framework of the Investisse-
ments dAvenir program (ANR-15-IDEX-02), through
the funding of the ”Origin of Life” project of the Univ.
Grenoble-Alpes.
Facilities: TESS, TRES, LCOGT, OSN,
TRAPPIST-North, MEarth-North, SOAR, Gem-
ini/NIRI, ESO 3.6m/HARPS, TNG/HARPS-N.
Software: AstroImageJ (Collins et al. 2017),
astropy (Astropy Collaboration et al. 2013, 2018),
BANZAI (McCully et al. 2018), batman (Kreidberg
2015), BGLS (Mortier et al. 2015), celerite (Foreman-
Mackey et al. 2017), emcee (Foreman-Mackey et al.
2013), EvapMass (Owen & Campos Estrada 2020),
EXOFAST (Eastman et al. 2013), EXOFASTv2 (Eastman
et al. 2019), exoplanet (Foreman-Mackey et al. 2019),
forecaster (Chen & Kipping 2017), PandExo (Batalha
et al. 2017), PyMC3 (Salvatier et al. 2016), scipy (Vir-
tanen et al. 2020), STARRY (Luger et al. 2019), Tapir
(Jensen 2013), TERRA (Anglada-Escude´ & Butler 2012),
TTV2Fast2Furious (Hadden 2019).
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Table 6. Point estimates of the LTT 3780 planetary system model parameters
Parameter Fiducial Model Valuesa EXOFASTv2 Model Valuesb
TESS light curve parameters
Baseline flux, f0 1.000072± 0.000070 1.000043± 0.000038
lnω0 1.64± 1.15 -
lnS0ω40 3.62
+0.40
−0.39 -
ln s2TESS 1.21± 0.01 -
TESS limb darkening coefficient, u1 0.28
+0.33
−0.20 0.30
+0.07
−0.05
TESS limb darkening coefficient, u2 0.16
+0.37
−0.28 0.32
+0.07
−0.06
Dilution - 0.023+0.047−0.048
RV parameters
lnλ/day 4.5+1.0−0.4 -
ln Γ −0.1+1.3−1.2 -
lnPGP/day 4.64
+0.14
−0.16 -
ln aHARPS/m/s 0.52
+0.69
−0.62 -
ln aHARPS-N/m/s 1.25
+0.70
−0.74 -
Jitter, sHARPS [m s
−1] 0.11+0.48−0.09 1.41
+0.70
−0.80
Jitter, sHARPS-N [m s
−1] 1.24+0.36−0.46 3.54
+0.99
−0.75
Systemic velocity, γHARPS [m s
−1] 195.5+1.4−1.5 195.4
+0.5
−0.5
Systemic velocity, γHARPS-N [m s
−1] 196.8+4.6−3.6 194.3
+1.0
−1.0
LTT 3780b (TOI-732.01) parameters
Log orbital period, lnPb −0.26338± 0.00007 -
Orbital period, Pb [days] 0.768448
+0.000055
−0.000053 0.7683881
+0.0000084
−0.0000083
Time of mid-transit, T0,b [BJD - 2,457,000] 1543.9115± 0.0011 1543.91199+0.00059−0.00051
Transit duration Db [hrs] 0.805
+0.049
−0.072 0.786
+0.024
−0.020
Transit depth, Zb [ppt] 1.087
+0.098
−0.103 1.076
+0.093
−0.089
Scaled semimajor axis, ab/Rs 7.03
+0.23
−0.21 7.05
+0.24
−0.22
Planet-to-star radius ratio, rp,b/Rs 0.0330
+0.0014
−0.0016 0.0328
+0.0014
−0.0014
Impact parameter, bb 0.35
+0.20
−0.23 0.43
+0.08
−0.12
Inclination, ib [deg] 87.1
+1.8
−1.7 86.5
+1.0
−0.7
Eccentricity, eb 0 (fixed) 0 (fixed)
Planet radius, rp,b [R⊕] 1.332+0.072−0.075 1.321
+0.074
−0.073
Log RV semi-amplitude, lnKb 1.23
+0.14
−0.17 1.26
+0.14
−0.17
RV semi-amplitude, Kb [m s
−1] 3.41+0.63−0.63 3.54
+0.54
−0.55
Planet mass, mp,b [M⊕] 2.62+0.48−0.46 2.77
+0.43
−0.43
Bulk density, ρb [g cm
−3] 6.1+1.8−1.5 6.5
+1.7
−1.4
Surface gravity, gb [m s
−2] 14.4+3.7−3.3 15.5
+3.6
−3.4
Escape velocity, vesc,b [km s
−1] 15.7+1.5−1.5 16.2
+1.3
−1.4
Semimajor axis, ab [AU] 0.01211
+0.00012
−0.00012 0.01212
+0.00012
−0.00012
Insolation, Fb [F⊕] 106+22−19 106
+23
−19
Equilibrium temperature, Teq,b [K]
Bond albedo = 0.0 892± 44 892± 44
Bond albedo = 0.3 816± 40 816± 40
Table 6 continued
Two planets spanning the radius valley around LTT 3780 27
Table 6 (continued)
Parameter Fiducial Model Valuesa EXOFASTv2 Model Valuesb
LTT 3780c (TOI-732.02) parameters
Log orbital period, lnPc 2.50582± 0.00023 -
Orbital period, Pc [days] 12.2519
+0.0028
−0.0030 12.252048
+0.000060
−0.000059
Time of mid-transit, T0,c [BJD - 2,457,000] 1546.8484± 0.0014 1546.8481+0.0011−0.0012
Transit duration Dc [hrs] 1.392
+0.050
−0.049 1.404
+0.048
−0.046
Transit depth, Zc [ppt] 3.24
+0.41
−0.37 3.13
+0.28
−0.28
Scaled semimajor axis, ac/Rs 44.6
+1.5
−1.3 44.7
+1.5
−1.4
Planet-to-star radius ratio, rp,c/Rs 0.0570
+0.0035
−0.0033 0.0560
+0.0024
−0.0025
Impact parameter, bc 0.65
+0.15
−0.36 0.71
+0.08
−0.15
Inclination, ic [deg] 89.18
+0.47
−0.22 88.95
+0.10
−0.09
ec cosωc - −0.05+0.07−0.08
ec sinωc - 0.15
+0.15
−0.13√
ec cosωc 0.13
+0.12
−0.15 -√
ec sinωc 0.07
+0.17
−0.19 -
Eccentricity, ec 0.06
+0.15
−0.14 0.18
+0.14
−0.11
Argument of periastron, ωc [deg] 124
+87
−147 111
+39
−27
Planet radius, rp,c [R⊕] 2.30+0.16−0.15 2.25
+0.13
−0.13
Log RV semi-amplitude, lnKc 1.49
+0.17
−0.17 1.60
+0.13
−0.15
RV semi-amplitude, Kc [m s−1] 4.44+0.82−0.68 4.94
+0.68
−0.67
Planet mass, mp,c [M⊕] 8.6+1.6−1.3 9.5
+1.3
−1.3
Bulk density, ρc [g cm−3] 3.9+1.0−0.9 4.6
+1.1
−0.9
Surface gravity, gc [m s−2] 16.0+3.7−3.3 18.3
+3.5
−3.1
Escape velocity, vesc,c [km s−1] 21.7+2.1−2.0 23.0
+1.7
−1.7
Semimajor axis, ac [AU] 0.07673
+0.00075
−0.00077 0.07678
+0.00076
−0.00077
Insolation, Fc [F⊕] 2.63+0.56−0.48 2.63
+0.56
−0.48
Equilibrium temperature, Teq,c [K]
Bond albedo = 0.0 353± 18 354± 18
Bond albedo = 0.3 323± 16 324± 16
aOur fiducial model features sequential modeling of the TESS light curve, with a SHO GP detrending
component plus two transiting planets, followed by the RV analysis conditioned on the results of the
transit analysis. The fiducial RV model includes a quasi-periodic activity model plus two keplerian orbital
solutions. The LTT 3780b keplerian component is fixed to a circular orbit.
bOur alternative analysis is a global model of the TESS light curve, ground-based light curves, and RVs
using the EXOFASTv2 software. The input light curves have already been detrended and the residual RV
noise is treated as an additive scalar jitter. This global model produces self-consistent results between
the transit and RV dataset and improves the precision on each planet’s orbital ephemeris by including
the ground-based transit light curves.
APPENDIX
A. LIMITS ON THE PLANET MASSES FOR
CONSISTENCY WITH MODELS OF
PHOTOEVAPORATION
Here we present the formalism used to estimate mass
limits on planets spanning the radius valley within
a multi-transiting system under the photoevaporation
model (Owen & Campos Estrada 2020). This model
is adopted from Owen & Wu (2017) in which a pop-
ulation of non-rocky planets is formed with a distri-
bution of Earth-like core masses plus H/He envelopes.
The energy-limited atmospheric mass loss rate due to
XUV heating by the host star, and subsequent thermal
escape, is M˙atm = ηppir
3
coreLXUV/4pia
2Gmcore where
ηp, rcore, a,mcore are the planet’s mass-loss efficiency,
core radius, orbital separation, and core mass respec-
tively, LXUV is the XUV luminosity of the host star
28 Cloutier et al.
and G is the gravitational constant. By writing the at-
mospheric mass as the product of the planet mass and
envelope mass fraction (Matm = mp X2), the mass loss
timescale under photoevaporation (tloss = Matm/M˙atm)
scales as
tloss ∝
m2p a
2 X2
ηp r3core LXUV
∝ m
3
p a
2 X2
r4core LXUV
(A1)
where we have adopted ηp ∝ v−2esc ∝ m−1corercore (Owen
& Wu 2017) and set mcore = mp by assuming that the
planet masses are dominated by their rocky core masses.
In this simple picture, Owen & Campos Estrada (2020)
set Equation A1 to the maximum mass loss timescale for
a rocky planet below the valley which is assumed to have
just lost the entirety of its initial H/He envelope. In or-
der to form the radius valley, this timescale must be less
than the maximum timescale for the gaseous (i.e. non-
rocky) planet to have retained its initial H/He envelope
with an atmospheric mass fraction of X2. This criterion
places the following constrains on the rocky and gaseous
planet parameters according to
tloss,gas
tloss,rock
≥ 1,(
mp,gas
mp,rock
)(
agas
arock
)2/3(
rcore,gas
rcore,rock
)−4/3
≥ 1. (A2)
The power of comparing planets within the same plan-
etary system is evidenced in Equation A2 in which the
unknown quantity LXUV is scaled out of the expression.
In the photoevaporation model, the stripped rocky
planet has been reduced to its Earth-like core such
that the core radius is equivalent to the planet’s radius;
rcore,rock = rp,rock. Noting that rcore ∝ m0.27core for Earth-
like bodies (Zeng et al. 2016), we write rcore,gas = m
0.27
p,gas
where the input radius and mass are each given in units
of the Earth. It follows from Equation A2 that the min-
imum mass of the gaseous planet under the photoevap-
oration model is
mp,gas
M⊕
≥
[(
mp,rock
M⊕
)(
arock
agas
)2/3 (
rp,rock
R⊕
)−4/3]1.56
.
(A3)
The inequality in Equation A3 must be satisfied for the
planetary parameters to be consistent with the photoe-
vaporation model. Similarly,
mp,rock
M⊕
≤
(
mp,gas
M⊕
)0.64(
agas
arock
)2/3 (
rp,rock
R⊕
)4/3
(A4)
represents the maximum mass of the rocky planet for
the system to be consistent with the photoevaporation
model.
A few notable caveats exist with this simplified model
(Owen & Campos Estrada 2020). Specifically, these cal-
culations assumed that the envelope mass fraction X2
for which the mass loss timescales are maximized, is in-
dependent of the planet properties. Furthermore, indi-
vidual gaseous planets may have envelope mass fractions
that are greater than that which is required to maximize
tloss,gas. Lastly, this simplified model ignores the con-
traction of the H/He envelope over time. This poses a
critical limitation as gaseous envelopes are likely to have
been more extended at early times when photoevapora-
tion was actively ongoing, compared to their present day
values.
These issues are alleviated by the EvapMass software
Owen & Campos Estrada (2020) which calculates the
value of X2 that maximizes the mass loss timescale and
self-consistently models the gaseous envelope structure
from the typical Kelvin-Helmholtz time of the gaseous
envelope (τKH ∼ 100 Myrs) to the present. However, at-
tempting these numerical calculations on the LTT 3780
system resulted in a failure to solve for a lower limit on
the LTT 3780c core mass. By default, EvapMass only
considers mcore,gas ≥ 0.1 M⊕, which is itself a very weak
constraint, such that the EvapMass calculation does not
provide any new insight into the minimum mass of LTT
3780c.
B. LIMITS ON THE PLANET MASSES FOR
CONSISTENCY WITH MODELS OF
CORE-POWERED MASS LOSS
Here we derive the constraints on the planet masses
in order to be consistent with the core-powered mass
loss model for sculpting the radius valley. Analogously
to the formalism presented in Appendix A, we com-
pare the timescales for core-powered mass loss of planets
spanning the radius valley and within the same multi-
transiting system.
Core-powered mass loss is another mechanism for
driving thermal escape of a planet’s atmosphere due to
the planetary core’s own cooling luminosity (Ginzburg
et al. 2018; Gupta & Schlichting 2019). Similarly to
the initial conditions assumed in the photoevaporation
Two planets spanning the radius valley around LTT 3780 29
model, here a population of non-rocky planets is formed
with a distribution of Earth-like core masses plus H/He
envelopes. Their atmospheres are described by a lower
convective region which is terminated at the radius of
the radiative-convective boundary (RCB), above which
the atmosphere becomes isothermal and heat is trans-
ported radiatively to the planet’s Bondi radius. The
Bondi radius is set by equating the planet’s escape veloc-
ity to its thermal sound speed and is RB = Gmcore/c
2
s,
where G is the gravitational constant, mcore is the core
mass, and the thermal sound speed is cs =
√
kBTeq/µ,
where kB is the Boltzmann constant, Teq is the equi-
librium temperature, and µ is the atmospheric mean
molecular weight, assumed to be 2 amu for H2. The
Bondi-limited regime represents the physical limit of the
atmospheric mass loss rate and is dictated by the gas
thermal velocity at RB.
The corresponding Bondi-limited mass loss rate is
M˙atm = 4piR
2
BcsρRCB exp (−Gmcore/c2sRRCB) where
ρRCB is the atmospheric density at the RCB whose ra-
dius is RRCB. The majority of the atmosphere’s mass
lies within its convective zone such that integrating an
adiabatic gas density profile over the convective zone
returns the approximate atmospheric mass
Matm ≈ 4piR3RCBρRCB
(
γ − 1
γ
RB
RRCB
)1/(γ−1)
(B5)
where γ is the adiabatic index which is fixed to 4/3
(Ginzburg et al. 2016). The resulting mass loss timescale
(tloss = Matm/M˙atm) scales as
tloss ∝ RB
cs
exp
(
Gmcore
c2sRRCB
)
,
∝ mp
T
3/2
eq
exp
(
c′mp
Teqrp
)
, (B6)
(B7)
where the constant c′ = Gµ/kB ∼ 104 R⊕ K M⊕−1, the
planet’s envelope mass fraction is assumed to be small
such that mcore ≈ mp, and the RRCB is treated as the
planet’s effective radius; RRCB ≈ rp.
Analogously to the photoevaporation scenario, for the
planetary parameters within a multi-transiting system
and spanning the radius valley to be consistent with
the core-powered mass loss scenario, we require that
the mass loss timescale of the gaseous (i.e. non-rocky)
planet exceeds that of the rocky planet. This leads to
the following condition:
tloss,gas
tloss,rock
≥ 1,(
mp,gas
mp,rock
)(
Teq,gas
Teq,rock
)−3/2
exp
[
c′
(
mp,gas
Teq,gas rp,gas
− mp,rock
Teq,rock rp,rock
)]
≥ 1. (B8)
The appearance of the planet masses as both linear fac-
tors and in the exponential function means that Equa-
tion B8 belongs to the class of Lambert W functions
of the form f(m) ∝ mem. Such functions do not have
analytical solutions but the limiting planet masses un-
der the core-powered mass loss model can be solved for
numerically.
All Authors and Affiliations
Ryan Cloutier,1 Jason D. Eastman,1 Joseph E. Rodriguez,1 Nicola Astudillo-Defru,2 Xavier Bonfils,3
Annelies Mortier,4 Christopher A. Watson,5 Manu Stalport,6 Matteo Pinamonti,7 Florian Lienhard,4
Avet Harutyunyan,8 Mario Damasso,7 David W. Latham,1 Karen A. Collins,1 Robert Massey,9
Jonathan Irwin,1 Jennifer G. Winters,1 David Charbonneau,1 Carl Ziegler,10 Elisabeth Matthews,11
Ian J. M. Crossfield,12 Laura Kreidberg,1 Samuel N. Quinn,1 George Ricker,11 Roland Vanderspek,11
Sara Seager,13, 14, 15 Joshua Winn,16 Jon M. Jenkins,17 Michael Vezie,11 Ste´phane Udry,6 Joseph D. Twicken,17, 18
Peter Tenenbaum,17 Alessandro Sozzetti,7 Damien Se´gransan,6 Joshua E. Schlieder,19 Dimitar Sasselov,1
Nuno C. Santos,20, 21 Ken Rice,22 Benjamin V. Rackham,11, 23 Ennio Poretti,8, 24 Giampaolo Piotto,25
David Phillips,1 Francesco Pepe,6 Emilio Molinari,26 Lucile Mignon,3 Giuseppina Micela,27 Claudio Melo,28
Jose´ R. de Medeiros,29 Michel Mayor,6 Rachel A. Matson,30 Aldo F. Martinez Fiorenzano,8
Andrew W. Mann,31 Antonio Magazzu´,8 Christophe Lovis,6 Mercedes Lo´pez-Morales,1 Eric Lopez,19
Jack J. Lissauer,17 Se´bastien Le´pine,32 Nicholas Law,31 John F. Kielkopf,33 John A. Johnson,1
Eric L. N. Jensen,34 Steve B. Howell,17 Erica Gonzales,35 Adriano Ghedina,8 Thierry Forveille,3
Pedro Figueira,36, 20 Xavier Dumusque,6 Courtney D. Dressing,37 Rene´ Doyon,38 Rodrigo F. D´ıaz,39
Luca Di Fabrizio,8 Xavier Delfosse,3 Rosario Cosentino,8 Dennis M. Conti,40 Kevin I. Collins,41
Andrew Collier Cameron,42 David Ciardi,43 Douglas A. Caldwell,17 Christopher Burke,11 Lars Buchhave,44
Ce´sar Bricen˜o,45 Patricia Boyd,19 Franc¸ois Bouchy,6 Charles Beichman,46 E´tienne Artigau,38 and
Jose M. Almenara3
1Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA, 02138, USA
2Departamento de Matema´tica y F´ısica Aplicadas, Universidad Cato´lica de la Sant´ısima Concepcio´n, Alonso de Rivera 2850, Concepcio´n,
Chile
3CNRS, IPAG, Universite´ Grenoble Alpes, 38000 Grenoble, France
4Astrophysics Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, UK
5Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast, BT7 1NN, UK
6Observatoire Astronomique de l’Universite´ de Gene`ve, 51 chemin des Maillettes, 1290 Versoix, Switzerland
7INAF - Osservatorio Astrofisico di Torino, Strada Osservatorio 20, Pino Torinese (To) 10025, Italy
8Fundacio´n Galileo Galilei-INAF, Rambla Jose´ Ana Fernandez Pe´rez 7, 38712 Bren˜a Baja, TF, Spain
9American Association of Variable Star Observers (AAVSO), 49 Bay State Rd, Cambridge, MA, 02138, USA
10Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, Ontario M5S 3H4, Canada
11Department of Earth, Atmospheric and Planetary Sciences, and Kavli Institute for Astrophysics and Space Research, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA
12Department of Physics & Astronomy, University of Kansas, 1082 Malott, 1251 Wescoe Hall Dr. Lawrence, KS, 66045, USA
13Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA
02139, USA
14Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
15Department of Aeronautics and Astronautics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
16Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
17NASA Ames Research Center, Moffett Field, CA, 94035, USA
18SETI Institute, Mountain View, CA 94043, USA
19NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA
20Instituto de Astrof´ısica e Cieˆncias do Espac¸o, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
21Departamento de F´ısica e Astronomia, Faculdade de Cieˆncias, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal
22SUPA, Institute for Astronomy, University of Edinburgh, Blackford Hill, Edinburgh, EH9 3HJ, Scotland, UK
2351 Pegasi b Fellow
24INAF-Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate (LC), Italy
25Dip. di Fisica e Astronomia Galileo Galilei - Universita` di Padova, Vicolo dell’Osservatorio 2, 35122, Padova, Italy
26INAF - Osservatorio Astronomico di Cagliari, via della Scienza 5, 09047, Selargius, Italy
27INAF - Osservatorio Astronomico di Palermo, Piazza del Parlamento 1, I-90134 Palermo, Italy
28European Southern Observatory, Alonso de Crdova 3107, Vitacura, Regin Metropolitana, Chile
29Departamento de F´ısica, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN, Brazil
30U.S. Naval Observatory, Washington, DC 20392, USA
31Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA
32Department of Physics and Astronomy, Georgia State University, Atlanta, GA 30302, USA
33Department of Physics and Astronomy, University of Louisville, Louisville, KY 40292, USA
34Dept. of Physics & Astronomy, Swarthmore College, Swarthmore PA 19081, USA
35Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA
Two planets spanning the radius valley around LTT 3780 31
36European Southern Observatory, Alonso de Co´rdova 3107, Vitacura, Regio´n Metropolitana, Chile
37Astronomy Department, University of California, Berkeley, CA, 94720, USA
38De´partement de physique, Universite´ de Montre´al, 2900 boul. E´douard-Montpetit, Montre´al, QC, H3C 3J7, Canada
39International Center for Advanced Studies (ICAS) and ICIFI (CONICET), ECyT-UNSAM, Campus Miguelete, 25 de Mayo y Francia,
(1650) Buenos Aires, Argentina
40American Association of Variable Star Observers, 49 Bay State Road, Cambridge, MA 02138, USA
41George Mason University, 4400 University Drive, Fairfax, VA, 22030 USA
42School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, UK
43Caltech/IPAC, 1200 E. California Blvd. Pasadena, CA 91125, USA
44DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 328, DK-2800 Kgs. Lyngby, Denmark
45Cerro Tololo Inter-American Observatory, Casilla 603, La Serena, Chile
46NASA Exoplanet Science Institute, Infrared Processing & Analysis Center, Jet Propulsion Laboratory, California Institute of
Technology, Pasadena CA, 91125, USA