# New Mass and Radius Constraints on the LHS 1140 Planets – LHS 1140 b is
Either a Temperate Mini-Neptune or a Water World

Charles Cadieux Institut Trottier de recherche sur les exoplanètes, Université
de Montréal, 1375 Ave Thérèse-Lavoie-Roux, Montréal, QC, H2V 0B3, Canada
Mykhaylo Plotnykov Department of Physics, University of Toronto, Toronto, ON
M5S 3H4, Canada  René Doyon Institut Trottier de recherche sur les
exoplanètes, Université de Montréal, 1375 Ave Thérèse-Lavoie-Roux, Montréal,
QC, H2V 0B3, Canada  Observatoire du Mont-Mégantic, Université de Montréal,
Montréal H3C 3J7, Canada  Diana Valencia Department of Physical &
Environmental Sciences, University of Toronto at Scarborough, Toronto, ON M1C
1A4, Canada  David A. Dunlap Dept. of Astronomy & Astrophysics, University of
Toronto, 50 St. George Street, Toronto, Ontario, M5S 3H4, Canada  Farbod
Jahandar Institut Trottier de recherche sur les exoplanètes, Université de
Montréal, 1375 Ave Thérèse-Lavoie-Roux, Montréal, QC, H2V 0B3, Canada  Lisa
Dang Institut Trottier de recherche sur les exoplanètes, Université de
Montréal, 1375 Ave Thérèse-Lavoie-Roux, Montréal, QC, H2V 0B3, Canada  Martin
Turbet Laboratoire de Météorologie Dynamique/IPSL, CNRS, Sorbonne Université,
Ecole Normale Supérieure, PSL Research University, Ecole Polytechnique, 75005
Paris, France  Laboratoire d’astrophysique de Bordeaux, Univ. Bordeaux, CNRS,
B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France  Thomas J. Fauchez
NASA Goddard Space Flight Center 8800 Greenbelt Road Greenbelt, MD 20771, USA
Integrated Space Science and Technology Institute, Department of Physics,
American University, Washington DC  NASA GSFC Sellers Exoplanet Environments
Collaboration  Ryan Cloutier Department of Physics & Astronomy, McMaster
University, 1280 Main St W, Hamilton, ON, L8S 4L8, Canada  Collin Cherubim
Earth and Planetary Science, Harvard University, 20 Oxford St, Cambridge, MA
02138, USA  Center for Astrophysics — Harvard & Smithsonian, 60 Garden Street,
Cambridge, MA 02138, USA  Étienne Artigau Institut Trottier de recherche sur
les exoplanètes, Université de Montréal, 1375 Ave Thérèse-Lavoie-Roux,
Montréal, QC, H2V 0B3, Canada  Observatoire du Mont-Mégantic, Université de
Montréal, Montréal H3C 3J7, Canada  Neil J. Cook Institut Trottier de
recherche sur les exoplanètes, Université de Montréal, 1375 Ave Thérèse-
Lavoie-Roux, Montréal, QC, H2V 0B3, Canada  Billy Edwards SRON, Netherlands
Institute for Space Research, Niels Bohrweg 4, NL-2333 CA, Leiden, The
Netherlands  Department of Physics and Astronomy, University College London,
London, United Kingdom  Tim Hallatt Department of Physics and Trottier Space
Institute, McGill University, Montréal, Québec, H3A 2T8, Canada  Institut
Trottier de recherche sur les exoplanètes, Université de Montréal, 1375 Ave
Thérèse-Lavoie-Roux, Montréal, QC, H2V 0B3, Canada  Benjamin Charnay LESIA,
Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université
Paris-Cité, 5 place Jules Janssen, 92195 Meudon, France  François Bouchy
Departement d’astronomie, Université de Genève, Chemin Pegasi, 51, CH-1290
Versoix, Switzerland  Romain Allart Institut Trottier de recherche sur les
exoplanètes, Université de Montréal, 1375 Ave Thérèse-Lavoie-Roux, Montréal,
QC, H2V 0B3, Canada  Lucile Mignon Departement d’astronomie, Université de
Genève, Chemin Pegasi, 51, CH-1290 Versoix, Switzerland  Frédérique Baron
Institut Trottier de recherche sur les exoplanètes, Université de Montréal,
1375 Ave Thérèse-Lavoie-Roux, Montréal, QC, H2V 0B3, Canada  Susana C. C.
Barros Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto,
CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal  Departamento de Fisica e
Astronomia, Faculdade de Ciencias, Universidade do Porto, Rua Campo Alegre,
4169-007 Porto, Portugal  Björn Benneke Institut Trottier de recherche sur les
exoplanètes, Université de Montréal, 1375 Ave Thérèse-Lavoie-Roux, Montréal,
QC, H2V 0B3, Canada  B. L. Canto Martins Departamento de Física Teórica e
Experimental, Universidade Federal do Rio Grande do Norte, Campus
Universitário, Natal, RN, 59072-970, Brazil  Nicolas B. Cowan Department of
Earth & Planetary Sciences, McGill University, 3450 rue University, Montréal,
QC H3A 0E8, Canada  Department of Physics and Trottier Space Institute, McGill
University, Montréal, Québec, H3A 2T8, Canada  J. R. De Medeiros Departamento
de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte,
Campus Universitário, Natal, RN, 59072-970, Brazil  Xavier Delfosse Univ.
Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France  Elisa Delgado-Mena
Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP,
Rua das Estrelas, PT4150-762 Porto, Portugal  Xavier Dumusque Departement
d’astronomie, Université de Genève, Chemin Pegasi, 51, CH-1290 Versoix,
Switzerland  David Ehrenreich Departement d’astronomie, Université de Genève,
Chemin Pegasi, 51, CH-1290 Versoix, Switzerland  Yolanda G. C. Frensch
Departement d’astronomie, Université de Genève, Chemin Pegasi, 51, CH-1290
Versoix, Switzerland  J. I. González Hernández  Instituto de Astrofísica de
Canarias, 38205 La Laguna, Tenerife, Spain  Departamento de Astrofísica,
Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain  Nathan C. Hara
Departement d’astronomie, Université de Genève, Chemin Pegasi, 51, CH-1290
Versoix, Switzerland  David Lafrenière Institut Trottier de recherche sur les
exoplanètes, Université de Montréal, 1375 Ave Thérèse-Lavoie-Roux, Montréal,
QC, H2V 0B3, Canada  Gaspare Lo Curto European Southern Observatory, Karl-
Schwarzschild-Strasse 2, 85748 Garching, Germany  Lison Malo Institut Trottier
de recherche sur les exoplanètes, Université de Montréal, 1375 Ave Thérèse-
Lavoie-Roux, Montréal, QC, H2V 0B3, Canada  Observatoire du Mont-Mégantic,
Université de Montréal, Montréal H3C 3J7, Canada  Claudio Melo European
Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching, Germany
Dany Mounzer Departement d’astronomie, Université de Genève, Chemin Pegasi,
51, CH-1290 Versoix, Switzerland  Vera Maria Passeger Instituto de Astrofísica
de Canarias, 38205 La Laguna, Tenerife, Spain  Departamento de Astrofísica,
Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain  Hamburger
Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany  Francesco Pepe
Departement d’astronomie, Université de Genève, Chemin Pegasi, 51, CH-1290
Versoix, Switzerland  Anne-Sophie Poulin-Girard  ABB, Québec, G1P 0B2, Canada
Nuno C. Santos Instituto de Astrofísica e Ciências do Espaço, Universidade do
Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal  Departamento de
Fisica e Astronomia, Faculdade de Ciencias, Universidade do Porto, Rua Campo
Alegre, 4169-007 Porto, Portugal  Danuta Sosnowska  Departement d’astronomie,
Université de Genève, Chemin Pegasi, 51, CH-1290 Versoix, Switzerland
Alejandro Suárez Mascareño Instituto de Astrofísica de Canarias, 38205 La
Laguna, Tenerife, Spain  Departamento de Astrofísica, Universidad de La
Laguna, 38206 La Laguna, Tenerife, Spain  Simon Thibault Centre d’optique,
photonique et lasers, Université Laval, Québec, G1V 0A6, Canada  Valentina
Vaulato Departement d’astronomie, Université de Genève, Chemin Pegasi, 51,
CH-1290 Versoix, Switzerland  Gregg A. Wade Department of Physics and Space
Science, Royal Military College of Canada, PO Box 17000, Station Forces,
Kingston, ON, Canada  François Wildi Departement d’astronomie, Université de
Genève, Chemin Pegasi, 51, CH-1290 Versoix, Switzerland

###### Abstract

The two-planet transiting system LHS 1140 has been extensively observed since
its discovery in 2017, notably with Spitzer, HST, TESS, and ESPRESSO, placing
strong constraints on the parameters of the M4.5 host star and its small
temperate exoplanets, LHS 1140 b and c. Here, we reanalyse the ESPRESSO
observations of LHS 1140 with the novel line-by-line framework designed to
fully exploit the radial velocity content of a stellar spectrum while being
resilient to outlier measurements. The improved radial velocities, combined
with updated stellar parameters, consolidate our knowledge on the mass of LHS
1140 b (5.60$\pm$0.19 M⊕) and LHS 1140 c (1.91$\pm$0.06 M⊕) with unprecedented
precision of 3%. Transits from Spitzer, HST, and TESS are jointly analysed for
the first time, allowing us to refine the planetary radii of b
(1.730$\pm$0.025 R⊕) and c (1.272$\pm$0.026 R⊕). Stellar abundance
measurements of refractory elements (Fe, Mg and Si) obtained with NIRPS are
used to constrain the internal structure of LHS 1140 b. This planet is
unlikely to be a rocky super-Earth as previously reported, but rather a mini-
Neptune with a $\sim$0.1% H/He envelope by mass or a water world with a water-
mass fraction between 9 and 19% depending on the atmospheric composition and
relative abundance of Fe and Mg. While the mini-Neptune case would not be
habitable, a water-abundant LHS 1140 b potentially has habitable surface
conditions according to 3D global climate models, suggesting liquid water at
the substellar point for atmospheres with relatively low CO2 concentration,
from Earth-like to a few bars.

††facilities: Spitzer, HST, TESS, ESO-VLT/ESPRESSO, ESO-La
Silla/NIRPS††software: emcee (Foreman-Mackey et al., 2013); Astropy (Astropy
Collaboration et al., 2018); radvel (Fulton et al., 2018); matplotlib (Hunter,
2007); juliet (Espinoza et al., 2019); batman (Kreidberg, 2015); SciPy
(Virtanen et al., 2020); NumPy (Harris et al., 2020) zeus (Karamanis et al.,
2021); seaborn (Waskom, 2021); exofile (github.com/AntoineDarveau/exofile);
corner (Foreman-Mackey, 2016); PSG (Villanueva et al., 2022)

##  1 Introduction

The last few years have been fruitful in the quest to uncover exoplanets
transiting nearby low-mass stars. Unlike their solar counterparts, M dwarfs
represent optimal targets for detailed studies of their planetary systems.
They have smaller sizes (0.1–0.6 R⊙) and masses (0.1–0.6 M⊙), facilitating the
characterization of exoplanets through transit and radial velocity (RV)
observations. As they are less luminous, their Habitable Zone (HZ) is more
compact than in our solar system, corresponding to orbital periods usually
well sampled by current surveys (typically 60 days for an M0, 3 days for an
M9). M dwarfs have at least twice as many small exoplanets with $M_{\rm p}\sin
i<10$ M⊕ than G-type stars (Sabotta et al., 2021) and make up the majority of
systems in the vicinity of the Sun (Reylé et al. 2021, 2022). We thus expect
the nearest HZ planets to orbit such kind of stars. This is exemplified with
Proxima Centauri (M5.5V), our closest neighbour (1.3 pc; Gaia Collaboration et
al. 2021), hosting a non-transiting terrestrial planet in the HZ (Anglada-
Escudé et al., 2016; Faria et al., 2022). The M5.5V dwarf GJ 1002 at 4.84 pc
also has two non-transiting Earth-mass companions in the HZ recently
discovered by Suárez Mascareño et al. (2023). The TRAPPIST-1 system (Gillon et
al., 2017) at 12.5 pc has seven terrestrial planets, including three in the
HZ, all transiting the M8V ultracool host. These transiting systems are
extremely valuable because the radius of exoplanets — sometimes even the mass
through transit timing variations as for TRAPPIST-1 (e.g., Agol et al. 2021) —
is only accessible via the transit method. Combined with dynamical mass
constraints from Doppler spectroscopy, the bulk density of exoplanets can be
obtained, revealing whether their interior is mostly rocky, gaseous, or
perhaps even water-rich (Luque & Pallé, 2022), but evidence of water worlds
remains elusive (Rogers et al., 2023).

The M4.5 dwarf LHS 1140 located at 15.0 pc is another intriguing system,
currently the second closest to a transiting HZ exoplanet after TRAPPIST-1. A
super-Earth on a 24.7-day temperate orbit was detected in 2017 (Dittmann et
al. 2017, hereafter D17) from MEarth photometry (Irwin et al., 2009), followed
by the discovery of a second rocky planet with a shorter 3.8-day period (Ment
et al. 2019, hereafter M19). The follow-up study of M19 presents a transit
visit of LHS 1140 b and c with the Spitzer Space Telescope, largely improving
the radius constraints of the two planets. Their masses were derived from
HARPS (Pepe et al., 2002) radial velocities, initially for b only by D17, and
subsequently for b and c by M19 using an extended data set. This planetary
system was revisited in 2020 (Lillo-Box et al. 2020, hereafter LB20) with the
ESPRESSO spectrograph (Pepe et al., 2021) and the Transiting Exoplanet Survey
Satellite (TESS; Ricker et al. 2015), offering an update of the bulk densities
of LHS 1140 b and c, while also hinting at a possible third non-transiting
planet on a longer orbit ($P_{\rm d}=78.9$ days). Lastly, transit spectroscopy
of LHS 1140 b has been obtained from the ground (Diamond-Lowe et al., 2020)
and from space (Edwards et al., 2021) with the Wide Field Camera 3 (WFC3) on
the Hubble Space Telescope (HST). Edwards et al. (2021) reported a tentative
detection of a hydrogen-dominated atmosphere with H2O on LHS 1140 b, but the
signal ($\sim$100 ppm) could also be explained by stellar contamination.

In this letter, we present a new analysis of archival data of LHS 1140 and
derive stellar abundances from near-infrared spectroscopy with NIRPS (Bouchy
et al., 2017). The ESPRESSO radial velocities were significantly improved
using a line-by-line extraction (Artigau et al., 2022) and, for the first
time, transit data sets from Spitzer, HST, and TESS were jointly analysed. We
describe the observations in Section 2 and characterize the host star in
Section 3. We present our revision of the mass and radius of the LHS 1140
planets and discuss their plausible internal structures in Section 4.
Concluding remarks follow in Section 5.

##  2 Observations

###  2.1 Spitzer photometry

We recovered four Spitzer transits of LHS 1140 b taken with the Infrared Array
Camera (Fazio et al., 2004) at 4.5 $\mu$m from the NASA/IPAC Infrared Science
Archive111irsa.ipac.caltech.edu/. These data include the double transit of LHS
1140 b and c analysed by M19, with three additional unpublished transits of
LHS 1140 b (PI: J. A. Dittmann) from the same program. The observations were
taken on UT2017-10-02, 2017-10-27, 2018-03-24, and 2018-04-18, hereafter
referred to as Transit 1 to 4 (Transit 4 is presented in M19).

The observations were acquired using the subarray mode with a 2 s exposure
producing datacubes of 64 subarray images of 32$\times$32 pixels. We used the
Spitzer Phase Curve Analysis (SPCA) pipeline (Dang et al., 2018; Bell et al.,
2021) to extract the photometry and decorrelate against instrumental
systematics. For Transits 1 and 3, we use a 3$\times$3 pixel area to extract
the target’s intensity for each subarray frame. We then median-binned each
datacube to mitigate the known subarray instrumental systematics and use Pixel
Level Decorrelation (PLD; Deming et al., 2015) to detrend against detector
systematics. Similarly to M19, we elect to discard the first 78 minutes of
Transit 4 during which the target’s centroid had not yet settled on the
detector. For Transit 2 and 4, we opted for a different detrending strategy as
the shorter baseline before transit tends to bias the retrieved eclipse depth
with PLD. Instead, we find that extracting the target photometry with an exact
circular aperture with a radius of 3.0 pixels centered on the target’s
centroid yields the optimal photometric scheme. We then binned each datacube
and detrended the instrumental systematics using a 2D polynomial as a function
of centroid. The stacked (phase-folded) transit of LHS 1140 b is presented in
Figure 1. The individual detrended transits are presented Figure A1.

Figure 1: Phase-folded transit of LHS 1140 b observed with Spitzer Infrared
Array Camera (at 4.5 $\mu$m). The transit of LHS 1140 c from Transit 4 is
masked (see Fig. A1 for individual transits). The open circles represent
8-minute binned photometry and the blue curve depicts the best-fit transit
model. The residuals of this fit are shown below.

###  2.2 HST WFC3 white light curve

Two transits of LHS 1140 b were observed with HST WFC3 on UT2017-01-28 and
UT2017-12-15 (PN: 14888; PI: J. A. Dittmann). Unfortunately, due to large
shifts in the position of the spectrum on the detector, the observation from
UT2017-01-28 could not be reliably analysed (Edwards et al., 2021). The
transit on UT2017-12-15 was successfully analysed by Edwards et al. (2021) to
constrain the transmission spectrum of LHS 1140 b near 1.4 $\mu$m. The
observations were conducted in the G141 grism configuration with the GRISM256
aperture (256$\times$256 subarray) and 103.13 s integration time. Readers are
referred to Edwards et al. (2021) for a complete description of the HST data
reduction that made use of the Iraclis software (Tsiaras et al., 2016). Here,
we include the extracted white light curve from HST (Fig. A2) for our transit
analysis.

###  2.3 TESS photometry

LHS 1140 (TIC 92226327, TOI-256) was observed with TESS at a 2-minute cadence
during its primary mission from September 20 to October 17, 2018 (Sector 3)
and during its first extended mission from September 23 to October 20, 2020
(Sector 30). We used the Presearch Data Conditioning Simple Aperture
Photometry (PDCSAP; Smith et al. 2012; Stumpe et al. 2012, 2014) data product
issued by the TESS Science Processing Operations Center (SPOC, Jenkins et al.
2016) at NASA Ames Research Center and available on the Mikulski Archive for
Space Telescopes222archive.stsci.edu/tess/. The PDCSAP data includes
corrections for instrumental systematics and for flux dilution from known Gaia
sources within several TESS pixels (21$\arcsec$ per pixel). The light curve
from Sector 3 was reprocessed with a more recent release of SPOC (version
5.0.20), which applies the new background correction implemented for the
extended mission to the first sectors of TESS. This new correction typically
reduces the inferred transit depths by less than 2%. Using the same pipeline
(SPOC v5.0) for Sectors 3 and 30 ensures consistent transit depths for LHS
1140 b and c between primary and extended mission data. The full TESS light
curve of LHS 1140 shown in Figure A3 captures 2 and 11 transits of planet b
and c, respectively, twice as many as in LB20 based on Sector 3 data only. The
phase-folded transits from TESS are also shown in the same Figure A3.

###  2.4 ESPRESSO radial velocity

We retrieved publicly available ESPRESSO data of LHS 1140 from the European
Southern Observatory (ESO) science archive333archive.eso.org/ (Delmotte et
al., 2006). These data consist of the same 117 spectra analysed in LB20 and
taken with the SINGLEHR21 mode between October 2018 and December 2019. We used
the bias & dark subtracted, extracted and flat-fielded spectra reduced with
the ESPRESSO pipeline (version
2.2.1)444eso.org/sci/software/pipelines/espresso/. The RV extraction from the
reduced data was performed with the line-by-line (LBL, version 0.52) method of
Artigau et al. (2022) available as an open source
package555github.com/njcuk9999/lbl. A simple telluric correction is first
performed inside the LBL code by fitting a TAPAS (Bertaux et al., 2014)
atmospheric model. This correction step, comparable to the approach of Allart
et al. (2022), has been demonstrated to improve the RV precision of ESPRESSO
particularly for M-type stars.

At the core of the LBL method, first explored by Dumusque (2018), Doppler
shifts are measured on the smallest spectral range possible, i.e., a spectral
line, from a high signal-to-noise ratio (SNR) template spectrum of the star
and its first derivative (Bouchy et al., 2001). This template is constructed
by coadding all our 117 telluric-corrected spectra. Then, the statistical
consistency between all per-line velocities ($\sim$38 000 for LHS 1140) is
verified using a simple mixture model (Appendix B of Artigau et al. 2022) that
effectively remove high-sigma outliers to produce a final error-weighted
average of valid lines. This approach fully exploits the RV content of a
stellar spectrum and is conceptually similar to widely employed template-
matching algorithms (e.g., Anglada-Escudé & Butler 2012, Astudillo-Defru et
al. 2017, Zechmeister et al. 2018, Silva et al. 2022) while being more
resilient to outlying spectral features (e.g., telluric residuals, cosmic
rays, detector defects).

Figure 2: Phase-folded Keplerian signals of LHS 1140 b (top) and c (bottom)
with ESPRESSO from RVs produced with the line-by-line (LBL) method in blue and
from cross-correlation function (CCF) in red (Lillo-Box et al., 2020). Open
and solid data points represent pre- and post-fiber upgrade of ESPRESSO (June
2019). The best-fit circular orbital solutions (black curves) of LHS 1140 b
($K_{\rm b}=3.80\pm 0.11$ m s-1) and c ($K_{\rm c}=2.42\pm 0.07$ m s-1) are
respectively improved by 50% and 70% compared with previous estimates with
CCF. The residuals RMS is equivalent to 0.50 m s-1 for LBL and 1.28 m s-1 for
CCF.

Following LB20, we separately analysed the data taken before and after the
fiber link change of ESPRESSO in June 2019 (Pepe et al., 2021), hereafter
designated as “pre” and “post” velocities. Using an iterative sigma-clipping
algorithm, we removed two epochs (BJD = 2458703.787210 and 2458766.704332)
flagged as $>$3$\sigma$ outliers. The final radial velocities are given in
Table B1 and show a median uncertainty of 0.36 m s-1 and dispersion (RMS) of
4.07 m s-1. As a comparison, the published values of LB20 derived from the
cross-correlation function (CCF) technique have a median precision of 0.99 m
s-1, almost three times larger than LBL, and a 4.76 m s-1 scatter. Figure 2
presents a comparison between LBL and CCF for the best-fit orbits of LHS 1140
b and c. The full LBL RV sequence is shown in Figure B1. Given the extreme
precision of ESPRESSO with LBL, a joint analysis with the HARPS data also
available through the ESO archive has resulted in identical semi-amplitudes
for LHS 1140 b and c. For this reason and to simplify the analysis, we opted
to only use ESPRESSO in this work. The ESPRESSO observations span
approximately 400 days, a long enough baseline to characterize signals at
longer periods, such as the candidate LHS 1140 d ($P_{\rm d}=78.9$ days) or
the rotation of the star ($P_{\rm rot}=131$ days; D17). As discussed in
Appendices D.1 and D.3, we find no evidence for LHS 1140 d and attribute this
80-day signal most likely to stellar activity.

###  2.5 NIRPS high-resolution spectroscopy

We acquired 29 high-resolution spectra of LHS 1140 with the Near-InfraRed
Planet Searcher (NIRPS; Bouchy et al. 2017; Wildi et al. 2022) during one of
its commissioning phases (Prog-ID 60.A-9109) from 2022-11-26 to 2022-12-06.
NIRPS is a new echelle spectrograph designed for precision RV at the ESO 3.6-m
telescope in La Silla, Chile covering the $YJH$ bands (980–1800 nm). The
instrument is equipped with a high-order Adaptive Optics (AO) system and two
observing modes, High Accuracy (HA, $R\approx 85\,000$, 0.4′′ fiber) and High
Efficiency (HE, $R\approx 70\,000$, 0.9′′ fiber), that can both be utilized
simultaneously with HARPS. LHS 1140 was observed in HE mode as an RV standard
star to test the stability of the instrument preceding the official start of
NIRPS operation in April 2023. The observations were reduced with APERO
v0.7.271 (Cook et al., 2022), the standard data reduction software for the
SPIRou near-infrared spectrograph (Donati et al., 2020), fully compatible with
NIRPS. We built a template spectrum of LHS 1140 from the telluric-corrected
data product from APERO to derive independent stellar parameters and the
abundances of several elements (Sect. 3.2). This template spectrum combines 29
individual spectra each with a SNR per pixel of about 70 in the middle of $H$
band.

##  3 Stellar Characterization

The star LHS 1140 was characterized in previous studies (D17; M19; LB20). In
this section, we summarize our work to revise the stellar mass and radius and
to measure the effective temperature and stellar abundances with NIRPS. An
analysis of the stellar kinematics confirming the age ($>$5 Gyr, D17) and
galactic thin disk membership of LHS 1140 is presented in Appendix C.1.

###  3.1 Stellar mass and radius update

We pulled the $K_{\rm s}$ magnitude (8.82$\pm$0.02) of LHS 1140 from 2MASS
(Skrutskie et al., 2006) and its distance $d$ from Gaia DR3 (14.96$\pm$0.01
pc; Gaia Collaboration et al. 2021). Then, from the absolute $K_{\rm s}$
magnitude ($M_{K_{\rm s}}$) to $M_{\star}$ empirical relation of Mann et al.
(2019), we obtain a stellar mass of $0.1844\pm 0.0046$ M⊙, with uncertainty
propagating the errors on $K_{\rm s}$, $d$, and the scatter of this relation.
This revised and more precise stellar mass is consistent with that of M19
($M_{\star}=0.179\pm 0.014$ M⊙) obtained from a similar mass–luminosity
calibration (Benedict et al., 2016), but using a smaller sample of nearby
binaries. In a similar way, but using the $M_{K_{\rm s}}$–$R_{\star}$
relationship of Mann et al. (2015), we obtain a radius of $0.2153\pm 0.0065$
R⊙ for LHS 1140. M19 determine the stellar radius from an analysis of the
transits, yielding a slightly more precise $R_{\star}=0.2139\pm 0.0041$ R⊙. To
make sure that our results are completely independent of previous analyses, we
first adopt the value derived from Mann et al. (2015) as a prior, then further
constrained the radius from the stellar density inferred from transits. This
Bayesian method is detailed in Appendix C.2 and results in a new stellar mass
and radius of $M_{\star}=0.1844\pm 0.0045$ R⊙ and $R_{\star}=0.2159\pm 0.0030$
R⊙. The stellar parameters of LHS 1140 are listed in Table C.3.

###  3.2 Stellar abundances from NIRPS

We follow the methodology of Jahandar et al. (2023), also applied in Cadieux
et al. (2022) for TOI-1452 (M4) and in Gan et al. (2023) for TOI-4201 (M0.5),
to derive the effective temperature as well as the abundances of several
chemical species in LHS 1140 from the NIRPS template spectrum. A global fit
($\chi^{2}$ minimization) to a selection of strong spectral lines using ACES
stellar models (Allard et al. 2012; Husser et al. 2013) convolved to match
NIRPS resolution resulted in a $T_{\rm eff}=3096\pm 48$ K and a [M/H] =
$0.01\pm 0.04$ for LHS 1140. Note we fixed $\log g=5$ (cgs) for our grid of
models in accordance to LHS 1140 (Table C.3). This method was empirically
calibrated for log $g$ of 5.0$\pm$0.2 dex (Jahandar et al., 2023).

We then performed a series of fits for a fixed $T_{\rm eff}=3100$ K on
individual spectral lines of known chemical species to derive their elemental
abundances (again following Jahandar et al. 2023). We show an example of this
method in Figure C2 for the Al I line at 1675.514 nm from which we measure
[Al/H] = $0.0\pm 0.1$ dex from this single line. The average abundances for
all chemical species detected in LHS 1140 are given in Table C2 including the
refractory elements Fe, Mg, and Si that form the bulk material of planetary
cores and mantles. As shown in Table C3, LHS 1140 features a relatively low
Fe/Mg weight ratio (1.03${}^{+0.40}_{-0.29}$) compared to the Sun (1.87$\pm
0.22$) and other solar neighbourhood M dwarfs, with a C/O measurement
consistent with the solar value. The measured Fe/Mg abundance ratio is used
later as input to planetary internal structure models (Sect. 4.2).

##  4 Results & Discussion

###  4.1 New density measurements

We measure the physical and orbital parameters of LHS 1140 b and c by jointly
fitting transit and Keplerian models to the photometric (Spitzer, HST, and
TESS) and RV (ESPRESSO) observations. The details of this joint transit RV fit
are presented in Appendix D.1. Notably, the best-fit solution is two planets
on circular orbits (Table D1) with no evidence of candidate LHS 1140 d. We
adopt the average radius measured by Spitzer and TESS for LHS 1140 c but
discuss an important discrepancy between the two measurements in Appendix D.2.

We infer a mass of 5.60$\pm$0.19 M⊕ for LHS 1140 b and 1.91$\pm$0.06 M⊕ for
LHS 1140 c, as well as planetary radii of 1.730$\pm$0.025 R⊕ for b and
1.272$\pm$0.026 R⊕ for c. The LHS 1140 planets are among the best-
characterized exoplanets to date, with relative uncertainties of only 3% for
the mass and 2% for the radius, reaching a similar precision to the TRAPPIST-1
planets (Agol et al., 2021). These measurements correspond to bulk densities
of $5.9\pm 0.3$ g cm-3 and $5.1\pm 0.4$ g cm-3 for planet b and c,
respectively. The results of previous studies for the semi-amplitudes ($K$)
and scaled radii ($R_{\rm p}/R_{\star}$) of the planets are shown in Table 1.
Since LB20, our updated $R_{\rm p}/R_{\star}$ ratios have increased back to
M19 values. This change results from incorporating additional transits with
Spitzer and HST, as we retrieve the same $R_{\rm p}/R_{\star}$ as LB20 to
1$\sigma$ when fitting the TESS data only (see Fig. D1). Note our revision of
the mass and radius of LHS 1140 b and c is dominated (by more than 80%) by $K$
and $R_{\rm p}/R_{\star}$ changes, not by the update of stellar parameters.

Table 1: Comparison of the semi-amplitudes and scaled radii of the LHS 1140
planets from different studies

Parameter | D17 | M19 | LB20 | This work
---|---|---|---|---
LHS 1140 b |  |  |  |
$K$ (m s-1) | 5.34$\pm$1.10 | 4.85$\pm$0.55 | 4.21$\pm$0.24 | 3.80$\pm$0.11
$R_{\rm p}/R_{\star}$ (%) | 7.08$\pm$0.13 | 7.39$\pm$0.01 | 7.02$\pm$0.19 | 7.33$\pm$0.04
LHS 1140 c |  |  |  |
$K$ (m s-1) | – | 2.35$\pm$0.49 | 2.22$\pm$0.20 | 2.42$\pm$0.07
$R_{\rm p}/R_{\star}$ (%) | – | 5.49$\pm$0.01 | 5.02$\pm$0.16 | 5.39$\pm$0.08

Note. — D17 with MEarth and HARPS. M19 with MEarth (extended), Spitzer and
HARPS (extended). LB20 with TESS, HARPS (M19), and ESPRESSO. This work with
Spitzer (extended), HST, TESS (extended), and ESPRESSO (LB20).

Figure 3: Mass–radius diagram of transiting exoplanets around M dwarfs (gray
points) with well-established mass and radius (relative uncertainty $<30$%)
from the NASA Exoplanet Archive (Akeson et al., 2013). Various theoretical
composition curves from Guillot & Morel (1995); Valencia et al. (2007, 2013);
Aguichine et al. (2021) are plotted with the water-rich models assuming an
Earth-like interior (33% iron by mass). The synthetic population of
terrestrials enveloped in H/He (0.1–30% initial mass fraction) of Rogers et
al. 2023 is highlighted in orange. This region also highlights interior model
degeneracy where the nature (H/He-rich or water-rich) of sub-Neptunes cannot
be reliably determined from mass and radius alone. The mass and radius
posteriors (1- and 2-$\sigma$ contours) of LHS 1140 b (green) and LHS 1140 c
(purple) from our joint transit RV analysis are drawn. Published values from
Lillo-Box et al. 2020 (LB20) derived from HARPS+ESPRESSO and TESS (Sector 3)
are shown with open circles. The results of Ment et al. 2019 (M19) from HARPS
and MEarth+Spitzer are presented with open squares.

We compare our updated mass and radius to the M dwarf exoplanet population in
Figure 3 with various pure composition curves included in the same figure. A
detailed analysis of the internal structure of LHS 1140 b is presented in
Section 4.2. First examining LHS 1140 b in Figure 3, we see that our revised
mass and radius are off the Earth-like track, contradicting previous results
from M19 and LB20 that this planet is a rocky, larger version of Earth (super-
Earth). The mode of the distribution lies above the pure Mg–Si rock sequence,
a region of the mass–radius diagram requiring an additional input of light
elements, i.e., gas (H2, He) or ices (e.g., H2O, CH4, NH3), to explain the
observed radius. LHS 1140 b is on the lower limit of the synthetic sub-Neptune
population around M dwarfs of Rogers et al. 2023 (orange region in Fig. 3)
that have undergone thermal evolution and atmospheric mass loss
(photoevaporation) over 5 Gyr assuming initial H/He mass fraction between 0.1%
and 30%. With a small $T_{\rm eq}$ of 226 K, Rogers et al. 2023 predict a
$\sim$0.1% H/He mass fraction for LHS 1140 b which we confirm through
simulation in Section 4.2.1. Alternatively, the planet could be purely rocky
or with a water-mass fraction of 10–20%, clearly not as high as the water-rich
(50% H2O) population suggested by Luque & Pallé (2022). Note this latter
scenario would involve a different formation mechanism, as suggested by recent
studies (Cloutier & Menou, 2020; Luque & Pallé, 2022; Piaulet et al., 2023;
Cherubim et al., 2023), where small planets around M dwarfs could directly
accrete icy materials outside the water snow line before migrating inwards, in
which case sub-Neptunes would actually be water worlds rather than H/He-
enveloped planets.

For LHS 1140 c, our mass measurement agrees with previous studies, but we show
in Appendix D.2 that Spitzer and TESS radii are in 4$\sigma$ disagreement,
complicating the determination of its internal structure. In Figure 3, we
present the average Spitzer+TESS radius of LHS 1140 c most compatible with a
rocky interior depleted in iron relative to Earth, but should the planet be
smaller, as measured by TESS, an Earth-like interior remains plausible.
However, given the planet size and higher $T_{\rm eq}$ of 422 K, a hydrogen-
dominated atmosphere or an important water content ($\gtrsim 10\%$ by mass)
similar to LHS 1140 b are formally rejected.

###  4.2 Nature of LHS 1140 b

The unprecedented precisions of both the mass and radius of the LHS 1140
planets combined with stellar abundance measurements provide a unique
opportunity to better constrain the nature of these planets. Because of the
radius uncertainty associated with LHS 1140 c discussed above, we focus our
analysis on LHS 1140 b. The mass–radius diagram of Figure 3 suggests three
potential scenarios: (1) a mini-Neptune depleted in hydrogen, (2) a pure rocky
(and airless) planet and (3) a water world. All three possibilities are
discussed below.

To address scenarios 2 and 3, we follow the method of Plotnykov & Valencia
(2020) also applied to the water-world candidate TOI-1452 b (Cadieux et al.,
2022) to constrain both the core-mass fraction (CMF) and water-mass fraction
(WMF) of the planet. The adaptation of this method to LHS 1140 b is further
detailed in Appendix E.1 with the posterior distributions available in
Appendix E.2. In brief, this interior analysis treats the Fe/Mg ratio either
as a free output parameter completely constrained by the mass-radius data (the
no prior case) or as direct input informed by the measured stellar value (the
stellar prior case) with
$\mathrm{Fe/Mg_{planet}}\sim\mathcal{N}(\mathrm{Fe/Mg_{star}},\sigma_{\rm
star}^{2}$). This latter case assumes that stellar abundances are a good proxy
of planetary abundances as suggested by planet formation studies (e.g., Bond
et al. 2010, Thiabaud et al. 2015, Unterborn et al. 2016) and empirically
(e.g., Dorn et al. 2017, Bonsor et al. 2021) though this correlation is not
necessarily 1:1 (Adibekyan et al., 2021).

####  4.2.1 Hydrogen-poor mini-Neptune

An Earth-like interior (CMF = 33%, WMF $\sim$ 0) overlain by a solar mixture
of hydrogen-helium contributing $\sim$0.1% of the mass, $\sim$10% of the
radius could explain the density of LHS 1140 b. Here, we simulate the
photoevaporation history of LHS 1140 b for 10 Gyr using the method of Cherubim
et al. (2023) to verify whether such hydrogen-rich envelope could survive at
present day. These simulations take into account thermal evolution,
photoevaporation (e.g., Owen & Wu 2017) from stellar extreme ultraviolet (XUV;
10–130 nm) and core-powered atmospheric escape (e.g., Ginzburg et al. 2018).

The results for a range of initial envelope mass fractions ($f_{\rm atm,0}$
between 0.1% and 12%) are shown in Figure 4. Assuming that LHS 1140 b did not
undergo important migration after formation, it appears that a $f_{\rm
atm,0}=0.1$–0.2% (brown and purple curves in Fig. 4) is in agreement with the
observed radius after 5 Gyr, the minimum age estimate of the system. Since gas
accretion models typically predict initial envelopes with mass fractions
$\gtrsim$1% (Ginzburg et al., 2016), such a small $f_{\rm atm,0}$ for LHS 1140
b would imply a formation in a gas-poor environment in less than 0.1 Myr (Lee
& Connors, 2021) or that it lost part of its atmosphere during giant impacts
(Inamdar & Schlichting, 2016). The relatively large semi-major axis of LHS
1140 b ($\sim$0.1 au) is just beyond the instellation needed to strip the
atmosphere: the final $f_{\rm atm}$ after 10 Gyr is close to the initial
$f_{\rm atm,0}$. In other words, the radius evolution over the simulation
timescale is dominated by the cooling/contraction of the atmosphere.

Figure 4: Primordial H/He atmosphere photoevaporation simulation of LHS 1140
b. Each curve corresponds to different initial envelope mass fractions $f_{\rm
atm,0}$. These simulations model thermal contraction, XUV-driven atmospheric
escape, and core-powered mass loss using the methodology of Cherubim et al.
(2023). A $f_{\rm atm,0}$ = 0.1–0.2% is consistent with the observed radius
given the age of the system ($>$5 Gyr).

####  4.2.2 Pure rocky planet

This is the special case of a rocky planet with no water envelope, i.e., the
WMF forced to zero. With no prior on the Fe/Mg ratio, our model converges to a
very small CMF (${4.3}_{-2.7}^{+4.1}$%) essentially consistent with a coreless
planet with a predicted Fe/Mg ratio (0.37${}^{+0.12}_{-0.07}$) significantly
lower (2.3$\sigma$) than observed for the host star (1.03${}^{+0.40}_{-0.29}$)
and much smaller than the lowest value ever measured in M dwarfs of the solar
neighbourhood (see Fig. E1). Moreover, this model converges to a larger mass
and smaller radius than observed (2.3$\sigma$ offset in density). We argue
that the inconsistency with the observations coupled with the challenge of
forming highly iron depleted (coreless) planets (Carter et al. 2015; Scora et
al. 2020; Spaargaren et al. 2023) make this scenario implausible for LHS 1140
b. This conclusion is in line with exoplanet demographics (Rogers, 2015) and
the empirical rocky-to-gaseous transition around M dwarfs (Cloutier & Menou,
2020) that most $\sim$1.6 R⊕ exoplanets are not rocky.

####  4.2.3 Water world

For this scenario, we also include an atmospheric layer, essentially a (small)
fixed radius correction associated with a potential atmosphere. For the
general case of a water world receiving more irradiation than the runaway
greenhouse threshold ($T_{\rm eq}\gtrsim 300$ K; Turbet et al. 2020; Aguichine
et al. 2021), the outer layer is likely to be supercritical, which would
significantly inflate the radius, requiring a proper joint modeling of the
warm water layer in vapor/supercritical state on top of a core+mantle
interior. While we defer this general case to a future publication (Plotnykov
et al. in prep.), LHS 1140 b with a small $T_{\rm eq}=226\pm 6$ K does not
warrant such a detailed treatment since a potential outer water layer on this
planet is most likely to be either in frozen or liquid state as the planet
resides in the Water Condensation Zone (Turbet et al., 2023). We thus assume
the atmospheric layer of LHS 1140 b to be an Earth-like atmosphere with a
surface pressure of 1 bar and surface temperature equal to $T_{\rm eq}$. The
radius correction (a few tens of kilometers) for such a thin atmosphere is
negligible.

Two prior cases for the Fe/Mg abundance ratio are considered. The
unconstrained case (no prior) yields CMF $={28.3}_{-15.9}^{+14.3}$% and a WMF
$={18.7}_{-9.8}^{+12.6}$% while assuming that the planet shares the same Fe/Mg
ratio as the host star (stellar prior), we obtain CMF $={20.5}_{-5.8}^{+5.5}$%
and WMF $={13.7}_{-4.5}^{+5.4}$%. As shown in Table 2, adopting a solar Fe/Mg
ratio instead of those measured on LHS 1140 yields an even larger WMF. We
tested changing the surface temperature and pressure (using climate
predictions from Sect. 4.3) to generate fully solid/liquid water surface. The
effect of phase change is small: both CMF and WMF remained within the reported
uncertainty for all models.

A variant of this model is the Hycean world (Madhusudhan et al., 2021), i.e.,
a water world surrounded by a thin H/He-rich layer as was recently proposed
for the temperate mini-Neptune K2-18 b (Madhusudhan et al., 2023). This new
result opens the possibility that LHS 1140 b may be a lower-mass version of
such a Hycean planet in the middle of the radius valley (Fulton et al., 2017).
In this scenario, the lower mean molecular weight of the atmosphere yields a
higher radius correction (up to 250 km for $\mu$ $\sim$ 2) corresponding to
$\sim$2% of the planet radius. This case with stellar prior on Fe/Mg still
yields a significant WMF $={9.3}_{-3.9}^{+4.6}$% with CMF
$={21.7}_{-6.6}^{+5.4}$%.

The main conclusion from this modeling exercise summarized in Table 2 is that
LHS 1140 b is unlikely to be a rocky super-Earth. The planet is either a
unique mini-Neptune with a thin $\sim$0.1% H/He atmosphere or a water world
with a WMF in the 9–19% range depending on the atmospheric composition and the
Fe/Mg ratio of the planetary interior. Transmission spectroscopic observations
with JWST (Gardner et al., 2023) will be key to discriminate between these
scenarios.

Table 2: Summary of the interior models of LHS 1140 b

Model | CMF (%) | WMF (%) | Fe/Mg [w]
---|---|---|---
LHS 1140 |  |  |
Host star (reference) | – | – | 1.0${}^{+0.4}_{-0.3}$
LHS 1140 b |  |  |
Purely rocky (no prior) | ${4.3}_{-2.7}^{+4.2}$ | – | ${0.4}_{-0.1}^{+0.1}$
Water world (no prior) | ${28.3}_{-15.9}^{+14.3}$ | ${18.7}_{-9.8}^{+12.6}$ | ${1.6}_{-0.9}^{+2.5}$
Water world |  |  |
(stellar prior) | ${20.5}_{-5.8}^{+5.5}$ | ${13.7}_{-4.5}^{+5.4}$ | ${1.1}_{-0.3}^{+0.3}$
Water world |  |  |
(solar prior) | ${27.8}_{-4.2}^{+4.6}$ | ${17.1}_{-5.0}^{+5.2}$ | ${1.8}_{-0.2}^{+0.2}$
Hycean world∗ |  |  |
(stellar prior) | ${21.7}_{-6.6}^{+5.4}$ | ${9.3}_{-3.9}^{+4.6}$ | ${1.1}_{-0.3}^{+0.3}$

Note. — ∗The Hycean model is derived from the Water world model (stellar
prior) by subtracting 250 km to the planetary radius corresponding to 5
atmospheric scale heights of H2.

###  4.3 3D GCM of LHS 1140 b and prospects for atmospheric characterization

Figure 5: Results of Global Climate Model (GCM) simulations of LHS 1140 b
assuming an Earth-like atmosphere (1 bar N2, 400 ppm CO2; panels a, c, d, e)
and a thick CO2-dominated atmosphere (5 bar CO2; panels b, f, g, h). Panels a,
b: Surface temperature maps of LHS 1140 b. The black line indicates the line
of stability between liquid water and sea ice. The extent of the ice-free
ocean strongly depends on the amount of CO2 in the atmosphere. Panels c, d, e,
f, g, and h: Vertical profiles of the atmospheric temperatures, water vapor,
and cloud mixing ratios (both H2O and CO2 ice clouds). The solid bold lines
indicate the global mean vertical profiles and the dotted lines indicate
terminator vertical profiles (impacting transit spectra).

Here we consider the case of a water world with a thin atmosphere for LHS 1140
b as this scenario presents broader implications for habitability. Planets
with large amounts of water are likely to have CO2+N2+H2O atmospheres (Forget
& Leconte, 2014; Kite & Ford, 2018), possibly with high amounts of CO2
(Marounina & Rogers, 2020). While the diversity of water-world atmospheres has
yet to be explored, we adopt here two distinct atmospheric compositions as a
first working hypothesis and proof of concept to predict the transmission
spectrum of LHS 1140 b: an Earth-like atmosphere (1 bar N2, 400 ppm CO2) and a
CO2-dominated atmosphere (5 bar CO2).

The simulations were computed with the Generic Planetary Climate Model
(hereafter simply called GCM), a state-of-the-art 3D climate model (Wordsworth
et al., 2011) historically known as the LMD (Laboratoire de Météorologie
Dynamique, Paris, France) Generic Global Climate Model. The model has been
widely applied to simulate all types of exoplanets, ranging from terrestrial
planets like the TRAPPIST-1 planets (Turbet et al., 2018; Fauchez et al.,
2019) to mini-Neptunes like GJ 1214 b (Charnay et al., 2015) or K2-18 b
(Charnay et al., 2021). The GCM uses an up-to-date generalized radiative
transfer and can simulate a wide range of atmospheric compositions (N2, H2O,
CO2, etc.) including clouds self-consistently.

The model was used to make realistic predictions of LHS 1140 b’s atmospheric
properties (temperature–pressure profile, water vapor, and cloud mixing
ratios), summarized in Figure 5. We find that no matter how much CO2 is
included in the model, the planet has a patch of liquid water at the
substellar point. The extent of the ice-free ocean grows with increasing
atmospheric CO2, due to the greenhouse effect. This result is similar to that
shown by Turbet et al. (2016); Boutle et al. (2017); Del Genio et al. (2018)
for Proxima b and Wolf et al. (2017); Turbet et al. (2018); Fauchez et al.
(2019) for TRAPPIST-1 planets, that water worlds synchronously rotating in the
Habitable Zone of low-mass stars almost always have surface liquid water, at
least at the substellar point.

Note that the GCM simulations presented here do not include dynamic ocean and
sea ice transport, which could slightly change the extent of the substellar
liquid water ocean depending on the amount of CO2 (Del Genio et al., 2019;
Yang et al., 2020). Note also that we assumed that LHS 1140 b is in
synchronous rotation. This is the most likely rotation mode given LHS 1140 b’s
proximity to its star and low eccentricity (Ribas et al., 2016), producing
gravitational tides which are expected to dominate atmospheric tides for this
planet (Leconte et al., 2015).

The outputs of the GCM were used to compute realistic transmission spectra
that take into account the 3D nature of the atmosphere. We used the Planetary
Spectrum Generator (PSG; Villanueva et al. 2018, 2022) to produce transmission
spectrum models (following the methodology of Fauchez et al. 2019) of LHS 1140
b based on the output of the two GCM simulations including the effects of
H2O/CO2 clouds. As shown in Figure 6, the strongest atmospheric feature
predicted by these models is CO2 near 4.3 $\mu$m with a strength of about 15
ppm. Changing the partial pressure of CO2 from 400 ppm to 5 bars produces a
similar CO2 bump as this molecule essentially condenses at higher
concentration to form ice particles at low altitude (see Fig. 5, panel h).

Figure 6: Predicted transmission spectrum of LHS 1140 b from 0.6 to 5.5 $\mu$m
for the Earth-like (black) and 5 bar CO2 (blue) global climate models (GCM,
Fig. 5). The bottom panel is a zoom of the top panel. Simulated JWST/NIRSpec
data with the G235H (green) and G395H (orange) dispersers are shown. We
estimate that 20 transits equally divided between G235H and G395H are required
to detect a secondary atmosphere around LHS 1140 b at 4$\sigma$. The red
dashed curve is a GCM-based representation of a mini-Neptune (H/He-rich) that
can be easily detected with a single visit.

LHS 1140 b was observed twice in transit with JWST in July 2023 during Cycle 1
(PID: 2334, PI: M. Damiano, unpublished). The two visits were made with
NIRSpec (Böker et al., 2023) using the Bright Object Time Series mode, one
transit with the G235H disperser (1.66–3.05 $\mu$m) and the other with G395H
(2.87–5.14 $\mu$m). We used PandExo (Batalha et al., 2017) to simulate NIRSpec
observations, keeping the same observing strategy of alternating between G235H
and G395H. For a degraded spectral resolution of $R\simeq 20$ and assuming a
conservative 5 ppm noise floor (Coulombe et al., 2023), these simulations
predict sensitivity of about 20 ppm for G235H/G395H per spectral bin and per
transit. As shown in Figure 6, the Cycle 1 data has the capability to identify
the mini-Neptune scenario, but should LHS 1140 b be a water world, we predict
that an additional 18 transits (20 in total) would be required to detect its
atmosphere (at 4$\sigma$). This estimation is made by simulating 1000
transmission spectra and comparing the log Bayesian evidence ($\ln Z$) between
a flat spectrum and the Earth-like model of Figure 6 with the median
simulation shown in the same figure yielding a $\Delta\ln Z=6.5$ or 4$\sigma$
(Benneke & Seager, 2013). Note, the optimal observing strategy has yet to be
fine-tuned depending on the level of stellar contamination yet to be
characterized. This may warrant some visits to be obtained regularly with
NIRISS SOSS (0.6–2.8 $\mu$m; Doyon et al. 2023, Albert et al. 2023).

It should be noted that only four transits are observable every year with JWST
as a result of the 24.7-day period of LHS 1140 b and the fact that the system
is near the ecliptic. An in-depth atmospheric characterization will
realistically require that all  future transit events of this planet be
observed with JWST over several years (at least 3 years to detect a 15 ppm CO2
signal at 3$\sigma$). Irrespective of the nature of LHS 1140 b, we advocate
initiating an extensive campaign as soon as possible considering the
uniqueness of this temperate world.

##  5 Summary & Conclusion

In this letter, we revisited the M4.5 LHS 1140 system hosting two transiting
small exoplanets including LHS 1140 b in the Habitable Zone. We applied the
novel line-by-line precision radial velocity method of Artigau et al. (2022)
to publicly available ESPRESSO data, previously analysed by Lillo-Box et al.
(2020) using the cross-correlation function technique. The improvement on the
radial velocities is significant: the errors are reduced by almost a factor
three, the residual dispersion is halved, and no important excess white noise
is detected. By jointly fitting the RVs with transits from Spitzer (3 new
archival transits), HST, and TESS (new Sector 30), we update the planetary
mass and radius to 5.60$\pm$0.19 M⊕ and 1.730$\pm$0.025 R⊕ for LHS 1140 b,
1.91$\pm$0.06 M⊕ and 1.272$\pm$0.026 R⊕ for LHS 1140 c. The improved radial
velocity data do not support the existence of the non-transiting candidate LHS
1140 d announced by Lillo-Box et al. (2020).

Our revised mass and radius measurements reveal that LHS 1140 b is unlikely to
be a rocky super-Earth as previously reported, as it would require: (1) A
density larger (by 2.3$\sigma$) than observed, (2) A core-mass fraction
consistent with a coreless planet (CMF $={4.3}_{-2.7}^{+4.2}$%), (3) A
planetary Fe/Mg weight ratio smaller (2.3$\sigma$) than measured on its host
star and never measured in any solar neighbourhood M dwarfs. Instead, our
analysis shows that LHS 1140 b could either be one of the smallest known mini-
Neptune ($\sim$0.1% H/He by mass) with an atmosphere stable to mass loss over
the lifetime of the system or a water world with a significant water-mass
fraction of ${13.7}_{-4.5}^{+5.5}$% when the iron-to-magnesium weight ratio of
the planet is informed by those measured with NIRPS on the host star (Fe/Mg =
1.03${}^{+0.40}_{-0.29}$). For LHS 1140 c, our updated density is consistent
with a rocky world depleted in iron relative to Earth’s, but this result is
highly influenced by radius measurement currently discrepant between Spitzer
and TESS to 4$\sigma$.

We recommend in-depth transit spectroscopy with JWST to characterize the
atmosphere on LHS 1140 b which we predict would create a CO2 feature at 4.3
$\mu$m, potentially as small as $\sim$15 ppm according to self-consistent 3D
global climate modeling of the planet in the water world hypothesis. These
simulations show that the atmospheric CO2 concentration controls the surface
temperature and the extent of a liquid water ocean. For an Earth-like case (1
bar N2, 400 ppm CO2), liquid water is limited to a small patch at the
substellar point, while for a CO2-dominated atmosphere (5 bar CO2), almost a
whole hemisphere is covered. These future observations could reveal the first
exoplanet with a potentially habitable atmosphere and surface.

We thank the anonymous referee for constructive comments and suggestions that
improved the presentation of this letter.

This study uses public ESPRESSO data under program IDs 0102.C-0294(A),
0103.C-0219(A), and 0104.C-0316(A) (PI: J. Lillo-Box).

This work is partly supported by the Natural Science and Engineering Research
Council of Canada and the Trottier Institute for Research on Exoplanets
through the Trottier Family Foundation.

We acknowledge the use of public TESS Alert data from pipelines at the TESS
Science Office and at the TESS Science Processing Operations Center. 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 letter
includes data collected by the TESS mission that are publicly available from
the Mikulski Archive for Space Telescopes (MAST).

This work has been carried out within the framework of the NCCR PlanetS
supported by the Swiss National Science Foundation (SNSF) under grants
51NF40_182901 and 51NF40_205606. This project has received funding from the
SNSF for project 200021_200726. F.P. would like to acknowledge the SNSF for
supporting research with ESPRESSO and NIRPS through grants nr. 140649, 152721,
166227, 184618 and 215190.

This project has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation program (grant
agreement SCORE No 851555)

Co-funded by the European Union (ERC, FIERCE, 101052347). Views and opinions
expressed are however those of the author(s) only and do not necessarily
reflect those of the European Union or the European Research Council. Neither
the European Union nor the granting authority can be held responsible for
them.

M.T. thanks the Gruber Foundation for its generous support to this research,
support from the Tremplin 2022 program of the Faculty of Science and
Engineering of Sorbonne University, and the Generic PCM team for the teamwork
development and improvement of the model. This work was performed using the
High-Performance Computing (HPC) resources of Centre Informatique National de
l’Enseignement Supérieur (CINES) under the allocations No. A0100110391 and
A0120110391 made by Grand Équipement National de Calcul Intensif (GENCI).

T.J.F. acknowledges support from the GSFC Sellers Exoplanet Environments
Collaboration (SEEC), which is funded in part by the NASA Planetary Science
Divisions Internal Scientist Funding Model.

R.A. is a Trottier Postdoctoral Fellow and acknowledges support from the
Trottier Family Foundation. This work was supported in part through a grant
from the Fonds de Recherche du Québec - Nature et Technologies (FRQNT).

J.I.G.H., V.M.P., and A.S.M. acknowledge financial support from the Spanish
Ministry of Science and Innovation (MICINN) project PID2020-117493GB-I00 and
A.S.M. from the Government of the Canary Islands project ProID2020010129.

This work was supported by Fundação para a Ciência e a Tecnologia (FCT)
through national funds and by FEDER through COMPETE2020 - Programa Operacional
Competitividade e Internacionalização by these grants: UIDB/04434/2020;
UIDP/04434/2020. The research leading to these results has received funding
from the European Research Council through the grant agreement 101052347
(FIERCE). E.D.M. acknowledges the support from through Stimulus FCT contract
2021.01294.CEECIND and by the following grants: UIDB/04434/2020 &
UIDP/04434/2020 and 2022.04416.PTDC.

B.L.C.M. and J.R.M. acknowledge continuous grants from the Brazilian funding
agencies CNPq and Print/CAPES/UFRN. This study was financed in part by the
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) -
Finance Code 001.

T.H. acknowledges support from an NSERC Alexander Graham Bell CGS-D
scholarship.

X.D. acknowledges support by the French National Research Agency in the
framework of the Investissements d’Avenir program (ANR-15-IDEX-02), through
the funding of the “Origin of Life” project of the Grenoble-Alpes University.

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##  Appendix A Light curves

In this appendix, we present the light curves of LHS 1140 from Spitzer, HST,
and TESS. The four individual transits of LHS 1140 b and one of LHS 1140 c
acquired with Spitzer are presented in Figure A1. The single transit visit
from HST with the Wide Field Camera 3 (white light curve) is shown in Figure
A2. Lastly, the full TESS light curves from Sectors 3 and 30 are presented in
Figure A3.

Figure A1: Individual Spitzer transits of LHS 1140 b (Transit 1–4) and c
(Transit 4 only). The best-fit transit models of the planets are shown in blue
with the residual of this fit shown below. Figure A2: White light curve
transit of LHS 1140 b with the Wide Field Camera 3 on HST. The best-fit
transit model is shown in blue with the residuals of this fit shown on the
bottom panel.

Figure A3: Top panels: Normalized PDCSAP light curve of LHS 1140 from TESS
Sectors 3 and 30. The blue and red vertical ticks and data points highlight
the transits of planet b and c. Bottom panels: Phase-folded transit of LHS
1140 b (left) and c (right). The open circles represent the binned photometry,
respectively 12- and 8-minute bins for b and c. The best-fit transit models
are depicted with blue curves. The residuals of the fits are shown below their
respective transit.

##  Appendix B Radial velocity measurements

The ESPRESSO radial velocity of LHS 1140 extracted with the line-by-line
method are shown in Figure B1 and listed in Table B1 fully available online.

Figure B1: Radial velocity time series of LHS 1140 with ESPRESSO produced with
the line-by-line method. The data before (pre) and after (post) the fiber
upgrade of ESPRESSO (June 2019) are distinguished with open and solid circles,
respectively. The full RV model (planet b, planet c, and activity GP) is
represented by an orange curve, with the activity GP component highlighted
with a green dashed curve (details in Appendix D.1). Table B1: ESPRESSO radial
velocity of LHS 1140 obtained with the line-by-line method

BJD - 2 400 000 | RV (m s-1) |  $\sigma_{\rm RV}$ (m s-1)
---|---|---
58416.711656 | $-13457.505$ | 0.364
58424.576752 | $-13459.164$ | 0.360
58425.528804 | $-13456.943$ | 0.343
58431.527205 | $-13462.007$ | 0.453
58431.714392 | $-13462.893$ | 0.423
58432.733559 | $-13458.241$ | 0.383
58434.555946 | $-13457.993$ | 0.346
… | … | …

Note. — Table B1 is published in its entirety in machine-readable format.

##  Appendix C Supplementary material of the stellar characterization

###  C.1 Stellar age

We analysed the kinematics of LHS 1140 to characterize its age. This was done
by assessing whether the star belongs to the Galaxy’s thin or thick disk
stellar populations; thick disk stars are older ($\sim$10 Gyr) than their
counterparts in the thin disk, have different chemistry ([Fe/H]$\sim$-0.5,
[$\alpha$/Fe]$\sim$+0.3; Reddy et al. 2006), and are kinematically hotter,
with larger velocity dispersions relative to the Local Standard of Rest (LSR),
and larger orbital excursions from the Galactic midplane (Binney & Tremaine,
2008). We employed the astrometric solution from Gaia DR3 (Gaia Collaboration
et al., 2023). We note that the solution’s renormalized unit weight error
ruwe=1.53 indicates that there is some uncertainty in the astrometry
(ruwe$\lesssim$1.4 for well-behaved solutions; Lindegren, 2018). The orbit of
LHS 1140 was integrated forward in time 60 Myr using the Monte Carlo model
outlined in Hallatt & Wiegert (2020).

These calculations produce a velocity with respect to the Local Standard of
Rest $(U_{\rm LSR},V_{\rm LSR},W_{\rm LSR})=(14.38\pm 0.041,-38.52\pm
0.09,11.18\pm 0.41)$ km s-1, yielding $V_{\rm tot}=\sqrt{U^{2}_{\rm
LSR}+V^{2}_{\rm LSR}+W^{2}_{\rm LSR}}=42.61\pm 0.20$ km s-1 (adopting the
Local Standard of Rest from Bland-Hawthorn & Gerhard 2016). This places LHS
1140 in the thin disk, where $V_{\rm tot,thin}\lesssim 50$ km s-1 (e.g.,
Bensby et al., 2003; Hawkins et al., 2015). Its orbital oscillation amplitude
above/below the Galactic midplane is $131\pm 5$ pc, significantly smaller than
that of thick disk stars ($\sim$1 kpc; e.g., Li & Zhao 2017) and consistent
with that of thin disk stars $\sim$a few Gyr old (see Fig. 20 of Kordopatis et
al., 2023). This result for the age of LHS 1140 is consistent with D17 ($>$5
Gyr) estimated from its slow rotation period and absence of H$\alpha$
emission. We thus adopt that LHS 1140 has a relatively old age $>$5 Gyr and is
a thin disk star.

###  C.2 Bayesian inference of stellar mass and radius from transits

Measured directly from transit light curves, the orbital period ($P$) and the
scaled semi-major axis ($a/R_{\star}$) of an exoplanet allow the determination
of the density of its host star (Seager & Mallén-Ornelas, 2003):

$\rho_{\star\rm{,transit}}=\frac{3\pi}{GP^{2}}\left(\frac{a}{R_{\star}}\right)^{3}$
(C1)

While Equation C1 is fundamentally true for all orbits, as it is essentially a
reformulation of Kepler’s Third Law (with $G$ the gravitational constant), the
$a/R_{\star}$ inferred from transit can be significantly biased when assuming
a circular orbit (e.g., Kipping 2010, Dawson & Johnson 2012, Kipping 2014).
Following the notation of Van Eylen & Albrecht (2015), the true stellar
density ($\rho_{\star}$) when photo-eccentric effects are considered is given
by:

$\frac{\rho_{\star}}{\rho_{\star\rm{,transit}}}=\frac{\left(1-e^{2}\right)^{3/2}}{\left(1+e\sin\omega\right)^{3}}$
(C2)

where $e$ and $\omega$ are respectively the orbital eccentricity and argument
of periastron of the transiting planet. Unaccounted eccentricity as small as
$e\sim 0.1$ can potentially induce a 30% error in $\rho_{\star}$. From our
joint transit RV analysis (Appendix D.1), we measure
$\rho_{\star}/\rho_{\star\rm{,transit}}$ of $1.00\pm 0.03$ for LHS 1140 b and
$1.02\pm 0.04$ for LHS 1140 c consistent with perfectly circular orbits
($e_{\rm b}<0.043$, $e_{\rm c}<0.050$ with 95% confidence). As both orbital
solutions satisfy $\rho_{\star}\approx\rho_{\star\rm{,transit}}$, we hereafter
drop the transit subscript when referring to stellar density obtained from our
transit light curves. As summarized in Figure C1, our measurement of
$\rho_{\star}$ constrained by Spitzer, HST, and TESS has resulted in new
posteriors for the mass and radius of the star LHS 1140, namely
$M_{\star}=0.1844\pm 0.0045$ M⊙ and $R_{\star}=0.2159\pm 0.0030$ R⊙. This
Bayesian approach is taken to improve the precision on $M_{\star}$ and
$R_{\star}$, otherwise the dominant sources of uncertainty for the inferred
planetary mass and radius.

Figure C1: Left panel: Stellar density ($\rho_{\star}$) distribution of LHS
1140 using mass and radius from Mann et al. 2015, 2019 (black) and posterior
distributions of $\rho_{\star}$ inferred from TESS (red), TESS+Spitzer
(purple), and TESS+Spitzer+HST (blue) transits. Right panel: Bayesian
inference of the stellar mass and radius of LHS 1140 using the
TESS+Spitzer+HST constraints on $\rho_{\star}$ as a measurement and Mann et
al. (2015, 2019) as a prior. The positive covariance in
$M_{\star}$–$R_{\star}$ space indicates that both parameters are likely to
vary in the same direction to produce a constant $\rho_{\star}$ constrained by
the transits.

###  C.3 Additional Tables and Figure

We recapitulate the stellar parameters of LHS 1140 in Table C.3. After, we
present the stellar abundance determination from NIRPS (Sect. 3.2) in Table C2
and give corresponding chemical weight ratios in Table C3. An example of this
chemical spectroscopy analysis for the Al I line (1675.514 nm) is presented in
Figure C2.

Figure C2: NIRPS template spectrum of LHS 1140 (black dashed line) around the
Al I line (1675.514 nm). The orange envelope depicts the flux dispersion
measured on 29 individual observations. Three ACES models with a fixed $T_{\rm
eff}=3100$ K and metallicities of $-0.5$ (red line), 0.0 (blue line) and 0.5
dex (green line) are shown. For this single line, we measure [Al/H] = $0.0\pm
0.1$ dex. This figure illustrates the precision of the NIRPS data to constrain
elemental abundances often different from that of iron ([Fe/H] = $-0.15\pm
0.09$ dex). Table C1: LHS 1140 stellar parameters

Parameter | Value | Ref.
---|---|---
Astrometry and kinematics
RA (J2016.0) | 00:44:59.33 | 1
DEC (J2016.0) | -15:16:17.54 | 1
$\mu_{\alpha}\cos\delta$ (mas $\cdot$ yr-1) | 318.152 $\pm$ 0.049 | 1
$\mu_{\delta}$ (mas $\cdot$ yr-1) | -596.623 $\pm$ 0.054 | 1
$\pi$ (mas) | 66.8287 $\pm$ 0.0479 | 1
$d$ (pc) | 14.9636 $\pm$ 0.0107 | 1
$U$ (km s-1) | 14.38 $\pm$ 0.041 | 2
$V$ (km s-1) | -38.52 $\pm$ 0.09 | 2
$W$ (km s-1) | 11.18 $\pm$ 0.41 | 2
Physical parameters
$M_{\star}$ (M⊙) | 0.1844 $\pm$ 0.0045 | 2
$R_{\star}$ (R⊙) | 0.2159 $\pm$ 0.0030 | 2
$\rho_{\star}$ (g $\cdot$ cm-3) | 25.8 $\pm$ 1.0 | 3
$T_{\rm eff}$ (K) | 3096 $\pm$ 48 | 2
$L_{\star}$ (L⊙) | 0.0038 $\pm$ 0.0003 | 3
SpT | M4.5V | 4
$\left[{\rm Fe/H}\right]$ (dex) |  $-0.15$ $\pm$ 0.09 | 2
log $g$ (cgs) | 5.041 $\pm$ 0.016 | 3
Age |  $>5$ Gyr | 4
$P_{\rm rot}$ (days) | 131 $\pm$ 5 | 4

References. — (1) Gaia DR3 (Gaia Collaboration et al., 2021). (2) This work.
(3) This work derived from $M_{\star}$, $R_{\star}$, and $T_{\rm eff}$ (4)
Dittmann et al. (2017).

Table C2: LHS 1140 stellar abundances measured with NIRPS for various chemical
species with important features in the near-infrared

Element |  [X/H] |  $\sigma$ |  # of lines
---|---|---|---
Fe I |  -0.15 |  0.09 |  3
Al I |  0.00 |  0.10 |  2
Mg I |  0.11 |  0.10 |  2
Si I |  -0.20 |  0.10 |  1
Ca I |  0.20 |  0.10 |  1
O I∗ |  0.00 |  0.01 |  82
C I |  0.10 |  0.10 |  3
$<>^{{\dagger}}$ |  0.01 |  0.04 |  –

Note. — ∗The oxygen abundance is inferred from OH lines.

†Average abundance of all elements.

Table C3: LHS 1140 stellar abundance weight ratios∗

Ratios |  LHS 1140 |  Sun† |  M dwarf‡
---|---|---|---
Fe/Mg [w] |  1.03${}^{+0.40}_{-0.29}$ |  1.87 $\pm$ 0.22 |  [0.89, 2.92]
Mg/Si [w] |  1.94${}^{+0.79}_{-0.56}$ |  0.95 $\pm$ 0.09 |  [0.69, 1.66]
Fe/O [w] |  0.15${}^{+0.04}_{-0.03}$ |  0.21 $\pm$ 0.03 |  [0.08, 0.28]
C/O [w] |  0.56${}^{+0.17}_{-0.13}$ |  0.44 $\pm$ 0.06 |  [0.21, 0.60]

Note. — ∗Weight ratios calculated using $\textrm{X/Y
[w]}=10^{A\left(X\right)}/10^{A\left(Y\right)}\times(m_{\rm X}/m_{\rm Y})$
with $A\left(\textrm{X}\right)=\left[\textrm{X/H}\right]+A_{\rm
solar}\left(\textrm{X}\right)$ the absolute logarithmic abundance, $A_{\rm
solar}\left(\textrm{X}\right)$ taken from Table 2 of Asplund et al. (2021),
and $m_{\rm X}$ the atomic mass of element X.

†Solar weight ratios from Asplund et al. (2021).

‡95% confidence interval of the M dwarf population ($\sim$1000) of APOGEE DR16
(Majewski et al. 2016; Ahumada et al. 2020)

##  Appendix D Data analysis

###  D.1 Joint transit RV fit

The joint analysis of the photometric (Spitzer, HST, and TESS) and RV
(ESPRESSO) data is done with juliet (Espinoza, 2018), an all-in-one package
that combines transit and RV modeling using batman (Kreidberg, 2015) and
radvel (Fulton et al., 2018) with multiple sampling options (e.g., Markov
Chain Monte Carlo, nested sampling). Here, we select the dynesty (Speagle,
2020) sampler in juliet for parameter estimations and Bayesian log-evidence
($\ln Z$) calculations relevant for model comparisons. The dynesty package
implements dynamic nested sampling algorithms (Higson et al., 2019) designed
for more efficient and robust estimations of complex posterior distributions.
We follow the dynesty
documentation666dynesty.readthedocs.io/en/stable/index.html and choose the
random slice sampling option since the number of free parameters exceeds 20.

The orbit of planet $k$ ($k$: ‘b’, ‘c’, ‘d’) is described by four parameters,
the orbital period $P_{k}$, the time of inferior conjunction $t_{0,k}$, the
eccentricity $e_{k}$, and the argument of periastron $\omega_{k}$, and one
systemic parameter, the stellar density $\rho_{\star}$, common for all
planets. For multi-planetary systems, a single $\rho_{\star}$ exists, which
eliminates the need to fit semi-major axes ($a_{k}/R_{\star}$) for each planet
(Equation C1). We define a Gaussian prior on the stellar density of LHS 1140
based on Mann et al. (2015, 2019):
$\rho_{\star}\sim\mathcal{N}\left(26.0,2.6^{2}\right)$ g cm-3. For the
transiting planets b and c, we follow the Espinoza et al. (2019)
transformation of the transit impact parameter $b$ and planet-to-star radius
ratio $p=R_{\rm p}/R_{\star}$ into $r_{1}$ and $r_{2}$ parameters to only
sample physically plausible regions in $b$–$p$ space. We model the baseline
flux of the Spitzer, HST, and TESS light curves with the parameter $M$
described in Espinoza (2018) and include per-instrument extra jitter terms
($\sigma_{\rm Spitzer}$, $\sigma_{\rm HST}$, and $\sigma_{\rm TESS}$).

Synthetic spectra of M dwarfs often show significant discrepancy with the
observations (Blanco-Cuaresma, 2019), implying that theoretical limb-darkening
(LD) predictions may be unreliable. Patel & Espinoza (2022) have found
systematic offsets between empirical quadratic LD coefficients
($u_{1}$,$u_{2}$) and theoretical predictions in the TESS bandpass of the
order $\Delta u_{1}$,$\Delta u_{2}\approx 0.2$ for cool stars similar to LHS
1140. Differing from previous transit analyses (D17; M19; LB20; Edwards et al.
2021), we do not fix or apply Gaussian priors on the LD coefficients, but let
them vary freely (uniform priors). The stellar LD effects in the Spitzer, HST,
and TESS transits are modeled using per-instrument quadratic $q_{1}$ and
$q_{2}$ parameters (Kipping, 2013) constructed to only allow physical
solutions for values between 0 and 1. Note fixing the LD parameters to those
measured by previous studies for the same instrument does not change the
median of our $R_{\rm p}/R_{\star}$ posteriors.

For the Keplerian component, a semi-amplitude $K_{k}$ for each planet is
fitted, as well as instrumental RV offsets ($\gamma_{\rm pre}$, $\gamma_{\rm
post}$) and extra white noise terms ($\sigma_{\rm pre}$, $\sigma_{\rm post}$)
for ESPRESSO pre- and post-fiber upgrade. When testing for possible eccentric
orbits, we sample uniformly $\sqrt{e_{k}}\cos\omega_{k}$ and
$\sqrt{e_{k}}\sin\omega_{k}$ between -1 and 1. We include in juliet a Gaussian
Process (GP) to model stellar activity in the ESPRESSO RVs. Our GP
implementation in juliet runs george (Ambikasaran et al., 2015) with a quasi-
periodic covariance kernel (Haywood et al. 2014; Rajpaul et al. 2015):

$k_{i,j}=A^{2}\exp\left[-\frac{|t_{i}-t_{j}|^{2}}{2\ell^{2}}-\Gamma\sin^{2}\left(\frac{\pi|t_{i}-t_{j}|}{P_{\rm
rot}}\right)\right]$ (D1)

where $|t_{i}-t_{j}|$ is the time interval between data $i$ and $j$, $A$ is
the amplitude of the GP, $\ell$ is the coherence timescale, $\Gamma$ scales
the periodic component of the GP, and $P_{\rm rot}$ is the stellar rotation
period. We adopt a Gaussian prior on the known rotation period of the star
$P_{\rm rot}\sim\mathcal{N}\left(131,5^{2}\right)$ days. The priors for the
other GP hyperparameters are listed in Table D2 and mostly follow the
recommendation of Stock et al. 2023 (GP Prior III) when the rotation period is
already constrained.

We inspected three different joint models ($\mathcal{M}$):

  * •

Two planets, LHS 1140 b and c, on circular orbits ($\mathcal{M}_{\rm 2cp}$;
$e_{\rm b}=e_{\rm c}=0$, $\omega_{\rm b}=\omega_{\rm c}=90^{\circ}$)

  * •

Two planets, LHS 1140 b and c, on eccentric orbits ($\mathcal{M}_{\rm 2ep}$)

  * •

Three planets, LHS 1140 b, c, and the candidate planet d reported by LB20, on
circular orbits ($\mathcal{M}_{\rm 3cp}$; $e_{\rm b}=e_{\rm c}=e_{\rm d}=0$,
$\omega_{\rm b}=\omega_{\rm c}=\omega_{\rm d}=90^{\circ}$)

The difference in Bayesian log-evidence ($\Delta\ln Z$) yields the probability
that one model describes better the observations over another. The empirical
scale of Trotta 2008 (see Table 1 therein) serves to interpret the
significance of $\Delta\ln Z$ and to select the “best” model. A $\Delta\ln
Z>5$ constitutes “strong” evidence in favour of the model with the highest
$\ln Z$. A $2.5<\Delta\ln Z<5$ corresponds to “moderate” evidence, but a
$\Delta\ln Z\leq 2.5$ means that neither model should be favoured. Multiple
runs of each $\mathcal{M}$ were carried with dynesty to verify the consistency
of $\ln Z$.

For the two planet models $\mathcal{M}_{\rm 2cp}$ and $\mathcal{M}_{\rm 2ep}$,
we obtain a $\Delta\ln Z=0.8\pm 0.9$ in favour of the circular orbit solutions
(inconclusive). We report from model $\mathcal{M}_{\rm 2ep}$ upper limits on
$e_{\rm b}$ and $e_{\rm c}$ (95% confidence) of 0.043 and 0.050, respectively,
implying that in all likelihood, the orbit of LHS 1140 b and c are de facto
circular. For this reason, we select the simpler $\mathcal{M}_{\rm 2cp}$ as
the preferred model. We present the relevant planetary parameters derived from
the joint transit RV fit for model $\mathcal{M}_{\rm 2cp}$ in Table D1. The
priors and posteriors (16th, 50th, and 84th percentiles) of the free
parameters of model $\mathcal{M}_{\rm 2cp}$ are reported in Table D2. The
best-fit transit models of the Spitzer, HST, and TESS light curves are
respectively shown in Figures 1, A2, and A3. The phase-folded RVs with the
best-fit orbital solutions of LHS 1140 b and c is shown in Figure 2 with the
full RV model (Keplerian + activity GP) presented in Figure B1. This full RV
model yields a residual RMS of 41 cm s-1 for the “pre” data consistent with
the median RV errors of 42 cm s-1. For the “post” data, the residual
dispersion of 54 cm s-1 is larger than the typical RV errors of 34 cm s-1 so
that a $\sigma_{\rm post}=36\pm 6$ cm s-1 jitter term is needed to fully
describe the scatter.

The reanalysis of the ESPRESSO data with the LBL framework is an opportunity
to test the presence of the candidate LHS 1140 d on a 78.9-day orbit reported
by LB20. For model $\mathcal{M}_{\rm 3cp}$, we chose the same priors on
$P_{\rm d}$, $t_{\rm 0,d}$, and $K_{\rm d}$ as in LB20, namely
$\mathcal{U}\left(70,120\right)$ days,
$\mathcal{U}\left(2458350,2458400\right)$ BJD, and
$\mathcal{U}\left(0,10\right)$ m s-1. This fit converges to a small semi-
amplitude of $0.9^{+0.8}_{-0.6}$ m s-1 and an undefined period of
$87^{+14}_{-9}$ days for a planet d. The Bayesian log-evidence does not
increase when adding a third planet with $\Delta\ln Z=-1.0\pm 0.9$ between
$\mathcal{M}_{\rm 3cp}$ and $\mathcal{M}_{\rm 2cp}$. We also reject a $K_{\rm
d}$ larger than 2.21 m s-1 at 2$\sigma$, corresponding to the median signal
detected in LB20. LHS 1140 could realistically have other planets, but given
the precision of our RV measurements, we see no evidence of an additional
companion sharing the parameters of candidate LHS 1140 d. In Appendix D.3, we
further demonstrate that an 80-day RV signal is most likely of stellar origin.

###  D.2 Transit depth discrepancy for LHS 1140 c

In LB20, the radius of LHS 1140 b and c measured by TESS was slightly smaller
(by 1.5$\sigma$ and 2$\sigma$ respectively) compared with previous results by
M19 obtained with Spitzer (see Fig. 3). Here, our joint analysis of Spitzer,
HST (for LHS 1140 b only), and TESS data has resulted in a similar discrepancy
for planet c, but not for b. In Figure D1, we show the transit impact
parameter ($b$) and scaled radius ($p=R_{\rm p}/R_{\star}$) of LHS 1140 b and
c derived from fitting each instrument independently. The $b$–$p$ posteriors
of LHS 1140 b agree well for all available instruments, but we detect a
4$\sigma$ tension for the $p$ of LHS 1140 c measured by Spitzer and TESS.

We remain cautious before interpreting the transit depth discrepancy of LHS
1140 c as real because we only have a single visit with Spitzer. It is
possible that data reduction systematics affected the depth measurement.
Nonetheless, it is worth mentioning that Spitzer Channel 2 at 4.5 $\mu$m
covers a strong CO2 feature. We detect a difference of 500 ppm between the
Spitzer and TESS bandpasses, meaning that if excess atmospheric absorption is
causing this discrepancy, it would be readily detectable with JWST. This work
calls for better radius determination for LHS 1140 c, particularly obtaining
the full near-infrared transmission spectrum of this planet with JWST to
reveal its true radius that we currently report as an average between Spitzer
and TESS (see Joint in Fig. D1) and test whether its atmosphere is CO2-rich.

Table D1: Planetary parameters derived from the joint transit RV fit

Parameter | LHS 1140 b | LHS 1140 c | Description
---|---|---|---
Orbital parameters
$P$ (days) | 24.73723 $\pm$ 0.00002 | 3.777940 $\pm$ 0.000002 | Period
$t_{\rm 0}$ (BJD - 2 457 000) | 1399.9300 $\pm$ 0.0003 | 1389.2939 $\pm$ 0.0002 | Time of inferior conjunction
$a$ (au) | 0.0946 $\pm$ 0.0017 | 0.0270 $\pm$ 0.0005 | Semi-major axis
$i$ (∘) | 89.86 $\pm$ 0.04 | 89.80${}^{+0.14}_{-0.19}$ | Inclination
$e$ |  $<0.043$ (95%) |  $<0.050$ (95%) | Eccentricity
Transit parameters
$b$ | 0.23${}^{+0.05}_{-0.07}$ | 0.09${}^{+0.09}_{-0.06}$ | Impact parameter
$\delta$ (ppt) | 5.38 $\pm$ 0.06 | 2.90 $\pm$ 0.09 | Depth
$t_{14}$ (hours) | 2.15 $\pm$ 0.05 | 1.13 $\pm$ 0.02 | Duration
Physical parameters
$R_{\rm p}$ (R⊕) | 1.730 $\pm$ 0.025 | 1.272 $\pm$ 0.026 | Radius
$M_{\rm p}$ (M⊕) | 5.60 $\pm$ 0.19 | 1.91 $\pm$ 0.06 | Mass
$\rho$ (g $\cdot$ cm-3) | 5.9 $\pm$ 0.3 | 5.1 $\pm$ 0.4 | Bulk density
$S$ (S⊕) | 0.43 $\pm$ 0.03 | 5.3 $\pm$ 0.4 | Insolation
$T_{\rm eq}$ $\left[A_{\rm B}=0\right]$ (K) | 226 $\pm$ 4 | 422 $\pm$ 7 | Equilibrium temperature

Table D2: Prior and posterior distributions of the joint transit RV fit

Parameter | Prior1 | Posterior | Description
---|---|---|---
Stellar parameter |  |  |
$\rho_{\star}$ (g $\cdot$ cm-3) | $\mathcal{N}\left(26.0,2.6^{2}\right)$ | 25.8 $\pm$ 1.0 | Stellar density
LHS 1140 b |  |  |
$P_{\rm b}$ (days) | $\mathcal{U}\left(24.7,24.8\right)$ | 24.73723 $\pm$ 0.00002 | Orbital period
$t_{\rm 0,b}$ (BJD - 2 457 000) | $\mathcal{U}\left(1399.9,1400.0\right)$ | 1399.9300 $\pm$ 0.0003 | Time of inferior conjunction
$r_{\rm 1,b}$ | $\mathcal{U}\left(0,1\right)$ | 0.49 $\pm$ 0.03 | Parameterization2 for $b$ and $p$
$r_{\rm 2,b}$ | $\mathcal{U}\left(0,1\right)$ | 0.0733 $\pm$ 0.0004 | Parameterization2 for $b$ and $p$
$K_{\rm b}$ (m s-1) | $\mathcal{U}\left(0,10\right)$ | 3.80 $\pm$ 0.11 | RV semi-amplitude
LHS 1140 c |  |  |
$P_{\rm c}$ (days) | $\mathcal{U}\left(3.7,3.8\right)$ | 3.777940 $\pm$ 0.000002 | Orbital period
$t_{\rm 0,c}$ (BJD - 2 457 000) | $\mathcal{U}\left(1389.25,1389.35\right)$ | 1389.2939 $\pm$ 0.0002 | Time of inferior conjunction
$r_{\rm 1,c}$ | $\mathcal{U}\left(0,1\right)$ | 0.39 $\pm$ 0.05 | Parameterization2 for $b$ and $p$
$r_{\rm 2,c}$ | $\mathcal{U}\left(0,1\right)$ | 0.0539 $\pm$ 0.0008 | Parameterization2 for $b$ and $p$
$K_{\rm c}$ (m s-1) | $\mathcal{U}\left(0,10\right)$ | 2.42 $\pm$ 0.07 | RV semi-amplitude
Photometric parameters |  |  |
$q_{\rm 1,Spitzer}$ | $\mathcal{U}\left(0,1\right)$ | 0.016${}^{+0.018}_{-0.009}$ | Limb-darkening parameter3
$q_{\rm 2,Spitzer}$ | $\mathcal{U}\left(0,1\right)$ | 0.42${}^{+0.36}_{-0.28}$ | Limb-darkening parameter3
$M_{\rm Spitzer}$ (ppm) | $\mathcal{N}\left(0,1\,000^{2}\right)$ | 34 $\pm$ 23 | Baseline flux
$\sigma_{\rm Spitzer}$ (ppm) | $\mathcal{LU}\left(1,1\,000\right)$ | 15${}^{+57}_{-12}$ | Extra white noise
$q_{\rm 1,HST}$ | $\mathcal{U}\left(0,1\right)$ | 0.28 $\pm$ 0.08 | Limb-darkening parameter3
$q_{\rm 2,HST}$ | $\mathcal{U}\left(0,1\right)$ | 0.12${}^{+0.11}_{-0.08}$ | Limb-darkening parameter3
$M_{\rm HST}$ (ppm) | $\mathcal{N}\left(0,1\,000^{2}\right)$ |  $-25$ $\pm$ 22 | Baseline flux
$\sigma_{\rm HST}$ (ppm) | $\mathcal{LU}\left(1,1\,000\right)$ | 12${}^{+38}_{-10}$ | Extra white noise
$q_{\rm 1,TESS}$ | $\mathcal{U}\left(0,1\right)$ | 0.33${}^{+0.20}_{-0.12}$ | Limb-darkening parameter3
$q_{\rm 2,TESS}$ | $\mathcal{U}\left(0,1\right)$ | 0.56 $\pm$ 0.27 | Limb-darkening parameter3
$M_{\rm TESS}$ (ppm) | $\mathcal{N}\left(0,1000^{2}\right)$ | 9 $\pm$ 48 | Baseline flux
$\sigma_{\rm TESS}$ (ppm) | $\mathcal{LU}\left(1,1\,000\right)$ | 17${}^{+116}_{-14}$ | Extra white noise
RV parameters |  |  |
$\gamma_{\rm pre}$ (m s-1) | $\mathcal{U}\left(-10,10\right)$ | 1.3 $\pm$ 1.5 | RV offset4
$\gamma_{\rm post}$ (m s-1) | $\mathcal{U}\left(-10,10\right)$ | -0.6 $\pm$ 1.4 | RV offset4
$\sigma_{\rm pre}$ (m s-1) | $\mathcal{LU}\left(10^{-3},10\right)$ | 0.04${}^{+0.18}_{-0.03}$ | Extra white noise
$\sigma_{\rm post}$ (m s-1) | $\mathcal{LU}\left(10^{-3},10\right)$ | 0.36 $\pm$ 0.06 | Extra white noise
RV activity GP |  |  |
$A$ (m s-1) | $\mathcal{LU}\left(10^{-3},10\right)$ | 2.8${}^{+1.0}_{-0.6}$ | Amplitude of the GP
$\ell$ (days) | $\mathcal{LU}\left(100,1000\right)$ | 164${}^{+62}_{-42}$ | Timescale of the GP
$\Gamma$ | $\mathcal{LU}\left(0.1,10\right)$ | 3.7${}^{+1.5}_{-1.2}$ | Periodic scale of the GP
$P_{\rm rot}$ (days) | $\mathcal{N}\left(131,5^{2}\right)$ | 133 $\pm$ 3 | Rotation period

Note. — ${}^{1}\mathcal{U}\left(a,b\right)$ is the uniform distribution
between value $a$ and $b$, $\mathcal{LU}\left(a,b\right)$ is the log-uniform
(Jeffreys) distribution between value $a$ and $b$,
$\mathcal{N}\left(\mu,\sigma^{2}\right)$ is the normal distribution with mean
$\mu$ and variance $\sigma^{2}$.

2Parameterization of the transit impact parameter ($b$) and the planet-to-star
radius ratio ($p=R_{\rm p}/R_{\star}$) outlined in Espinoza (2018).

${}^{3}q_{1},q_{2}$ are related to the quadratic limb-darkening coefficients
$u_{1},u_{2}$ by the transformations described in Kipping (2013).

4Relative to the median RV (-13 458.5 and -13 450.5 m s-1 for pre- and post-
fiber change data).

Figure D1: Posterior distributions (1 and 2$\sigma$ contours) for the transit
impact parameter ($b$) and scaled radius ($p=R_{\rm p}/R_{\star}$) of LHS 1140
b and c. Different colors refer to fit on TESS (red), Spitzer (purple), and
HST (blue) data only. The black contours are the final joint posteriors on all
available instruments. A $\sim$4$\sigma$ tension in $p$ exists between Spitzer
and TESS for LHS 1140 c.

###  D.3 Validating genuine Keplerian signals with line-by-line radial
velocity

The LBL method allows to verify the achromaticity of the inferred semi-
amplitudes of the LHS 1140 planets. The three-planet model $\mathcal{M}_{\rm
3cp}$ can be applied on velocities derived per spectral bins of
$\Delta\lambda\approx 20$ nm in the entire ESPRESSO domain. For genuine
Keplerian signals:

  * •

(chromaticity test) the $K_{\lambda}$ calculated for different bands are
achromatic, i.e., $dK_{\lambda}/d\lambda=0$.

  * •

(coherence test) the $K_{\lambda}$ add constructively (coherent period and
phase), yielding a consistent weighted average (value and uncertainty) with
$K$ resulting from the full spectral range.

  * •

(noise test) the semi-amplitude uncertainties ($\sigma_{K}$) should scale with
RV precision ($\sigma_{\rm RV}$) according to the Cloutier et al. (2018)
formalism, i.e., $\sigma_{K}=\sigma_{\rm RV}\sqrt{2/N_{\rm RV}}$ when no
important extra jitter is detected.

These three criteria can be tested for LHS 1140 b, c, and the non-transiting
candidate d. As summarized in Figure D2, we measure no chromaticity for the
Keplerian signals of LHS 1140 b and c, respectively with
$dK_{\lambda}/d\lambda=0.11\pm 0.10$ and $0.03\pm 0.08$ m s-1 per 100 nm. For
the candidate LHS 1140 d, the signal is marginally larger in the blue
wavelengths of ESPRESSO ($dK_{\lambda}/d\lambda=-0.42\pm 0.26$ m s-1 per 100
nm). Similarly, since the Doppler signals of LHS 1140 b and c are perfectly
coherent, the weighted average of the $K_{\lambda}$ are consistent with the
$K$ obtained from the full spectral range (see Fig. D2). This is not observed
for the 80-day signal associated with candidate d for which fitting a
Keplerian model on RVs derived from the full ESPRESSO wavelength range is
three times less accurate. Finally, given the RV precision of this data set
varying from 4.73 to 0.65 m s-1 in the 450–750 nm interval, we find that LHS
1140 b and c follow the Cloutier et al. (2018) formalism, but not d (see Fig.
D2, right). Interestingly, the spectral interval 700–725 nm covering only 8%
of the ESPRESSO domain contains 30% of all the RV content of LHS 1140. The
tests presented in this section provide evidence against the existence of LHS
1140 d first announced by LB20 as a candidate non-transiting planet.

Figure D2: Validating Keplerian signals in the ESPRESSO spectral domain of LHS
1140. Left panels: Semi-amplitudes $K_{\lambda}$ obtained with model
$\mathcal{M}_{\rm 3cp}$ from LBL radial velocities extracted for different
bands ($\Delta\lambda\approx 20$ nm). The per-band velocities have
uncertainties ($\sigma_{\rm RV}$) varying from 4.73 to 0.65 m s-1 (orange
dashed lines). A genuine Keplerian signal is achromatic
($dK_{\lambda}/d\lambda=0$). We measure no chromatic slopes for LHS 1140 b and
c, but the signal of candidate LHS 1140 d is marginally larger in the blue
wavelengths of ESPRESSO ($dK_{\lambda}/d\lambda=-0.42\pm 0.26$ m s-1 per 100
nm). A coherent signal such as a Doppler shift affecting all wavelengths
should produce consistent $K$ between the full spectrum constraints (1$\sigma$
confidence regions in blue) and the weighted average of the $K_{\lambda}$
(1$\sigma$ confidence interval between the red dotted lines). Assuming a
coherent signal, the $K_{\rm d}$ inferred from the full ESPRESSO domain should
have an uncertainty $\sigma_{K_{\rm d}}\sim 0.18$ m s-1, which is inconsistent
with observations. Right panels: Semi-amplitude uncertainties $\sigma_{K}$
with increasing RV precision (smaller $\sigma_{\rm RV}$). A coherent signal in
wavelengths should follow the Cloutier et al. (2018) formalism
($\sigma_{K}=\sigma_{\rm RV}\sqrt{2/N_{\rm RV}}$), which is not seen for LHS
1140 d. The LBL data set shows no evidence of an 80-day signal associated with
the candidate planet LHS 1140 d.

##  Appendix E Supplementary material of the internal structure analysis

###  E.1 Interior modeling

In this appendix, we summarize the method of Plotnykov & Valencia (2020)
adapted to constrain the detailed internal structure of LHS 1140 b.

We used a Bayesian analysis with Markov Chain Monte Carlo (MCMC) sampling with
emcee (Foreman-Mackey et al., 2013) coupled to the internal structure model of
Valencia et al. (2007). The model assumes three layers for the interior of the
planet: a condensed water (liquid/ice) layer at the surface, a mantle (Mg-Si
rock) and a core (Fe-Ni-Si alloy). A fixed atmospheric layer is also
considered for models in which the atmosphere could significantly contribute
to the planet radius. The water layer is described by the equation of state
(EOS) of Hemley et al. 1987; Wagner & Pruß 2002; Stewart & Ahrens 2005 and we
adopt the density mixing model with EOS parameters of Stixrude & Lithgow-
Bertelloni (2011) and Morrison et al. (2018) for the mantle and the core,
respectively. The lower mantle is assumed to be composed of bridgmanite/post-
perovskite and wustite (at different proportions to that of Earth), while the
upper mantle is modeled as pure olivine ($\mathrm{Mg_{2}SiO_{4}}$). This
choice was made in light of the possible low Si content of the star that may
indicate olivine formation is favoured compared to pyroxenes
($\mathrm{Mg_{2}Si_{2}O_{6}}$).

Important ingredients to the model are the abundance ratios (by weight) of
refractory elements, namely Fe/Mg and Mg/Si. We explored a no prior (Fe/Mg
unconstrained) and a stellar prior (Fe/Mg following the star) models for the
water world case of LHS 1140 b (Sect. 4.2.3). For the pure rocky case (Sect.
4.2.2), the planet Fe/Mg ratio must be lower than that of the host star to
produce the observed density. Consequently, only the unconstrained Fe/Mg
analysis was done. Note that because we model three layers for the interior,
the no prior case cannot fully constrain both the CMF and WMF, i.e., planetary
interior models are inherently degenerate in this case. For all models, the
Mg/Si ratio in the mantle is assumed to be that of the host star:
$\mathrm{Mg/Si_{planet}}\sim\mathcal{N}(\mathrm{Mg/Si_{star}},\sigma_{\rm
star}^{2}$). Despite LHS 1140 having a Mg/Si approximately twice that of the
Sun/Earth (see Table C3), this ratio only weakly influences the final radius
of the planet meaning that our results do not depend on the exact mineralogy
of the rocks.

We report the posterior distributions of our interior analysis in Appendix E.2
for all interior models considered. Additionally, we compare the Fe/Mg
distributions of LHS 1140 b for different scenarios in Figure E1.

###  E.2 Posterior distributions

We summarize the posterior distributions of Fe/Mg for LHS 1140 b in Figure E1
for the pure rocky (Sect. 4.2.2) and water world (Sect. 4.2.3) scenarios. The
posteriors from our MCMC sampling are also presented in the following corner
plots of Figures E2, E3, and E4 showing the results for a bare rock, a water
world (no prior, stellar prior, and solar prior cases), and a Hycean world,
respectively.

Figure E1: Fe/Mg distribution for LHS 1140 b according to different
assumptions (no prior or stellar prior) for the bare rock (red) and water
world (green and purple) models compared to the host star (black). We plot the
kernel density estimate of the interior model posterior, which is normalized
to have mode of 1. We include the M dwarfs distribution of Fe/Mg from the
APOGEE DR16 (gray histogram, sample size of $\sim$1000; Majewski et al. 2016;
Ahumada et al. 2020) for comparison. Figure E2: Posterior distribution for LHS
1140 b interior parameters for the bare rock scenario (WMF = 0). Chemical
weight ratios Fe/Si and Fe/Mg are derived quantities. The red lines (and red
cross) in Fe/Si and Fe/Mg space correspond to the stellar measurements. The
vertical black dashed lines represent 16th and 84th percentiles of the
posterior. Figure E3: Posterior distribution for LHS 1140 b interior
parameters for the water world scenario (WMF $>$ 0) for different Fe/Mg
assumptions: no prior (black), stellar prior (red) and Sun prior (blue). For
the stellar and Sun prior cases, the log-probability function is modified to
include the restriction posed by Fe/Mg and Mg/Si ratios measured on the host
star or the Sun (Table C3). The red lines (and red cross) in Fe/Si and Fe/Mg
space correspond to the stellar measurements. The vertical red dashed lines
represent 16th and 84th percentiles of the posterior for the stellar prior
case. Note the values in the parameter titles are for the stellar prior case
only. Figure E4: Posterior distribution for LHS 1140 b interior parameters for
the Hycean world scenario (icy planet with 250 km H2 atmosphere on top). Here,
we use the same assumptions as the stellar prior water world model. The red
lines (and red cross) represent the stellar ratios, while the vertical black
dashed lines are the 16th and 84th percentiles of the posterior. Note the
simulation radius is smaller ($\Delta R_{\rm p}\sim 0.03\mathrm{R_{\oplus}}$)
due to H2 atmosphere which is not included in our interior model.