11institutetext:  Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France 22institutetext: Observatoire de Genève, Département d’Astronomie, Université de Genève, Chemin Pegasi 51b, 1290 Versoix, Switzerland 33institutetext: Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Alonso de Rivera 2850, Concepción, Chile 44institutetext: Astrophysics Group, Keele University, Staffordshire ST5 5BG, UK 55institutetext: Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA 66institutetext: Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, Ontario M5S 3H4, Canada 77institutetext: Department of Physics, University of Warwick, Coventry, UK 88institutetext: Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill Road, Coventry, UK 99institutetext: Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA 1010institutetext: George Mason University, 4400 University Drive, Fairfax, VA, 22030 USA 1111institutetext: Department of Astronomy and Tsinghua Centre for Astrophysics, Tsinghua University, Beijing 100084, China 1212institutetext: Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA 1313institutetext: Institute for Computational Science, University of Zurich, Winterthurerstr. 190, CH-8057 Zurich, Switzerland 1414institutetext: Département de physique, Université de Montréal, 2900 boul. Édouard-Montpetit, Montréal, QC, H3C 3J7, Canada 1515institutetext: Université de Montréal, Département de Physique & Institut de Recherche sur les Exoplanètes, Montréal, QC H3C 3J7, Canada 1616institutetext: International Center for Advanced Studies (ICAS) and ICIFI(CONICET), ECyT-UNSAM, Campus Miguelete, 25 de Mayo y Francia(1650), Buenos Aires, Argentina 1717institutetext: European Southern Observatory, Alonso de Córdova 3107, Vitacura, Región Metropolitana, Chile 1818institutetext: Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal 1919institutetext: Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal 2020institutetext: Departamento de Física, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN, Brazil 2121institutetext: Instituto de Astrofísica de Canarias (IAC), E-38200 La Laguna, Tenerife, Spain 2222institutetext: Dept. Astrofísica, Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife, Spain 2323institutetext: Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 2424institutetext: Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 2525institutetext: Department of Aeronautics and Astronautics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA 2626institutetext: Department of Astrophysical Sciences, Princeton University, NJ 08544, USA 2727institutetext: NASA Ames Research Center, Moffett Field, CA 94035, USA 2828institutetext: SETI Institute, Mountain View, CA 94043, USA 2929institutetext: Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA

# TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA

M. Cointepas Corresponding author:marion.cointepas@univ-grenoble-
alpes.frTOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited
with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited
with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited
with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited
with ExTrA J.M. Almenara TOI-269 b: An eccentric sub-Neptune transiting a M2
dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2
dwarf revisited with ExTrA X. Bonfils TOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrA F. Bouchy TOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrA N. Astudillo-Defru
TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA F. Murgas TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrA J.F. Otegi TOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrA A. Wyttenbach TOI-269 b: An eccentric sub-
Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-
Neptune transiting a M2 dwarf revisited with ExTrA D.R. Anderson TOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA É. Artigau
TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA B.L. Canto Martins TOI-269 b: An eccentric sub-Neptune transiting a M2
dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2
dwarf revisited with ExTrA D. Charbonneau TOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrA K.A. Collins TOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA K.I. Collins
TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA J-J. Correia TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrA S. Curaba TOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrA A. Delboulbé TOI-269 b: An eccentric sub-
Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-
Neptune transiting a M2 dwarf revisited with ExTrA X. Delfosse TOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA R.F. Díaz
TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA C. Dorn TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrA R. Doyon TOI-269 b: An eccentric sub-Neptune transiting a
M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a
M2 dwarf revisited with ExTrA P. Feautrier TOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrA P. Figueira TOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrA T. Forveille TOI-269 b:
An eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b:
An eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA G. Gaisne
TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA T. Gan TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrA L. Gluck TOI-269 b: An eccentric sub-Neptune transiting a
M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a
M2 dwarf revisited with ExTrA R. Helled TOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrA C. Hellier TOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrA L. Jocou TOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA P. Kern
TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA S. Lafrasse TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrA N. Law TOI-269 b: An eccentric sub-Neptune transiting a
M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a
M2 dwarf revisited with ExTrA I.C. Leão TOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrA C. Lovis TOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrA Y. Magnard TOI-269 b:
An eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b:
An eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA A.W. Mann
TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA D. Maurel TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrA J.R. de Medeiros TOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrA C. Melo TOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrA T. Moulin TOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA F. Pepe
TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA P. Rabou TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrA S. Rochat TOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrA D.R. Rodriguez TOI-269 b: An eccentric sub-
Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-
Neptune transiting a M2 dwarf revisited with ExTrA A. Roux TOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA N.C. Santos
TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA D. Ségransan TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrA E. Stadler TOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrA E.B. Ting TOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrA J.D. Twicken TOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA S. Udry
TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA W.C. Waalkes TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrA R.G. West TOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrA A. Wünsche TOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrA C. Ziegler TOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric
sub-Neptune transiting a M2 dwarf revisited with ExTrA G. Ricker TOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA R. Vanderspek
TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf revisited with
ExTrA D.W. Latham TOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting a M2 dwarf
revisited with ExTrA S. Seager TOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune transiting
a M2 dwarf revisited with ExTrA J. Winn TOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrATOI-269 b: An eccentric sub-Neptune
transiting a M2 dwarf revisited with ExTrA J.M. Jenkins TOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrATOI-269 b: An
eccentric sub-Neptune transiting a M2 dwarf revisited with ExTrA

(Received ; Accepted)

We present the confirmation of a new sub-Neptune close to the transition
between super-Earths and sub-Neptunes transiting the M2 dwarf TOI-269 (TIC
220479565, $V=14.4$ mag, $J=10.9$ mag, $R_{\star}=0.40\leavevmode\nobreak\
R_{\odot}$, $M_{\star}=0.39\leavevmode\nobreak\ M_{\odot}$, d = 57 pc). The
exoplanet candidate has been identified in multiple TESS sectors, and
validated with high-precision spectroscopy from HARPS and ground-based
photometric follow-up from ExTrA and LCO-CTIO. We determined mass, radius, and
bulk density of the exoplanet by jointly modeling both photometry and radial
velocities with juliet. The transiting exoplanet has an orbital period of
$P=3.6977104\pm 0.0000037$ days, a radius of $2.77\pm 0.12$ $R_{\oplus}$, and
a mass of $8.8\pm 1.4$ $M_{\oplus}$. Since TOI-269 b lies among the best
targets of its category for atmospheric characterization, it would be
interesting to probe the atmosphere of this exoplanet with transmission
spectroscopy in order to compare it to other sub-Neptunes. With an
eccentricity e = $0.425^{+0.082}_{-0.086}$, TOI-269 b has one of the highest
eccentricities of the exoplanets with periods less than 10 days. The star
being likely a few Gyr old, this system does not appear to be dynamically
young. We surmise TOI-269 b may have acquired its high eccentricity as it
migrated inward through planet-planet interactions.

###### Key Words.:

Planetary systems – Techniques: photometric – Techniques: radial velocities –
Stars : low-mass – Planets and satellites: detection

##  1 Introduction

Low-mass stars offer particular advantages, and are particularly interesting,
when looking for small and cool exoplanets. The transit depth and the radial-
velocity semi-amplitude provoked by rocky exoplanets around M dwarfs is much
higher than those caused by similar planets orbiting around larger stars of
earlier spectral type, which makes such planets easier to detect. Even more
importantly, such systems are also ideal targets for atmospheric
characterization by transmission or thermal emission spectroscopy (e.g.,
Kempton et al. 2018, Batalha et al. 2018). Planets orbiting around M dwarfs
are therefore important objects to obtain precise mass, radius, and bulk
density measurements of transiting exoplanets smaller than Neptune, which are
crucial to better understanding the so-called radius valley between the super-
Earth and sub-Neptune populations (e.g., Fulton et al. 2017, Mayo et al. 2018,
Cloutier & Menou 2020, and Hardegree-Ullman et al. 2020).

The Transiting Exoplanet Survey Satellite (TESS, Ricker et al. 2015) is a NASA
all-sky survey designed to detect transiting exoplanets orbiting nearby stars,
with a specific focus on exoplanets smaller than Neptune. With its array of
four cameras, the satellite has been delivering, since July 2018, both 2 min
cadence photometry on pre-selected targets and full-frame images (FFIs) with a
cadence of 30 min (no longer the case, however, for the extended mission that
began on July 5, 2020, when TESS started collecting FFIs at 10 min cadence).
Each pointing corresponds to a sector of the sky that is observed for a period
of about 27 days. TESS is focusing on relatively bright stars, which is
crucial for the confirmation of transiting candidates and to enable follow-up
observations and characterization of confirmed exoplanets. TESS has identified
more than 200 exoplanet candidates orbiting M dwarfs to date, including a few
super-Earths with masses measured thanks to high-precision radial velocities
(e.g., GJ357 b - Luque et al. 2019; LTT3780 b - Cloutier et al. 2020).

The Exoplanets in Transits and their Atmospheres (ExTrA) facility (Bonfils et
al. 2015) was developed to specifically perform from the ground high-precision
spectro-photometry in the near-infrared on mid- to late M dwarf stars. ExTrA
consists of a set of three 60 cm telescopes equipped with multi-object fiber
positioners and a low-resolution near-IR spectrograph. ExTrA is being used to
confirm TESS planet detections, refine transit parameters, and search for
additional exoplanets in the same systems.

In this paper we report the discovery of a new transiting exoplanet around the
M2 dwarf TOI-269, which was first detected as a candidate by TESS. The target
was then confirmed with ground-based photometry and its mass measured thanks
to HARPS radial velocities (RVs). Section 2 presents a detailed analysis of
the stellar properties of TOI-269. Section 3 describes the observations and
data used in this study, including a description of ExTrA. Section 4 presents
the global analysis of the available data in order to constrain the planetary
properties. Section 5 presents a discussion of our results, and Section 6
presents our conclusions.

##  2 Stellar parameters

TOI-269 is an M dwarf at a distance of $57.023\pm 0.076$ pc (Gaia
Collaboration et al. 2018, Lindegren et al. 2018, and Bailer-Jones et al.
2018). The astrometry, photometry, and stellar parameters are reported in
Table 1.

Table 1: Stellar parameters for TOI-269 (TIC 220479565, UCAC4 180-005252,
2MASS J05032306-5410378, WISE J050323.09-541039.1, APASS 26149036).

Parameter | Value | Refs
---|---|---
Astrometry |  |
Right ascension (J2015.5), $\alpha$ | 05h03m23.11s | 1,2
Declination (J2015.5), $\delta$ |  $-$54o10’39.8” | 1,2
Parallax, [mas] | $17.508\pm 0.023$ | 1,2
Distance, d [pc] | $57.023\pm 0.076$ | 1,2
Proper motion RA [mas/year] | $26.472\pm 0.43$ | 1,2
Proper motion D [mas/year] | $120.750\pm 0.43$ | 1,2
Photometry |  |
V [mag] | $14.37\pm 0.11$ | 3
TESS magnitude [mag] | $12.2958\pm 0.0074$ | 3
J [mag] | $10.909\pm 0.026$ | 4
H [mag] | $10.304\pm 0.022$ | 4
$K_{s}$ [mag] | $10.100\pm 0.023$ | 4
Stellar parameters |  |
Spectral type | M2V | 5
$M_{K_{s}}$ [mag] | $6.320\pm 0.023$ | 6
Effective temperature, $T_{\rm eff}$ [K] | $3514\pm 70$ | 6,7
Surface gravity, log g [cgs] | $4.831\pm 0.029$ | 6
Metallicity, [Fe/H] [dex] | $-0.29\pm 0.12$ | 6,7
Stellar radius, $R_{\star}$ [$R_{\odot}$] | $0.398\pm 0.012$ | 6
Stellar mass, $M_{\star}$ [$M_{\odot}$] | $0.3917\pm 0.0095$ | 6
log $R^{\prime}_{HK}$ | $-5.320\pm 0.142$ | 6

  * •

References : 1) Gaia Collaboration et al. (2018), 2) Lindegren et al. (2018),
3) Stassun et al. (2019), 4) Cutri et al. (2003), 5) Pecaut & Mamajek (2013),
6) This work, 7) Yee et al. (2017),

We derived the mass of the star with the empirical relationship between
$M_{K_{s}}$ and $M_{\star}$ of Mann et al. (2019) and using their M_-M_K-
code111https://github.com/awmann/M_-M_K-. An apparent magnitude of
$K_{s}=10.100\pm 0.023$ leads to an absolute magnitude of $M_{K_{s}}=6.320\pm
0.023$ and a mass of $M_{\star}=0.3917\pm 0.0095\leavevmode\nobreak\
M_{\odot}$. We used another empirical relation from Mann et al. (2015) to
estimate the radius of the star also from the value of the apparent magnitude
and found $R_{\star}=0.398\pm 0.012\leavevmode\nobreak\ R_{\odot}$, which is
the same value as provided in the TESS Input Catalog (TIC-v8; Stassun et al.
2019). With both mass and radius we infer a stellar density of
$\rho_{\star}=8.76\pm 0.87\leavevmode\nobreak\ g$/$cm^{3}$. The analysis by
Mann includes stars with close-to-solar metallicities. However, using
SpecMatch-Emp222https://github.com/samuelyeewl/specmatch-emp (Yee et al. 2017)
and HARPS high-resolution spectra of TOI-269, we estimated that the star has a
metallicity of ${\rm[Fe/H]}=-0.29\pm 0.12$ (Yee et al. 2017). To verify the
impact of such sub-solar metallicity on the stellar parameters, we performed
an analysis of the spectral energy distribution combined with stellar
evolution model (Appendix C). It leads to similar results for the stellar mass
and radius. To be more conservative, in the rest of this paper we use the
relations in Mann et al. (2015, 2019) without taking into account the stellar
metallicity. With SpecMatch-Emp, we also obtain an effective temperature
$T_{\rm eff}=3514\pm 70\leavevmode\nobreak\ K$ and radius $R_{\star}=0.41\pm
0.04\leavevmode\nobreak\ R_{\odot}$. We report the $T_{\rm eff}$ value in
Table 1, but discard the $R_{\star}$ value, which we found to be less precise
than that of the Mann et al. (2015) relationship. An analysis of the WISE
(Wright et al. 2010a) data for TOI-269 shows no IR excess, pointing to the
absence of circumstellar material around the star, at least in the WISE bands.

We estimated the age of the star using gyrochronology with the different
rotation periods that we calculated (see Sections 3.2.3 and 3.3). We used the
relation from Engle & Guinan (2011), which determines the stellar age through
measures of the rotation period of the star. If we used the estimation of the
rotation period from the HARPS spectra ($P_{\rm rot}=69\pm 15$ days), we
obtained a stellar age of $4.19\pm 0.97$ Gyr. We also calculated the age with
the rotation period measured from WASP-South ($P_{\rm rot}=35.7\pm 2.0$ days)
and found $2.16\pm 0.27$ Gyr. At this point, we cannot conclude which rotation
period is the correct one, but it appears that the system is not newly formed.
We confirmed these estimations using the relations from Barnes (2010), Barnes
& Kim (2010), and Meibom et al. (2015), which describe the rotational
evolution of main sequence stars taking into account the stellar mass
dependence, as we obtained an age of $5.8^{+2.4}_{-1.9}$ Gyr from the HARPS
rotation period and $2.36^{+0.45}_{-0.35}$ Gyr from the WASP-South data. In
terms of activity, we found the star to be rather quiet and slowly rotating
(see next section).

##  3 Observations

###  3.1 TESS photometry

TOI-269 was observed in six TESS sectors (3, 4, 5, 6, 10, and 13) from
September 2018 to July 2019 with the two-minute cadence. The TESS photometric
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 TOI-269 was corrected for dilution by known contaminating
sources in the TESS aperture. Given the large TESS pixel size of 21”, it was
essential to verify that no visually close-by targets were present that could
affect the depth of the transit and to check for a contaminating eclipsing
binary. A plot of the target pixel file (TPF) and the aperture mask that is
used for the simple aperture photometry (SAP), generated with tpfplotter
(Aller et al. 2020), is shown in Fig. 1. We can see that one star overlaps the
TESS aperture, but its faintness results in minimal dilution of the TESS light
curve. The CROWDSAP value in the TESS data (which is the ratio of target flux
to total flux in the aperture) ranges from 0.9829 to 0.9932 in all TESS
sectors used for this analysis. This value corresponds to the $\sim$ 1%
dilution expected from the star visible in the TESS aperture with a magnitude
difference of 5 with TOI-269.

A potential transit signal with 3.698-day period was identified in the SPOC
transit search (Jenkins 2002, Jenkins et al. 2010, 2020) of the TOI-269 light
curve. This was promoted to TOI planet candidate status and designated as
TOI-269.01 by the TESS Science Office based on the SPOC data validation
results; the results indicate that the 4900 ppm signature based on 35
individual transits was consistent with that of a transiting planet (Twicken
et al. 2018, Li et al. 2019). The difference image centroids analysis
performed in the data validation (DV) report shows that the source of the
transits is within 1 arcsec of the target, and furthermore that the DV reports
are very clean; the transiting planet’s signature passes all of DV tests,
including the odd/even transit depth test, the ghost diagnostic, and the
statistical bootstrap test. These tests are described in Twicken et al. (2018)
and can exclude a false positive created by the second star in TESS aperture.

A recent work by Canto Martins et al. (2020), which reports a search for
rotation period among 1000 TESS TOIs using fast Fourier transform,
Lomb–Scargle, and wavelet techniques, accompanied by a rigorous visual
inspection shows that TOI-269 does not indicate any sign of chromospherical
activity all along the observed time ranges, and that it is among the quietest
stars in the sample.

Figure 1: TESS target pixel file image of TOI-269 in Sector 3 (created with
tpfplotter, Aller et al. 2020). The electron counts are color-coded. The red
bordered pixels are used in the simple aperture photometry. The size of the
red circles indicates the Gaia DR2 magnitudes of all nearby stars.

###  3.2 Ground-based photometry

####  3.2.1 ExTrA photometry

ExTrA is a new facility composed of three 60 cm telescopes that are located at
La Silla Observatory (Bonfils et al. 2015). It is dedicated to searching for
exoplanets transiting nearby M dwarfs with near-infrared photometry. The
instrument relies on a new approach that involves combining photometry with
spectroscopic information in order to mitigate the disruptive effect of
Earth’s atmosphere, as well as effects introduced by instruments and
detectors. On each telescope five field units (FUs) are used to collect the
light from the main target and four selected comparison stars. The FUs are
composed of fibers accurately positioned that all feed a single near-infrared
spectrograph with low spectral resolution ($R\sim 200$ or $R\sim 20$) and that
covers the 0.9–1.6 $\mu$m range. The wide spectral domain enables the
simultaneous collection of more photons which increases the sensitivity. ExTrA
has the advantage of multiplexing, meaning that we can use a single
spectrograph (so a single detector) to record the light from several
telescopes. Although all three telescopes can observe the same field, most of
the time they will observe different fields in order to maximize the transit
search efficiency. For now all the telescopes are observing the same target in
order to better understand the performance and limitations of the instrument.
On each telescope each FU is composed of two ”buttons”: the science button and
the centering button. The centering button is composed of a bundle of 19
fibers in a hexagonal arrangement, used to calculate the position of the stars
accurately, and then apply a relative offset to center the star in the science
button. Each science button is composed of two channels, one with an aperture
of 8” (optimized for bright stars), and a second one with an aperture of 4” in
order to reduce the background contribution (optimized for faint stars).
Finally, each channel has two fibers: one to collect the light of the star and
another to collect the sky background close to the star. Thus, the
spectrograph images the fiber bundles in centering mode, and with a different
light path disperses the science fibers using a prism.

We observed TOI-269 with an 8” fiber aperture using the low-resolution mode
($R\sim 20$). We used Gaia DR2 4770833527616320512 as a guiding star to
correctly point our target and comparison stars. The five stars we observed
for that specific field of view were 2MASS J05021375-5416532 on the field unit
1 (FU1), 2MASS J05032583-5353188 on the FU3, 2MASS J05020219-5351064 on the
FU4, 2MASS J05001046-5407021 on the FU5, and finally our target star, which
was positioned on the FU2. The four comparison stars come from the 2MASS
catalog (Skrutskie et al. 2006). The field of view of TOI-269 used for each
night of observations with ExTrA is presented in the Appendix in Fig. 18. At
low resolution the spectrum of the star only covers 43 pixels of the 640
available in the detector in the spectral dimension. We first subtracted the
sky flux and normalized by the flat. We made sure by looking at the absolute
flux of all the stars that the night was clear and that we did not have any
strong flux loss that could cause issues in the photometry. We created a
template of all the exposures to remove any outliers. We distributed a weight
(proportional to the variance of flux versus time) for each pixel/wavelength
in order to mitigate the effect of the Earth’s atmosphere, especially in the
water bands. We then obtained the differential photometry for each star (our
target and the four comparison stars) by normalizing with a template that
includes the photometry of the different stars. The photometry is still
affected by some systematic effects that are still under investigation. One of
them may come from the fact that there are some differential motions of the
stars during the observing sequence which introduce differential centering on
the fibers aperture. A decorrelation with the position of the star inside the
fiber is not possible because we cannot monitor the XY position of the star
inside the fiber aperture during an acquisition. This problem is being
investigated by observing the same field with the centering bundle only during
a whole night, and then applying the measured offsets on all subsequent
nights. For this work, we only present the light curve of our main target
TOI-269 and we removed systematic trends applying Gaussian processes that
allow us to model non-white noise effects for which we do not have a good
model at hand. TOI-269 b transits were observed with ExTrA on December 18,
2019, December 29, 2019, and March 1, 2020, with an exposure time of 60
seconds. Telescope 1 was not in operation during the first two nights. In
total, seven light curves of TOI-269 were obtained with ExTrA.

####  3.2.2 LCOGT Photometry

We observed full transits of TOI-269 b in Sloan $i^{\prime}$-band on UTC 2019
March 02 (and respectively UTC 2020 October 13, only used in Section 4.4 as
the global analysis had already been done at this time) from the LCOGT (Brown
et al. 2013) 1.0 m network nodes at Cerro Tololo Inter-American Observatory
(CTIO) (and Siding Spring Observatory). We also observed an ingress with
nearly full transit coverage in ${\rm I_{c}}$-band on UTC 2019 April 07 from
the LCOGT 1.0 m network node at CTIO. We used the TESS Transit Finder, which
is a customized version of the tapir software package (Jensen 2013) to
schedule our transit observations. The $4096\times 4096$ LCOGT SINISTRO
cameras have an image scale of 0.389$\arcsec$ per pixel, resulting in a
$26\arcmin\times 26\arcmin$ field of view. The images were calibrated by the
standard LCOGT BANZAI pipeline (McCully et al. 2018), and photometric data
were extracted with AstroImageJ (Collins et al. 2017). The images were mildly
defocused and have typical stellar point spread functions with a full width
half maximum (FWHM) of $\sim 2\aas@@fstack{\prime\prime}3$; circular apertures
with radius $\sim 4\aas@@fstack{\prime\prime}3$ were used to extract the
differential photometry.

####  3.2.3 WASP-South photometry

The field of TOI-269 was observed by WASP-South (an array of eight cameras
using 200 mm, f/1.8 lenses backed by $2048\times 2048$ CCDs; Pollacco et al.
2006) over the three consecutive years, 2009, 2010, and 2011. Observations
spanned 180 days in each year, accumulating a total of 18 100 photometric data
points (Fig. 2). At a magnitude of $V$ = 14.4, TOI-269 is at the faint end of
the WASP range, but the field is relatively sparse, and the next-brightest
star in the 48 arcsec extraction aperture is 4 magnitudes fainter.
Combining all the data, and searching for a rotational modulation using the
methods presented in Maxted et al. (2011), we find a possible periodicity of
35.7 $\pm$ 2.0 d, where the error allows for possible phase changes over the
observation span (Fig. 3). The modulation has an amplitude of 10 mmag, and an
estimated false alarm probability of less than 1%.

Figure 2: WASP-South light curve of TOI-269 showing the time sampling. Figure
3: Periodogram of the WASP-South light curves of TOI-269 from 2009–2011,
showing a possible rotational modulation with a period of 36 days. The
horizontal line corresponds to the estimated 1% false alarm level.

###  3.3 Radial velocities: HARPS

We obtained 81 spectra of TOI-269 with the High Accuracy Radial velocity
Planet Searcher (HARPS; Mayor et al. 2003) echelle spectrograph at the ESO
3.6m telescope at La Silla Observatory in Chile. The HARPS optical
spectrograph has a resolution of R=115,000 and is stabilized in pressure and
temperature, in order to achieve a sub-m/s precision. The observations span
275 days and were taken between UT January 18, 2019, and October 20, 2019
(Prog-ID 1102.C-0339(A)).
The HARPS observations were acquired without simultaneous wavelength
calibration and with an exposure time of 1,800 seconds, although seven of them
have exposures of 1,200 or 2,400 seconds, resulting in a total open shutter
time of 41.2 hours. These data were reduced with the Data Reduction
Software333http://www.eso.org/sci/facilities/lasilla/instruments/harps/doc/DRS.pdf.
Radial velocities were computed through maximum likelihood between individual
spectra and a master stellar spectrum following the recipes described in
Astudillo-Defru et al. (2017b). Reduced spectra have a median signal-to-noise
ratio of $\sim$13 at 650 nm, resulting in a median radial velocity precision
of 7.5 m/s and presenting a dispersion of 8.5 m/s.

We also performed an analysis with HARPS data using the DACE platform
444https://dace.unige.ch (Buchschacher & Alesina 2019) that can be used to
compute periodograms for parameters available in RVs data and to represent
correlations between different indicators. We did not find any sign of a
strong stellar activity in the different indicators (CCF-FWHM, S-index, Na-
index) derived from the spectra except in H$\alpha$ with a peak around 54
days. The low value of $logR^{\prime}_{HK}=-5.32\pm 0.14$, derived from the
HARPS combined spectra, indicates a chromospherically inactive star with
likely a long rotation period estimated to $P_{\rm rot}=69\pm 15$ days,
according to Astudillo-Defru et al. (2017a).
This value is compatible with 2$\sigma$ to the WASP-South value, but we could
also imagine that the signal found in the WASP data comes from two stellar
spots at the surface of the star and could correspond to $P_{\rm rot}/2$.

###  3.4 SOAR speckle imaging

High angular resolution imaging is needed to search for nearby sources that
could contaminate the TESS photometry, resulting in an underestimated
planetary radius, or could be the source of astrophysical false positives,
such as background eclipsing binaries. We searched for stellar companions to
TOI-269 with speckle imaging on the 4.1 m Southern Astrophysical Research
(SOAR) telescope (Tokovinin 2018) on 18 February 2019 UT, observing in Cousins
$I$ band, a visible band-pass similar to TESS. More details of the
observations are available in Ziegler et al. (2020). The 5$\sigma$ detection
sensitivity and speckle auto-correlation functions from the observations are
shown in Fig. 4. No nearby stars were detected within 3″of TOI-269 in the SOAR
observations.

Figure 4: I-band 5$\sigma$ contrast curve from SOAR speckle imaging of TOI-269
(TIC 220479565). The inset depicts the corresponding speckle auto-correlation
function.

##  4 Analysis and modeling

We used the software package juliet (Espinoza et al. 2019) to model separately
and jointly the photometric and radial-velocity data. The algorithm is built
on many publicly available tools for the modeling of transits (batman,
Kreidberg 2015), RVs (radvel, Fulton et al. 2018), and Gaussian processes
(GPs) (george, Ambikasaran et al. 2015; celerite, Foreman-Mackey et al. 2017).
In order to compare different models, juliet efficiently computes the Bayesian
evidence (lnZ) using dynesty (Speagle 2020), a python package to estimate
Bayesian posteriors and evidence using nested sampling methods. Nested
sampling algorithms sample directly from the given priors instead of starting
off with an initial parameter vector around a likelihood maximum found via
optimization techniques, as is done in common sampling methods. During our
different analysis, we made sure that we had enough live points given the
number of free parameters so that we would not miss peaks in the parameter
space. We started the analysis using only TESS photometry, and then HARPS RVs
measurements in order to constrain the priors and use them for a joint
analysis of all our data.

###  4.1 TESS photometry

First, using juliet, we modeled the TESS PDCSAP light curve where our planet
candidate was initially detected. The transit model fits the stellar density
$\rho_{\star}$ along with the planetary and jitter parameters. We chose the
priors of the orbital parameters from ExoFOP, except for the stellar density
that we calculated in section 2. We adopted a few parametrization
modifications when dealing with the transit photometry. We assigned a
quadratic limb-darkening law for TESS, as shown to be appropriate for space-
based missions (Espinoza & Jordán 2015), which was then parameterized with the
uniform sampling scheme $(q_{1},q_{2})$ introduced by Kipping (2013).
Additionally, rather than fitting directly for the planet-to-star radius ratio
($p=R_{p}/R_{\star}$) and the impact parameter of the orbit
($b=a/R_{\star}\cos{i}$), juliet used the parameterization introduced in
Espinoza (2018) and fit for the parameters $r_{1}$ and $r_{2}$ to guarantee
full exploration of physically plausible values in the (p,b) plane. We fixed
the TESS dilution factor to one based on our analysis of nearby companions.
Furthermore, we added in quadrature a jitter term $\sigma_{TESS}$ to the TESS
photometric uncertainties, which might be underestimated due to additional
systematics in the space-based photometry. The details of the priors and
posteriors, and the description of each parameter are presented in Table 3.
The best-fit transit model for the six sectors of TESS photometry is shown in
Fig. 5. We also represented the phase-folded light curve in the same figure.

Figure 5: Modeling of the TESS data. Left panel: TESS photometry time series
(20 min binned data) from Sectors 3, 4, 5, 6, 10, and 13 along with the median
of 1000 randomly chosen posterior samples (solid black line). Right panel:
Phase-folded light curve to the period of the planet (dark blue points
correspond to $\sim$ 5 min binned data).

###  4.2 HARPS radial velocities

As the star does not seem to be very active and has a long rotation period, we
decided that Gaussian processes were not required to model the HARPS data.
However, a small long-period trend seems visible in our dataset so we decided
to add a linear drift to the fit. We first computed the periodogram of the RV
time series where we subtracted the possible linear trend, and then the
Keplerian corresponding to the TOI-269 b period (see Fig. 6). We then analyzed
the radial-velocity data from HARPS using juliet. The intercept of the linear
model, which represents here the systemic velocity of the star, is computed at
time $t_{\gamma}=2\,458\,639$ BJDUTC, close to the middle of our observations.
This configuration of one planet with a possible additional long-term trend
(that is compatible with zero within 2$\sigma$) in the data appears to be the
simplest and model that best explains the current dataset. The priors are
taken from the TESS analysis and an overview of the HARPS data. The details of
the priors and posteriors, and the description of each parameter are presented
in Table 4.

Figure 6: Analysis of the HARPS radial velocities. Periodogram for RV time
series where a linear drift was subtracted is shown in the top panel. We can
see a peak at 3.7 days corresponding to the period of the planet, and another
at 1.36 days corresponding to its alias. Both peaks have a false alarm
probability $<<1\%$. The lower panel is the periodogram for RVs where a linear
drift and Keplerian (for the first planet) were subtracted; the highest peak
at 5.9 days has a false alarm probability of 20.8%.

###  4.3 Joint fit of all data

To obtain the most precise parameters of the TOI-269 system, we performed a
joint analysis of the TESS, LCO, and ExTrA photometry and velocity data from
HARPS using juliet. This time we fitted for the eccentricity and applied the
classical parameterization of (e,$\omega$) into
($\sqrt{e}\sin{\omega}$,$\sqrt{e}\cos{\omega}$), always ensuring that $e\leq
1$. We decided to use time-dependent Gaussian processes on the ExTrA and LCO-
CTIO photometry as the data had not been detrended yet. We decided on the
approximate Matern kernel introduced in Foreman-Mackey et al. (2017) because
when looking at the light curves there are no evident quasi-periodic
oscillations. We only use the three-transit duration around transit data for
TESS for reasons of computation time.
In total, we looked for the posterior distribution of 51 free parameters, and
as it is a large number of parameters, we used dynesty to perform this fit.
Before the final run for the joint modeling, we constrained our priors using
the previous results from juliet in order to optimize the search for the
posteriors and the computation time due to the large parameter space. Since we
used rather large priors for the planetary parameters for the fit of TESS data
and HARPS data separately, nested sampling is an efficient method for the
exploration of the parameter space, and as most of the planetary parameters
are specific to a given data type, they would not change significantly in a
joint fit. Using prior knowledge from the previous fit for the joint modeling
was therefore justified. Table 5 and Tables 2 and 6 show respectively the
priors and posteriors of all the parameters, along with the transit, RVs and
physical parameters derived using the stellar parameters presented in Section
2. Figure 7 shows the results of our joint fit to the data for ExTrA555The raw
and detrended fluxes are available in electronic form at the CDS.. The GPs we
used to account for the systematics clearly capture the observed trends in the
ExTrA photometry. We show the phased transits of the photometry instruments
after subtracting the GP component from the ExTrA and LCO-CTIO data in Fig. 8.
In Fig. 9 and Fig. 10, we present the radial-velocity component of the joint
fit modeled by the median and one-sigma error of 1000 randomly chosen
posterior samples, and the phase-folded data with the maximum a posteriori
model.
This analysis revealed an eccentric orbit for TOI-269 b, which is discussed in
the next section.

In order to estimate the precision of the new instrument ExTrA, we computed
the standard deviation of the residuals of TESS and ExTrA data phased at the
period of the planet (see Fig. 8 for the residuals of the phase-folded light
curves) for different bin sizes (from 2 to 64 min bins) and present the
results in Fig. 11. We can see that combining 7 ExTrA transits is similar to
combining 35 TESS transits to obtain the same precision on the dispersion of
the residuals, potentially correlated to the precision on the radius ratio. We
established that we need to fit the TESS and ExTrA light curves simultaneously
to constrain the parameters of the Gaussian processes, so that they filter
ExTrA photometry on a different timescale than the transit itself, but we do
obtain a better precision (1 to 5 transits) to measure the depth of the
transit with fewer ExTrA observations.

Figure 7: ExTrA light curves for the three nights of observations (columns)
and for each telescope (first line corresponding to telescope 1, second line
to telescope 2, and third line to telescope 3). Our raw data are shown in
blue, and modeled using Gaussian processes in black. The detrended light
curves are shown (gray dots), with the maximum a posteriori model transit (in
red). The residuals below correspond to the modeled transit subtracted from
detrended data points. Figure 8: Photometry data for TESS (35 transits), ExTrA
(7 transits; corrected for the GP component), and LCO-CTIO (2 transits;
corrected for the GP component) phase-folded to the period of the planet. The
black line is the maximum a posteriori model; the black points are $\sim$ 5
min binned data. Figure 9: HARPS radial-velocity measurements for TOI-269. The
data points with errors are shown in orange; the black line and gray band
correspond respectively to the median and $1\sigma$ of 1000 randomly chosen
posterior samples from the joint fit. Figure 10: HARPS RVs phase-folded to the
period of the transiting planet. The black line is the best-fit model from the
joint fit. Table 2: Posterior stellar and planetary parameters obtained from
our joint photometric and radial-velocity juliet analysis for TOI-269. The
posterior estimate corresponds to the median value. Error bars denote the 68%
posterior credibility intervals.

Parameter name | Posterior estimate | Description
---|---|---
Posterior parameters for TOI-269 |  |
$\rho_{\star}$ (g/cm3) | $8.98^{+0.83}_{-0.81}$ | Stellar density
$q_{1,TESS}$ | $0.39^{+0.33}_{-0.24}$ | Quadratic limb-darkening parameterization
$q_{2,TESS}$ | $0.22^{+0.30}_{-0.16}$ | Quadratic limb-darkening parameterization
$q_{1,LCO}$ | $0.35^{+0.28}_{-0.19}$ | Quadratic limb-darkening parameterization
$q_{2,LCO}$ | $0.36^{+0.35}_{-0.25}$ | Quadratic limb-darkening parameterization
$q_{1,ExTrA}$ | $0.133^{+0.16}_{-0.089}$ | Quadratic limb-darkening parameterization
$q_{2,ExTrA}$ | $0.43^{+0.36}_{-0.30}$ | Quadratic limb-darkening parameterization
Posterior parameters for TOI-269 b |  |
$P_{b}$ (days) | $3.6977104^{+0.0000037}_{-0.0000037}$ | Period of the planet
$t_{0}$ (BJD TBD) | $2458381.84668^{+0.00033}_{-0.00033}$ | Time of transit-center for the planet
$r_{1,b}$ | $0.700^{+0.078}_{-0.15}$ | Parameterization for p and b
$r_{2,b}$ | $0.0638^{+0.0020}_{-0.0021}$ | Parameterization for p and b
$S_{1,b}=\sqrt{e_{b}}sin(\omega_{b})$ | $0.614^{+0.077}_{-0.10}$ | Parameterization for $e$ and $\omega$
$S_{2,b}=\sqrt{e_{b}}cos(\omega_{b})$ | $0.18^{+0.15}_{-0.16}$ | Parameterization for $e$ and $\omega$
$K_{b}$ (m/s) | $7.6^{+1.2}_{-1.2}$ | Radial-velocity semi-amplitude of the planet
Long-term trend in RVs |  |
RV slope (m/s/day) | $0.0161^{+0.0081}_{-0.0081}$ | Linear trend : first parameter
RV intercept (km/s) at $t_{\gamma}$ | $37.22864^{+0.00082}_{-0.00082}$ | Linear trend : second parameter
Derived transit and RVs parameters |  |
$p=R_{p}/R_{\star}$ | $0.0638^{+0.0020}_{-0.0021}$ | Planet-to-star radius ratio
$b=(a/R_{\star})cos(i_{p})$ | $0.55^{+0.12}_{-0.22}$ | Impact parameter of the orbit
$i_{p}$ (deg) | $88.14^{+0.78}_{-0.90}$ | Inclination of the orbit
$e_{b}$ | $0.425^{+0.082}_{-0.086}$ | Eccentricity of the orbit
$\omega_{b}$ (deg) | $74^{+15}_{-15}$ | Argument of periastron
Derived physical parameters∗ |  |
$M_{p}(M_{\oplus})$ | $8.8^{+1.4}_{-1.4}$ | Planetary mass (in Earth mass)
$R_{p}(R_{\oplus})$ | $2.77^{+0.12}_{-0.12}$ | Planetary radius (in Earth radius)
$\rho_{p}(g/cm^{3})$ | $2.28^{+0.48}_{-0.42}$ | Planetary density
$a_{p}(au)$ | $0.0345^{+0.0015}_{-0.0015}$ | Semi-major axis
$T_{eq}(K)$ | $531^{+25}_{-25}$ | Equilibrium temperature of the planet†
$S(S_{\oplus})$ | $19.0^{+4.0}_{-3.3}$ | Planetary insolation (in Earth flux)

  * •

∗We sample from a normal distribution for the stellar mass, stellar radius,
and stellar temperature that is based on the results from Section 2.

  * •

†Equilibrium temperature was calculated assuming 0.3 Bond albedo and the semi-
major axis distance.

Figure 11: Dispersion of the residuals for TESS (35 combined transits) and
ExTrA (7 combined transits) data for different bin sizes.

###  4.4 TTVs analysis

We calculated the transit timing variations (TTVs) with all the photometric
datasets (TESS, LCOGT, ExTrA) using juliet. Instead of fitting a period $P$
and a time-of-transit center $t_{0}$, juliet looks for the individual transit
times. We fitted each ExTrA transit individually and one transit time for each
night of observations, which is more coherent for the analysis. Combining the
three telescopes reduces the error bars on each ExTrA estimation. The results
of the analysis showing the difference between the observed transit times and
the calculated linear ephemeris from all the transits is presented in Fig. 12.
No significant variation appears in the data.

Figure 12: Transit time variations. The observation minus the calculated
linear ephemeris (O-C) diagram derived using TESS (light blue), LCO-CTIO
(red), and ExTrA data (dark blue corresponding to telescope 1, purple to
telescope 2, green to telescope 3, and yellow to a transit time fit of all the
telescopes available for each night).

##  5 Discussion

###  5.1 Mass-radius diagram and internal structure

TOI-269 b, with a radius of $2.77\pm 0.12\leavevmode\nobreak\ R_{\oplus}$ and
a mass of $8.8\pm 1.4\leavevmode\nobreak\ M_{\oplus}$, lies within the
population of sub-Neptunes. With a stellar irradiation of 19 times the Earth,
TOI-269 b lies in the gas-dominated sub-Neptune population described by Fulton
et al. (2018). Figure 13 shows M-R curves tracing the compositions of pure-
iron, Earth-like, and pure-water planets and a planet with 95% water and 5%
H-He atmosphere subjected to a stellar radiation of $F/F_{\oplus}$= 20
(similar to that of TOI-269 b). For reference, also shown are exoplanets with
accurate and reliable mass and radius determinations (Otegi et al. 2020a,
accessible on the Data & Analysis Center for Exoplanet,
DACE666https://dace.unige.ch/exoplanets/). TOI-269 b sits above the pure-water
curve and below the 5% H-He curve, implying that the H-He mass fraction is
unlikely to exceed a few percent.

Determining the planetary internal structure is extremely challenging since
various compositions can lead to identical mass and radius (e.g., Rogers &
Seager 2010, Lopez & Fortney 2014, Dorn et al. 2015, 2017a, Lozovsky et al.
2018, and Otegi et al. 2020b). With the aim of at least partially breaking the
degeneracy, and in order to determine how well a given interior model compares
with the other possible models that also fit the data, we use a generalized
Bayesian inference method with a Nested sampling scheme. This approach allows
us to quantify the degeneracy and correlation of the planetary structural
parameters and to estimate the most likely region in the parameter space. We
modeled the interior of TOI-269 b considering a pure-iron core, a silicate
mantle, a pure-water layer, and a H-He atmosphere. The equations of state
(EOSs) used for the iron core are taken from Hakim et al. (2018), the EOS of
the silicate-mantle is calculated with PERPLE_X from Connolly (2009) using the
thermodynamic data of Stixrude & Lithgow-Bertelloni (2011), and the EOS for
the H-He envelope are from Chabrier et al. (2019) assuming a proto-solar
composition. For the pure-water layer the AQUA EOS from Haldemann et al.
(2020) is used. The thickness of the planetary layers were set by defining
their masses and solving the structure equations. To obtain the transit
radius, we follow Guillot (2010) and evaluate the location where the chord
optical depth $\tau_{ch}$ is $2/3$. It has been suggested that stellar
abundances can be used as a proxy for the planetary bulk abundances to reduce
the degeneracy (Dorn et al. 2017b, Brugger et al. 2017, and Otegi et al.
2020b), but the result is debated Plotnykov & Valencia (2020), and we
therefore opted not to use them.

Figure 14 shows a ternary diagram and an illustration of the inferred internal
composition of TOI-269 b. The ternary diagram shows the strong degeneracy of
internal composition leading to the same mass and radius, which cover almost
the whole diagram. We find a median H-He mass fraction of 0.8%, which
corresponds to a lower bound since enriched H-He atmospheres are more
compressed and, therefore increase the planetary H-He mass fraction. Formation
models suggest that sub-Neptunes are very likely to be formed via envelope
enrichment Venturini & Helled (2017). We also find that TOI-269 b can have a
significant water layer, accounting for nearly half of the planetary mass with
a thickness of about one Earth radius ($1.02^{+0.39}_{-0.37}$). The iron core
and silicate mantle have estimated relative mass fractions of 19% and 26%,
with large uncertainties. The degeneracy between the core and mantle in this
M-R regime does not allow us to accurately estimate the masses of these two
constituents. Since interior models cannot distinguish between water and H-He
as the source of low-density material, we also ran a three-layer model which
leaves out the H2O envelope. Under this assumption we find that the planet
would be nearly $4^{+1}_{-1}\%$ H-He, $43^{+24}_{-23}\%$ iron, and
$52^{+22}_{-23}\%$ rock by mass. These estimations with the three-layer model
set maximum limits since any water added would decrease these mass fractions.

Figure 13: Mass-radius diagram of exoplanets with accurate mass and radius
determination Otegi et al. (2020a). Also shown are the composition lines of
iron, an Earth-like planet, pure water, and 95% water+5% H-He subjected to an
insolation flux of 20$S_{\oplus}$ (similar to that of TOI-269b). The EOSs used
for the iron core are taken from Hakim et al. (2018), the EOS of the silicate-
mantle is calculated with PERPLE_X from Connolly (2009), and for pure-water
the AQUA EOS from Haldemann et al. (2020) is used.  Figure 14: Ternary diagram
of the inferred internal composition of TOI-269 b in mass (left) and radius
(right).

###  5.2 A significantly eccentric orbit

In our joint fit of photometric and velocimetric data, we derived a non-zero
eccentricity of $0.425^{+0.082}_{-0.086}$, with 99% of the posterior values
between 0.210 and 0.577. As shown on an eccentricity-period diagram with
exoplanets smaller than 10 Earth radii (Fig. 16), TOI-269 b has a remarkable
eccentricity with almost the highest value for planets with periods shorter
than 10 days.

To understand which part of our data constrains the eccentricity most, we
applied different fits and compared their posterior distributions (Fig. 15).
First, we fitted only the photometry using data from TESS, ExTrA, and LCO, and
without a prior on the stellar density. This yielded a broad distribution of
eccentricities showing that, although compatible with zero, the photometry
alone poorly constrains the eccentricity value. Second, we fitted only the
HARPS radial velocities, and we obtained an eccentricity of
$0.25^{+0.13}_{-0.10}$, close to the 2$\sigma$ threshold chosen by Lucy &
Sweeney (1971) to consider an eccentricity value to be significantly different
than zero. As expected, the posterior distribution is also narrower, showing
that radial velocity alone constrains the eccentricity more than the
photometry alone does. Actually, when fitting both photometry and radial-
velocity data together (but still without a prior on the stellar density), we
obtained a similar posterior distribution on eccentricities than that of our
fit with only radial velocity.

In Fig. 15 we also show the posterior distributions for the stellar density
when relevant (i.e., not when fitting RV alone). With posterior values ranging
from 10 to 100 $g/cm^{3}$, we see that the stellar density is poorly
constrained by either photometry alone or both photometry and radial velocity.
Most of these values are actually too high for such an early M dwarf. We also
see that there is a strong correlation between the stellar density and the
eccentricity of the planet. This introduces the importance of the prior on the
stellar density. In Fig. 15, we add the result of our joint fit of both
photometric and velocimetric data including the prior knowledge on the stellar
density (see Section 2). The narrow prior on stellar density selects a
fraction of an otherwise broad $e-\rho_{star}$ posterior density distribution.
At this point we can thus conclude that if some of the eccentricity is already
encoded in the radial-velocity data, most of the constraints eventually come
from the prior on the stellar density.

To lend more credit to this remarkable result, we also modeled the data by
imposing a circular orbit to TOI-269 b. It leads to a stellar density
$>25.8g/cm^{3}$ with a 99% confidence level, which is not compatible with the
radius and mass estimation we provided in Section 2, and therefore also
excludes that the orbit could be circular. As a side note, we also tried to
account for the finite integration time of the observations, in case the too
long integration times would bias the light curve toward lower stellar
densities (Kipping 2010), but it did not change our posterior distribution for
the stellar density.

Granted with a robust non-zero eccentricity, we turn to possible explanations.
Because the star is likely a few billion years old (Section 2), TOI-269 b
probably did not acquire its eccentricity recently. It may have reached its
present orbit with planet-planet migration and acquired a high eccentricity in
the process. We looked at the circularization timescale following Patra et al.
(2017). Determining which tidal quality factor to use for a specific exoplanet
is not simple, so we looked at the problem the other way around. Given the two
ages that we estimated for TOI-269, we would need a tidal quality factor Qp
larger than 1.5x$10^{5}$ and 2.8x$10^{5}$ in order to explain why the
exoplanet is not on a circular orbit yet. This range of values is high
compared to the tidal quality factors calculated for the Solar System planets,
where Qp is around 10-100 for the rocky planets (Goldreich & Soter 1966) and
up to $\sim\leavevmode\nobreak\ 30000$ for Jupiter using the excitation
frequency of Io (Lainey et al. 2009). However, in studies that target
exoplanets (e.g., Hansen 2012) it was shown that Qp can go as high as
$10^{7}-10^{8}$ for exoplanets that orbit close to the host star. The
discrepancy between the values of Qp for Jupiter and for the close-in
exoplanets can be explained by the fact that these planets are likely to be in
synchronous rotation, contrary to Jupiter, which has a fast rotation. A slower
synchronous rotation would make the dissipation via inertial waves less
efficient (e.g., Ogilvie & Lin 2004), and therefore the planets would take
more time to circularize. The observations can give us an upper value for Qp,
in order to explain why the planet is not circularized yet, but we would need
models of the internal structure and tidal dissipation specifically of TOI-269
b to constrain this factor more closely, and helps us give a lower limit on Qp
for example. It is also interesting to note that Correia et al. (2020)
proposed other mechanisms to explain non-null eccentricity of other warm
Neptunes, including excitation from distant planet or atmospheric escape. We
note that the RVs include a possible trend (0.0161$\pm$0.0081 m/s/day), and
therefore a possible hint of an outer companion. Given the $\sim$ 275-day time
span of observations with HARPS, if the possible companion were to have an
orbital period of twice this time span, its mass would be $30\pm 15$
$M_{\oplus}$.

Figure 15: Two-parameter joint posterior distributions for the stellar density
and planet eccentricity for three different analyses (photometry only; joint
radial velocity and photometry; and joint radial velocity and photometry with
a stellar density prior computed from the stellar radius and mass derived in
Section 2). The 39.3% and 86.5% two-variable joint confidence regions are
denoted by a thick and a thin line, respectively. Histograms of the marginal
posterior samples are presented at the top and at the right (for the
eccentricity, the radial velocity-only analysis is also shown). Figure 16:
Orbital eccentricity as a function of the orbital period with the planetary
radius (see color scale at right) from the Exoplanet.eu catalog.

###  5.3 Potential for atmospheric characterization

We calculated the transmission spectroscopic metric (TSM) in the J magnitude
using the equation from Kempton et al. (2018) and obtained a value of TSM =
$75^{+16}_{-12}$. This value takes into account the equilibrium temperature
when the planet is at a distance corresponding to its semi-major axis. For an
eccentric orbit and for transmission spectroscopy it would be more exact to
take into account the planet equilibrium temperature at the exact transit
moment (see details below). By doing so a corrected TSM of $89^{+19}_{-14}$ is
computed. To put this value into context, we also computed the TSM for
exoplanets with ${\rm R_{p}}\leq 5{\rm R_{\oplus}}$ orbiting M dwarf host
stars (${\rm T_{\rm eff}}\leq 3875$ [K]) using the NASA exoplanet archive on
February 16, 2021. The TSM values are shown relatively to the TOI-269 b value
in Fig.17. TOI-269 b lies among the best targets of its category (sub-Neptunes
around M dwarfs). So far, the atmospheric characterization of sub-Neptune
planets mostly delivered non-detections (e.g., on the warm GJ 1214 b by
Kreidberg et al. 2014), and the few detections obtained did not bring
conclusive results on their actual atmospheric contents. For example, the more
temperate K2-18 b (Cloutier et al. 2017) exhibits a near-infrared absorption
in its transmission spectrum first interpreted as due to water (Benneke et al.
2019, Tsiaras et al. 2019), but Bézard et al. (2020) argued that methane could
be responsible for this feature. Thus, it would be very interesting to probe
with transmission spectroscopy the atmospheres of newly discovered temperate
and warm sub-Neptunes such as TOI-269 b, TOI-270 c or d (Günther et al. 2019,
Van Eylen et al. 2021), or LTT 3780 c (Cloutier et al. 2020, Nowak et al.
2020) in order to see if they exhibit atmospheric features and if so, what
their natures are. Finally, detecting any atmospheric features could help in
constraining the extent and the mean molecular weight of the atmosphere, and
give some constraints on possible interior structures (see Section 5.1).

Interestingly, the orbit of TOI-269 b is found to be significantly eccentric.
The change in stellar irradiation due to the eccentricity throughout the
orbital revolution brings a change in equilibrium temperature by a factor of
$\sqrt{\frac{1+e}{1-e}}\sim 1.6\pm 0.1$. Thus, the planet temperature passes
from $\sim 400$ K near aphelion to $\sim 630$ K near perihelion. Depending of
the actual atmospheric conditions, some species such as sulfuric acid may
condense and vaporize throughout an orbital revolution, but details of such
phenomena are beyond the scope of this paper. We also note that the primary
transit happens $\sim 1.5$h after perihelion (at $\sim 1.02$ times the
perihelion radius), when the planet is the hottest. This means that TOI-269 b
is a slightly better target for transmission spectroscopy than by only
considering the semi-major axis or the orbital average equilibrium temperature
(see Fig.17).

Moreover, the currently found high eccentricity could hint that the planet may
have recently arrived in its position. As the host star is an M dwarf with a
convective envelope, strong tidal interactions are supposed to circularize the
planetary orbit rapidly (Correia et al. 2020). If the planet migrated recently
(e.g., due to a Lidov-Kozai mechanism), it is possible that strong to moderate
atmospheric escape also started recently and would be still in process
(Bourrier et al. 2018a). Such a scenario is supported by the observation of
atmospheric evaporation in the Neptune-sized planets GJ 436 b (Ehrenreich et
al. 2015), GJ 3470 b (Bourrier et al. 2018b, Palle et al. 2020), and HAT-P-11
b (Allart et al. 2018), which all possess eccentric orbits. Observing
evaporation in an eccentric sub-Neptune would be very informative on the
architecture and history of the system. For example, this is possible by
detecting the meta-stable helium infrared triplet at 1 083 nm (Oklopčić &
Hirata 2018, Spake et al. 2018) at high resolution (Allart et al. 2018,
Nortmann et al. 2018). Even though no helium detection has been reported to
date for sub-Neptune planets (Kasper et al. 2020, Gaidos et al. 2020a, b),
TOI-269 b could have a helium signal of 0.5–1.5% ($\gtrsim$50–150 scale-
height, depending on the atmospheric escape rate, thermospheric temperature,
and stellar high-energy irradiation; Nortmann et al. 2018; Kasper et al. 2020)
that could be detected with several transit observations with a high-
resolution infrared spectrograph such as NIRPS (Bouchy et al. 2017).

Figure 17: Transmission spectroscopic metric in the $J$ magnitude as a
function of the planetary equilibrium temperature. The TSM values are shown
relatively to the TOI-269 b (eccentricity-corrected) reference value of
$89^{+19}_{-14}$. Only planets orbiting M dwarf (${\rm T_{\rm eff}}\leq 3875$
[K]) and with ${\rm R_{p}}\leq 5{\rm R_{\oplus}}$ were selected. TOI-269 b is
shown as a black circle. The black arrow shows the range of equilibrium
temperature depending on planet position during the orbit. The crosses show
the locations of the orbital average, the semi-major axis, and the primary
transit. Other planets with and without measured masses are shown in dark gray
and light gray, respectively.

##  6 Conclusions

We presented the discovery and characterization of a sub-Neptune transiting
the M dwarf TOI-269. The planet was detected by the TESS mission, then
confirmed via ground-based transit follow-up observations with multiple
instruments and from precise RV measurements with HARPS by measuring its mass.
TOI-269 b contributes to the TESS Level One Science Requirement of delivering
50 transiting small planets (with radii smaller than $4R_{e}$) with measured
masses to the community. It will be re-observed in five sectors during the
TESS year-3 extended mission from Sept 2020 to April 2021, which will provide
new timing to perform a better TTV analysis.

The estimated average density of TOI-269 b is $2.28^{+0.48}_{-0.42}g/cm^{3}$,
which is significantly lower than the typical density of rock planets and
indicates the presence of a volatile envelope. Internal structure models with
four layers (an iron core, silicate mantle, water ocean, and H-He atmosphere),
although strongly degenerated, suggest that TOI-269 b has between 0.4% and 4%
H-He by mass. Our analysis suggests that TOI-269 b would be an interesting
target for atmospheric characterization in order to compare it with other sub-
Neptunes.

The ExTrA observations of this target allowed us to test the precision of our
instrument. Early M dwarfs with many TESS transits are not the primary targets
for ExTrA. It will be more competitive around late stars with one or a few
TESS transits in order to obtain a better precision for the planetary radius
and for the transit timings. As for measuring radii, we were able to show here
that the precision of one transit with ExTrA is comparable to that of five
transits with TESS (see Fig. 11). ExTrA could also detect other planets in
already-known planetary systems.

With such a high eccentricity, TOI-269 b is reminiscent of GJ 436 b (Bourrier
et al. 2018b) and follow-up observations similar to those conducted for this
planet would thus provide an instructive comparison. TOI-269 b is probably too
far away to detect an atmospheric escape in Ly-$\alpha$ (Ehrenreich et al.
2015), but could be attempted with transmission spectroscopy of the helium
triplet (Sect. 5.3). In addition, further RV monitoring will be valuable and,
actually, already anticipated with the forthcoming near-infrared spectrograph
NIRPS (Bouchy et al. 2017). They may detect the companion responsible for the
possible RV trend that we have identified in this paper, and will also measure
the Rossiter-McLaughlin anomaly to see if, like GJ 436 b, TOI-269 b also has a
misaligned orbit (Bourrier et al. 2018b).

###### Acknowledgements.

We are grateful to the ESO/La Silla staff for their continuous support. We
thank the referee for his careful reading of the manuscript and his thoughtful
comments. We acknowledge funding from the European Research Council under the
ERC Grant Agreement n. 337591-ExTrA. This paper includes data collected by the
TESS mission. Funding for the TESS mission is provided by the NASA Explorer
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. 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 makes use of observations from the LCOGT network. This work made use
of tpfplotter by J. Lillo-Box (publicly available in
www.github.com/jlillo/tpfplotter), which also made use of the python packages
astropy, lightkurve, matplotlib and numpy. We thank the Swiss National Science
Foundation (SNSF) and the Geneva University for their continuous support to
our planet search programs. This work has been in particular carried out in
the frame of the National Centre for Competence in Research ‘PlanetS’
supported by the Swiss National Science Foundation (SNSF). We thank La Silla
observatory staff for their support. N.A-D. acknowledges the support of
FONDECYT project 3180063. A.W. acknowledges the financial support of the SNSF
by grant number P400P2_186765. This material is based upon work supported by
the National Science Foundation Graduate Research Fellowship Program under
Grant No. DGE-1650115. This work was supported by FCT - Fundação para a
Ciência e a Tecnologia through national funds and by FEDER through COMPETE2020
- Programa Operacional Competitividade e Internacionalização 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. Based in part on observations obtained at the
Southern Astrophysical Research (SOAR) telescope, which is a joint project of
the Ministério da Ciência, Tecnologia e Inovações (MCTI/LNA) do Brasil, the US
National Science Foundation’s NOIRLab, the University of North Carolina at
Chapel Hill (UNC), and Michigan State University (MSU). FPE would like to
acknowledge the Swiss National Science Foundation (SNSF) for supporting
research with HARPS through the SNSF grants nr. 140649, 152721, 166227 and
184618. J.R.M acknowledges continuous grants from CNPq, CAPES and FAPERN
brazilian agencies. C.D. acknowledges support from the Swiss National Science
Foundation under grant PZ00P2_174028. This work is supported 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 Univ. Grenoble-Alpes. B.L.C.M and I.C.L. acknowledge continuous grants
from CNPq, CAPES and FAPERN brazilian agencies. We thank Emeline Bolmont for
interesting discussion about tidal dissipation.

## References

  * Alibert et al. (2010) Alibert, Y., Mordasini, C., Benz, W., & Naef, D. 2010, in EAS Publications Series, Vol. 42, EAS Publications Series, ed. K. Gożdziewski, A. Niedzielski, & J. Schneider, 209–225
  * Allard et al. (2012) Allard, F., Homeier, D., & Freytag, B. 2012, Philosophical Transactions of the Royal Society of London Series A, 370, 2765
  * Allart et al. (2018) Allart, R., Bourrier, V., Lovis, C., et al. 2018, Science, 362, 1384
  * Aller et al. (2020) Aller, A., Lillo-Box, J., Jones, D., Miranda, L. F., & Barceló Forteza, S. 2020, A&A, 635, A128
  * Ambikasaran et al. (2015) Ambikasaran, S., Foreman-Mackey, D., Greengard, L., Hogg, D. W., & O’Neil, M. 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence, 38, 252
  * Astudillo-Defru et al. (2017a) Astudillo-Defru, N., Delfosse, X., Bonfils, X., et al. 2017a, A&A, 600, A13
  * Astudillo-Defru et al. (2017b) Astudillo-Defru, N., Forveille, T., Bonfils, X., et al. 2017b, A&A, 602, A88
  * Bailer-Jones et al. (2018) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Mantelet, G., & Andrae, R. 2018, AJ, 156, 58
  * Barnes (2010) Barnes, S. A. 2010, ApJ, 722, 222
  * Barnes & Kim (2010) Barnes, S. A. & Kim, Y.-C. 2010, ApJ, 721, 675
  * Batalha et al. (2018) Batalha, N. E., Lewis, N. K., Line, M. R., Valenti, J., & Stevenson, K. 2018, ApJ, 856, L34
  * Benneke et al. (2019) Benneke, B., Wong, I., Piaulet, C., et al. 2019, ApJ, 887, L14
  * Bézard et al. (2020) Bézard, B., Charnay, B., & Blain, D. 2020, arXiv e-prints, arXiv:2011.10424
  * Bonfils et al. (2015) Bonfils, X., Almenara, J. M., Jocou, L., et al. 2015, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9605, Techniques and Instrumentation for Detection of Exoplanets VII, 96051L
  * Bouchy et al. (2017) Bouchy, F., Doyon, R., Artigau, É., et al. 2017, The Messenger, 169, 21
  * Bourrier et al. (2018a) Bourrier, V., Lecavelier des Etangs, A., Ehrenreich, D., et al. 2018a, A&A, 620, A147
  * Bourrier et al. (2018b) Bourrier, V., Lovis, C., Beust, H., et al. 2018b, Nature, 553, 477
  * Brown et al. (2013) Brown, T. M., Baliber, N., Bianco, F. B., et al. 2013, Publications of the Astronomical Society of the Pacific, 125, 1031
  * Brugger et al. (2017) Brugger, B., Mousis, O., Deleuil, M., & Deschamps, F. 2017, ApJ, 850, 93
  * Buchner et al. (2014) Buchner, J., Georgakakis, A., Nandra, K., et al. 2014, A&A, 564, A125
  * Buchschacher & Alesina (2019) Buchschacher, N. & Alesina, F. 2019, in Astronomical Society of the Pacific Conference Series, Vol. 521, Astronomical Data Analysis Software and Systems XXVI, ed. M. Molinaro, K. Shortridge, & F. Pasian, 757
  * Canto Martins et al. (2020) Canto Martins, B. L., Gomes, R. L., Messias, Y. S., et al. 2020, ApJS, 250, 20
  * Chabrier et al. (2019) Chabrier, G., Mazevet, S., & Soubiran, F. 2019, ApJ, 872, 51
  * Charbonneau et al. (2009) Charbonneau, D., Berta, Z. K., Irwin, J., et al. 2009, Nature, 462, 891
  * Chen et al. (2014) Chen, Y., Girardi, L., Bressan, A., et al. 2014, MNRAS, 444, 2525
  * Cloutier et al. (2017) Cloutier, R., Astudillo-Defru, N., Doyon, R., et al. 2017, A&A, 608, A35
  * Cloutier et al. (2020) Cloutier, R., Eastman, J. D., Rodriguez, J. E., et al. 2020, AJ, 160, 3
  * Cloutier & Menou (2020) Cloutier, R. & Menou, K. 2020, AJ, 159, 211
  * Collins et al. (2017) Collins, K. A., Kielkopf, J. F., Stassun, K. G., & Hessman, F. V. 2017, AJ, 153, 77
  * Connolly (2009) Connolly, J. A. D. 2009, Geochemistry, Geophysics, Geosystems, 10, Q10014
  * Correia et al. (2020) Correia, A. C. M., Bourrier, V., & Delisle, J. B. 2020, arXiv e-prints, arXiv:2005.02700
  * Cutri & et al. (2013) Cutri, R. M. & et al. 2013, VizieR Online Data Catalog, II/328
  * Cutri et al. (2003) Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, VizieR Online Data Catalog, II/246
  * Díaz et al. (2014) Díaz, R. F., Almenara, J. M., Santerne, A., et al. 2014, MNRAS, 441, 983
  * Dorn et al. (2015) Dorn, C., Khan, A., Heng, K., et al. 2015, A&A, 577, A83
  * Dorn et al. (2017a) Dorn, C., Venturini, J., Khan, A., et al. 2017a, A&A, 597, A37
  * Dorn et al. (2017b) Dorn, C., Venturini, J., Khan, A., et al. 2017b, A&A, 597, A37
  * Dotter et al. (2008) Dotter, A., Chaboyer, B., Jevremović, D., et al. 2008, ApJS, 178, 89
  * Ehrenreich et al. (2015) Ehrenreich, D., Bourrier, V., Wheatley, P. J., et al. 2015, Nature, 522, 459
  * Engle & Guinan (2011) Engle, S. G. & Guinan, E. F. 2011, in Astronomical Society of the Pacific Conference Series, Vol. 451, 9th Pacific Rim Conference on Stellar Astrophysics, ed. S. Qain, K. Leung, L. Zhu, & S. Kwok, 285
  * Espinoza (2018) Espinoza, N. 2018, Research Notes of the American Astronomical Society, 2, 209
  * Espinoza & Jordán (2015) Espinoza, N. & Jordán, A. 2015, MNRAS, 450, 1879
  * Espinoza et al. (2019) Espinoza, N., Kossakowski, D., & Brahm, R. 2019, MNRAS, 490, 2262
  * Evans et al. (2018) Evans, D. W., Riello, M., De Angeli, F., et al. 2018, A&A, 616, A4
  * Feroz et al. (2009) Feroz, F., Hobson, M. P., & Bridges, M. 2009, MNRAS, 398, 1601
  * Foreman-Mackey (2016) Foreman-Mackey, D. 2016, The Journal of Open Source Software, 1, 24
  * Foreman-Mackey et al. (2017) Foreman-Mackey, D., Agol, E., Ambikasaran, S., & Angus, R. 2017, AJ, 154, 220
  * Fulton et al. (2018) Fulton, B. J., Petigura, E. A., Blunt, S., & Sinukoff, E. 2018, PASP, 130, 044504
  * Fulton et al. (2017) Fulton, B. J., Petigura, E. A., Howard, A. W., et al. 2017, AJ, 154, 109
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1
  * Gaidos et al. (2020a) Gaidos, E., Hirano, T., Mann, A. W., et al. 2020a, MNRAS, 495, 650
  * Gaidos et al. (2020b) Gaidos, E., Hirano, T., Wilson, D. J., et al. 2020b, MNRAS, 498, L119
  * Goldreich & Soter (1966) Goldreich, P. & Soter, S. 1966, Icarus, 5, 375
  * Guillot (2010) Guillot, T. 2010, A&A, 520, A27
  * Günther et al. (2019) Günther, M. N., Pozuelos, F. J., Dittmann, J. A., et al. 2019, Nature Astronomy, 3, 1099
  * Hakim et al. (2018) Hakim, K., Rivoldini, A., Van Hoolst, T., et al. 2018, Icarus, 313, 61
  * Haldemann et al. (2020) Haldemann, J., Alibert, Y., Mordasini, C., & Benz, W. 2020, arXiv e-prints, arXiv:2009.10098
  * Hansen (2012) Hansen, B. M. S. 2012, ApJ, 757, 6
  * Hardegree-Ullman et al. (2020) Hardegree-Ullman, K. K., Zink, J. K., Christiansen, J. L., et al. 2020, ApJS, 247, 28
  * Harpsøe et al. (2013) Harpsøe, K. B. W., Hardis, S., Hinse, T. C., et al. 2013, A&A, 549, A10
  * Jenkins (2002) Jenkins, J. M. 2002, ApJ, 575, 493
  * Jenkins et al. (2010) Jenkins, J. M., Chandrasekaran, H., McCauliff, S. D., et al. 2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7740, Software and Cyberinfrastructure for Astronomy, ed. N. M. Radziwill & A. Bridger, 77400D
  * Jenkins et al. (2020) Jenkins, J. M., Tenenbaum, P., Seader, S., et al. 2020, Kepler Data Processing Handbook: Transiting Planet Search, Kepler Data Processing Handbook (KSCI-19081-003)
  * Jenkins et al. (2016) Jenkins, J. M., Twicken, J. D., McCauliff, S., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9913, Software and Cyberinfrastructure for Astronomy IV, 99133E
  * Jensen (2013) Jensen, E. 2013, Tapir: A web interface for transit/eclipse observability, Astrophysics Source Code Library
  * Kasper et al. (2020) Kasper, D., Bean, J. L., Oklopčić, A., et al. 2020, AJ, 160, 258
  * Kempton et al. (2018) Kempton, E. M. R., Bean, J. L., Louie, D. R., et al. 2018, PASP, 130, 114401
  * Kipping (2010) Kipping, D. M. 2010, MNRAS, 408, 1758
  * Kipping (2013) Kipping, D. M. 2013, MNRAS, 435, 2152
  * Kreidberg (2015) Kreidberg, L. 2015, PASP, 127, 1161
  * Kreidberg et al. (2014) Kreidberg, L., Bean, J. L., Désert, J.-M., et al. 2014, Nature, 505, 69
  * Lainey et al. (2009) Lainey, V., Arlot, J.-E., Karatekin, Ö., & van Hoolst, T. 2009, Nature, 459, 957
  * Li et al. (2019) Li, J., Tenenbaum, P., Twicken, J. D., et al. 2019, PASP, 131, 024506
  * Lindegren et al. (2018) Lindegren, L., Hernández, J., Bombrun, A., et al. 2018, A&A, 616, A2
  * Lopez & Fortney (2014) Lopez, E. D. & Fortney, J. J. 2014, ApJ, 792, 1
  * Lozovsky et al. (2018) Lozovsky, M., Helled, R., Dorn, C., & Venturini, J. 2018, ApJ, 866, 49
  * Lucy & Sweeney (1971) Lucy, L. B. & Sweeney, M. A. 1971, AJ, 76, 544
  * Luque et al. (2019) Luque, R., Pallé, E., Kossakowski, D., et al. 2019, A&A, 628, A39
  * Maíz Apellániz & Weiler (2018) Maíz Apellániz, J. & Weiler, M. 2018, A&A, 619, A180
  * Mann et al. (2019) Mann, A. W., Dupuy, T., Kraus, A. L., et al. 2019, ApJ, 871, 63
  * Mann et al. (2015) Mann, A. W., Feiden, G. A., Gaidos, E., Boyajian, T., & von Braun, K. 2015, ApJ, 804, 64
  * Maxted et al. (2011) Maxted, P. F. L., Anderson, D. R., Collier Cameron, A., et al. 2011, PASP, 123, 547
  * Mayo et al. (2018) Mayo, A. W., Vanderburg, A., Latham, D. W., et al. 2018, AJ, 155, 136
  * Mayor et al. (2003) Mayor, M., Pepe, F., Queloz, D., et al. 2003, The Messenger, 114, 20
  * McCully et al. (2018) McCully, C., Volgenau, N. H., Harbeck, D.-R., et al. 2018, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 10707, Proc. SPIE, 107070K
  * Meibom et al. (2015) Meibom, S., Barnes, S. A., Platais, I., et al. 2015, Nature, 517, 589
  * More et al. (1988) More, R. M., Warren, K. H., Young, D. A., & Zimmerman, G. B. 1988, Physics of Fluids, 31, 3059
  * Nortmann et al. (2018) Nortmann, L., Pallé, E., Salz, M., et al. 2018, Science, 362, 1388
  * Nowak et al. (2020) Nowak, G., Luque, R., Parviainen, H., et al. 2020, A&A, 642, A173
  * Ogilvie & Lin (2004) Ogilvie, G. I. & Lin, D. N. C. 2004, ApJ, 610, 477
  * Oklopčić & Hirata (2018) Oklopčić, A. & Hirata, C. M. 2018, ApJ, 855, L11
  * Otegi et al. (2020a) Otegi, J. F., Bouchy, F., & Helled, R. 2020a, A&A, 634, A43
  * Otegi et al. (2020b) Otegi, J. F., Dorn, C., Helled, R., et al. 2020b, A&A, 640, A135
  * Palle et al. (2020) Palle, E., Nortmann, L., Casasayas-Barris, N., et al. 2020, A&A, 638, A61
  * Patra et al. (2017) Patra, K. C., Winn, J. N., Holman, M. J., et al. 2017, AJ, 154, 4
  * Pecaut & Mamajek (2013) Pecaut, M. J. & Mamajek, E. E. 2013, ApJS, 208, 9
  * Plotnykov & Valencia (2020) Plotnykov, M. & Valencia, D. 2020, MNRAS, 499, 932
  * Pollacco et al. (2006) Pollacco, D. L., Skillen, I., Collier Cameron, A., et al. 2006, PASP, 118, 1407
  * Ricker et al. (2015) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, Journal of Astronomical Telescopes, Instruments, and Systems, 1, 014003
  * Rogers & Seager (2010) Rogers, L. A. & Seager, S. 2010, ApJ, 716, 1208
  * Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163
  * Smith et al. (2012) Smith, J. C., Stumpe, M. C., Van Cleve, J. E., et al. 2012, PASP, 124, 1000
  * Spake et al. (2018) Spake, J. J., Sing, D. K., Evans, T. M., et al. 2018, Nature, 557, 68
  * Speagle (2020) Speagle, J. S. 2020, MNRAS, 493, 3132
  * Stassun et al. (2019) Stassun, K. G., Oelkers, R. J., Paegert, M., et al. 2019, AJ, 158, 138
  * Stixrude & Lithgow-Bertelloni (2011) Stixrude, L. & Lithgow-Bertelloni, C. 2011, Geophysical Journal International, 184, 1180
  * Stumpe et al. (2014) Stumpe, M. C., Smith, J. C., Catanzarite, J. H., et al. 2014, PASP, 126, 100
  * Stumpe et al. (2012) Stumpe, M. C., Smith, J. C., Van Cleve, J. E., et al. 2012, PASP, 124, 985
  * Tokovinin (2018) Tokovinin, A. 2018, PASP, 130, 035002
  * Tsiaras et al. (2019) Tsiaras, A., Waldmann, I. P., Tinetti, G., Tennyson, J., & Yurchenko, S. N. 2019, Nature Astronomy, 3, 1086
  * Twicken et al. (2018) Twicken, J. D., Catanzarite, J. H., Clarke, B. D., et al. 2018, PASP, 130, 064502
  * Van Eylen et al. (2021) Van Eylen, V., Astudillo-Defru, N., Bonfils, X., et al. 2021, arXiv e-prints, arXiv:2101.01593
  * Venturini & Helled (2017) Venturini, J. & Helled, R. 2017, ApJ, 848, 95
  * Winters et al. (2019) Winters, J. G., Medina, A. A., Irwin, J. M., et al. 2019, AJ, 158, 152
  * Wright et al. (2010a) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010a, AJ, 140, 1868
  * Wright et al. (2010b) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010b, AJ, 140, 1868
  * Yee et al. (2017) Yee, S. W., Petigura, E. A., & von Braun, K. 2017, The Astrophysical Journal, 836, 77
  * Ziegler et al. (2020) Ziegler, C., Tokovinin, A., Briceno, C., et al. 2020, VizieR Online Data Catalog, J/AJ/159/19

##  Appendix A ExTrA field of view of TOI-269

Figure 18: Snapshot of the software for preparing observations for ExTrA. The
field of view of one telescope has a diameter of 1o (gray circle). Each of the
five field units (FUs) can be positioned in the part of the focal plane shown
with a rectangle of corresponding color. In this figure the field of TOI-269
is shown. Each FU is placed over a particular comparison star (green stars) or
the target (red star). On the left the location of each FU is magnified and
the fiber apertures are drawn to scale (colored circles; the first circle is
4”, the second circle is 8”). This is used to check if other stars appear near
the fibers. In red is the J magnitude of the star, in gray the Gaia magnitude.
The guiding star is located at the center and a magnified image is shown on
the right. The five arms correspond to the selected stars with their 2MASS J
magnitude and Gaia DR2 temperature indicated at the top right of the figure.

##  Appendix B Prior and posterior values for the different fits

Table 3: Prior and posterior values for the photometry fit of TESS data. The posterior estimate corresponds to the median value. Error bars denote the 68% posterior credibility intervals. Parameter Name | Prior | Posterior | Description
---|---|---|---
Parameters for TOI-269 b |  |  |
$P_{b}$ (days) | $\mathcal{N}(3.7,0.1^{2})$ | $3.697722^{+0.000017}_{-0.000016}$ | Period of the planet
$t_{0}$ (BJD TDB) | $\mathcal{N}(2458381.84,0.1^{2})$ | $245831.84601^{+0.00058}_{-0.00058}$ | Time of transit-center for the planet
$\rho_{\star}$ ($g/cm^{3}$) | $\mathcal{N}(8.760,0.870)$ | $9.10^{+0.82}_{-0.74}$ | Stellar density
$r_{1,b}$ |  $\mathcal{U}(0,1)$+ | $0.8983^{+0.0091}_{-0.0099}$ | Parametrization for p and b
$r_{2,b}$ | $\mathcal{U}(0,1)$ | $0.0725^{+0.0024}_{-0.0021}$ | Parametrization for p and b
$e_{b}$ | 0. | 0. | Eccentricity
$\omega_{b}$ (degrees) | 90. | 90. | Argument of periastron
Parameters for TESS |  |  |
$D_{TESS}$ | 1. | 1. | Dilution factor for TESS
$M_{TESS}$ | $\mathcal{N}(0,0.1^{2})$ | $-0.000015^{+0.000016}_{-0.000016}$ | Relative flux offset for TESS
$\sigma_{w,TESS}$ (ppm) | log$\mathcal{U}(0.01,100)$ | $0.58^{+8.1}_{-0.55}$ | Extra jitter term for TESS lightcurve
$q_{1,TESS}$ | $\mathcal{U}(0,1)$ | $0.128^{+0.22}_{-0.099}$ | Quadratic limb-darkening parametrization
$q_{2,TESS}$ | $\mathcal{U}(0,1)$ | $0.42^{+0.34}_{-0.28}$ | Quadratic limb-darkening parametrization
Table 4: Prior and posterior values for the RVs fit of the HARPS measurements. The posterior estimate corresponds to the median value. Error bars denote the 68% posterior credibility intervals. Parameter Name | Prior | Posterior | Description
---|---|---|---
Parameters for TOI-269 b |  |  |
$P_{b}$ (days) | $\mathcal{N}(3.697722,0.000017^{2})$ | $3.697723^{+0.000018}_{-0.000017}$ | Period of the planet
$t_{0}$ (BJD TDB) | $\mathcal{U}(2458381.84601,0.00058)$ | $3.697722^{+0.000017}_{-0.000016}$ | Time of transit-center for the planet
$K_{b}$ (m/s) | $\mathcal{U}(0,20)$ | $7.2^{+1.3}_{-1.2}$ | Radial-velocity semi-amplitude of the planet
$S_{1,b}=\sqrt{e_{b}}sin(\omega_{b})$ | $\mathcal{U}(-1,1)$ | $0.34^{+0.21}_{-0.30}$ | Parametrization for $e$ and $\omega$
$S_{2,b}=\sqrt{e_{b}}cos(\omega_{b})$ | $\mathcal{U}(-1,1)$ | $0.30^{+0.13}_{-0.20}$ | Parametrization for $e$ and $\omega$
RV parameters for HARPS |  |  |
$\sigma_{w,HARPS}$ (km/s) | log$\mathcal{U}(10^{-4},10^{-2})$ | $0.00039^{+0.00078}_{-0.00024}$ | Extra jitter term for HARPS
RV slope (km/s/days) | $\mathcal{U}(-1.,1.)$ | $\left(1.81^{+0.86}_{-0.89}\right){\times 10^{-5}}$ | Linear trend : first parameter
RV intercept (systemic velocity in km/s) | $\mathcal{U}(37.18,37.28)$ | $37.22861^{+0.00092}_{-0.00077}$ | Linear trend : second parameter
Table 5: Prior Values for the joint fit of TESS, ExTrA, LCO, and HARPS Parameter Name | Prior | Description
---|---|---
Parameters for TOI-269 b |  |
$P_{b}$ (days) | $\mathcal{U}(3.69769,3.69773)$ | Period of the planet
$t_{0}$ (BJD TDB) | $\mathcal{U}(2458381.845,2458381.849)$ | Time of transit-center for the planet
$\rho_{\star}$ $g/cm^{3}$ | $\mathcal{N}(8.760,0.870)$ | Stellar density
$r_{1,b}$ | $\mathcal{U}(0.3,1)$ | Parametrization for p and b
$r_{2,b}$ | $\mathcal{U}(0,0.1)$ | Parametrization for p and b
$S_{1,b}=\sqrt{e_{b}}sin(\omega_{b})$ | $\mathcal{U}(-1,1)$ | Parametrization for $e$ and $\omega$
$S_{2,b}=\sqrt{e_{b}}cos(\omega_{b})$ | $\mathcal{U}(-1,1)$ | Parametrization for $e$ and $\omega$
$K_{b}$ (km/s) | $\mathcal{U}(0,0.016)$ | Radial-velocity semi-amplitude of the planet
Parameters for TESS photometry |  |
$D_{TESS}$ | 1.0 | Dilution factor for TESS
$M_{TESS}$ | $\mathcal{N}(0,0.1^{2})$ | Relative flux offset for TESS
$\sigma_{w,TESS}$ (ppm) | log$\mathcal{U}(1,100)$ | Extra jitter term for TESS lightcurve
$q_{1,TESS}$ | $\mathcal{U}(0,1)$ | Quadratic limb-darkening parametrization
$q_{2,TESS}$ | $\mathcal{U}(0,1)$ | Quadratic limb-darkening parametrization
Parameters for LCO-CTIO photometry |  |
$D_{LCO}$ | 1.0 | Dilution factor for LCO-CTIO
$M_{LCO}$ | $\mathcal{N}(0,0.1^{2})$ | Relative flux offset for LCO-CTIO
$\sigma_{w,LCO}$ (ppm) | log$\mathcal{U}(1,2000)$ | Extra jitter term for LCO-CTIO lightcurve
$q_{1,LCO}$ | $\mathcal{U}(0,1)$ | Quadratic limb-darkening parametrization
$q_{2,LCO}$ | $\mathcal{U}(0,1)$ | Quadratic limb-darkening parametrization
Parameters of the GP |  |
$\sigma_{GP,LCO}$ (relative flux) | log$\mathcal{U}(10^{-6},1)$ | Amplitude of the GP
$\rho_{GP,LCO}$ (days) | log$\mathcal{U}(10^{-3},10)$ | Time-scale of the Matern kernel
Parameters for ExTrA photometry |  |
$D_{ExTrA}$ | 1.0 | Dilution factor for ExTrA
$M_{ExTrA}$ | $\mathcal{N}(0,0.1^{2})$ | Relative flux offset for each ExTrA light curve
$\sigma_{w,ExTrA}$ (ppm) | log$\mathcal{U}(1,1000)$ | Extra jitter term for each ExTrA light curve
$q_{1,ExTrA}$ | $\mathcal{U}(0,1)$ | Quadratic limb-darkening parametrization
$q_{2,ExTrA}$ | $\mathcal{U}(0,1)$ | Quadratic limb-darkening parametrization
Parameters of the GP for each ExTrA light curve (one for each night and each telescope) |  |
$\sigma_{GP,ExTrA}$ (relative flux) | log$\mathcal{U}(10^{-6},1)$ | Amplitude of the GP
$\rho_{GP,ExTrA}$ (days) | log$\mathcal{U}(10^{-3},10)$ | Time-scale of the Matern kernel
RV parameters for HARPS |  |
$\sigma_{w,HARPS}$ (km/s) | log$\mathcal{U}(10^{-4},10^{-2})$ | Extra jitter term for HARPS
RV slope (km/s/days) | $\mathcal{U}(-10^{-4},10^{-4})$ | Linear trend : first parameter
RV intercept (systemic velocity) (km/s) | $\mathcal{U}(37.22,37.24)$ | Linear trend : second parameter
Table 6: Posterior parameters for the different instruments used in the juliet analysis for TOI-269 b. The posterior estimate corresponds to the median value. Error bars denote the 68% posterior credibility intervals. Parameter name | Posterior estimate | Description
---|---|---
Posterior parameters for TESS photometry |  |
$M_{TESS}$ (ppm) | $0.00033^{+0.00012}_{-0.00012}$ | Relative flux offset
$\sigma_{w,TESS}$ (ppm) | $9.6^{+34}_{-7.4}$ | Extra jitter term
Posterior parameters for LCO-CTIO photometry |  |
$M_{LCO}$ (ppm) | $0.0009^{+0.0022}_{-0.0020}$ | Relative flux offset
$\sigma_{w,LCO}$ (ppm) | $890^{+120}_{-120}$ | Extra jitter term
Parameters of the GP |  |
$\sigma_{GP,LCO}$ (relative flux) | $0.0030^{+0.0044}_{-0.0014}$ | Amplitude of the GP
$\rho_{GP,LCO}$ (days) | $0.094^{+0.14}_{-0.051}$ | Time-scale of the Matern kernel
RV parameters for HARPS |  |
$\sigma_{w,HARPS}$ (m/s) | $0.39^{+0.68}_{-0.24}$ | Extra jitter term
Posterior parameters for ExTrA photometry |  |
Posterior parameters for night 1 of observations |  |
Telescope 2 |  |
$M_{ExTrA}$ (ppm) | $0.00005^{+0.050}_{-0.038}$ | Relative flux offset
$\sigma_{w,ExTrA}$ (ppm) | $22^{+160}_{-19}$ | Extra jitter term
$\sigma_{GP,ExTrA}$ (relative flux) | $0.059^{+0.095}_{-0.031}$ | Amplitude of the GP
$\rho_{GP,ExTrA}$ (days) | $0.23^{+0.23}_{-0.10}$ | Time-scale of the Matern kernel
Telescope 3 |  |
$M_{ExTrA}$ (ppm) | $-0.005^{+0.013}_{-0.025}$ | Relative flux offset
$\sigma_{w,ExTrA}$ (ppm) | $27^{+210}_{-24}$ | Extra jitter term
$\sigma_{GP,ExTrA}$ (relative flux) | $0.019^{+0.052}_{-0.013}$ | Amplitude of the GP
$\rho_{GP,ExTrA}$ (days) | $0.37^{+0.76}_{-0.25}$ | Time-scale of the Matern kernel
Posterior parameters for night 2 of observations |  |
Telescope 2 |  |
$M_{ExTrA}$ (ppm) | $0.0010^{+0.018}_{-0.012}$ | Relative flux offset
$\sigma_{w,ExTrA}$ (ppm) | $34^{+290}_{-31}$ | Extra jitter term
$\sigma_{GP,ExTrA}$ (relative flux) | $0.0163^{+0.028}_{-0.0079}$ | Amplitude of the GP
$\rho_{GP,ExTrA}$ (days) | $0.124^{+0.13}_{-0.052}$ | Time-scale of the Matern kernel
Telescope 3 |  |
$M_{ExTrA}$ (ppm) | $-0.0008^{+0.0023}_{-0.0017}$ | Relative flux offset
$\sigma_{w,ExTrA}$ (ppm) | $29^{+240}_{-26}$ | Extra jitter term
$\sigma_{GP,ExTrA}$ (relative flux) | $0.00232^{+0.0075}_{-0.00096}$ | Amplitude of the GP
$\rho_{GP,ExTrA}$ (days) | $0.035^{+0.13}_{-0.021}$ | Time-scale of the Matern kernel
Posterior parameters for night 3 of observations |  |
Telescope 1 |  |
$M_{ExTrA}$ (ppm) | $-0.00077^{+0.00036}_{-0.00032}$ | Relative flux offset
$\sigma_{w,ExTrA}$ (ppm) | $26^{+210}_{-23}$ | Extra jitter term
$\sigma_{GP,ExTrA}$ (relative flux) | $0.00067^{+0.00061}_{-0.00061}$ | Amplitude of the GP
$\rho_{GP,ExTrA}$ (days) | $0.016^{+0.42}_{-0.012}$ | Time-scale of the Matern kernel
Telescope 2 |  |
$M_{ExTrA}$ (ppm) | $-0.016^{+0.041}_{-0.039}$ | Relative flux offset
$\sigma_{w,ExTrA}$ (ppm) | $30^{+260}_{-27}$ | Extra jitter term
$\sigma_{GP,ExTrA}$ (relative flux) | $0.055^{+0.11}_{-0.034}$ | Amplitude of the GP
$\rho_{GP,ExTrA}$ (days) | $0.33^{+0.41}_{-0.17}$ | Time-scale of the Matern kernel
Telescope 3 |  |
$M_{ExTrA}$ (ppm) | $0.0053^{+0.018}_{-0.0098}$ | Relative flux offset
$\sigma_{w,ExTrA}$ (ppm) | $27^{+220}_{-24}$ | Extra jitter term
$\sigma_{GP,ExTrA}$ (relative flux) | $0.0160^{+0.026}_{-0.0073}$ | Amplitude of the GP
$\rho_{GP,ExTrA}$ (days) | $0.071^{+0.076}_{-0.029}$ | Time-scale of the Matern kernel

##  Appendix C Spectral energy distribution

We performed an independent determination of the stellar parameters of TOI-269
modeling the spectral energy distribution (SED) with stellar atmosphere and
evolution models. We constructed the SED using the magnitudes from Gaia DR2
(Evans et al. 2018; Maíz Apellániz & Weiler 2018), the 2-Micron All-Sky Survey
(2MASS, Skrutskie et al. 2006; Cutri et al. 2003), and the Wide-field Infrared
Survey Explorer (WISE, Wright et al. 2010b; Cutri & et al. 2013). We modeled
these magnitudes using the procedure described in Díaz et al. (2014). We used
informative priors for the effective temperature ($T_{\mathrm{eff}}$), and
metallicity ($[\rm{Fe/H}]$) from the analysis of the HARPS co-added spectra
with SpecMatch-Emp (Yee et al. 2017), and for the distance from Gaia DR2 (Gaia
Collaboration et al. 2018; Bailer-Jones et al. 2018). We used non-informative
priors for the rest of the parameters. We used the PHOENIX/BT-Settl stellar
atmosphere models (Allard et al. 2012), and two stellar evolution models:
Dartmouth (Dotter et al. 2008) and PARSEC (Chen et al. 2014). We did three
analyses, one using stellar atmosphere models only (BT-Settl) and another two
with the stellar atmosphere models and each of the stellar evolution models
(BT-Settl + Dartmouth, BT-Settl + PARSEC). The priors, posterior median, and
68.3% credible intervals (CI) for jump and derived parameters are listed in
Table 7. The data with the maximum a posteriori (MAP) stellar atmosphere model
is shown in Fig. 19.

Table 7: Modeling of the spectral energy distribution: Parameter, prior,
posterior median, and 68.3% CI for each of the analyses.

Parameter |  | Prior | Posterior | Posterior | Posterior
---|---|---|---|---|---
|  |  | BT-Settl | BT-Settl + Dartmouth |  BT-Settl + PARSEC
Effective temperature, $T_{\mathrm{eff}}$ | [K] |  $N$(3514, 70) |  3578${}^{+44}_{-38}$ |  3586${}^{+24}_{-20}$ |  3562$\pm$37
Surface gravity, $\log g$ | [cgs] |  $U$(-0.5, 6.0) |  5.46${}^{+0.37}_{-0.52}$ |  4.8648$\pm$0.0055 |  4.833${}^{+0.021}_{-0.036}$
Metallicity, $[\rm{Fe/H}]$ | [dex] |  $N$(-0.29, 0.12) |  -0.32$\pm$0.11 |  -0.325$\pm$0.082 |  -0.403${}^{+0.073}_{-0.085}$
Distance | [pc] |  $N$(57.023, 0.076) |  57.023$\pm$0.076 |  57.022$\pm$0.077 |  57.022$\pm$0.079
$E_{\mathrm{(B-V)}}$ | [mag] |  $U$(0,3) |  0.028${}^{+0.036}_{-0.020}$ |  0.025${}^{+0.030}_{-0.018}$ |  0.022${}^{+0.030}_{-0.016}$
Jitter Gaia | [mag] |  $U$(0, 1) |  0.069${}^{+0.10}_{-0.034}$ |  0.075${}^{+0.098}_{-0.034}$ |  0.082${}^{+0.12}_{-0.040}$
Jitter 2MASS | [mag] |  $U$(0, 1) |  0.025${}^{+0.043}_{-0.018}$ |  0.030${}^{+0.045}_{-0.021}$ |  0.026${}^{+0.044}_{-0.018}$
Jitter WISE | [mag] |  $U$(0, 1) |  0.025${}^{+0.044}_{-0.018}$ |  0.023${}^{+0.040}_{-0.017}$ |  0.029${}^{+0.053}_{-0.021}$
Radius, $R_{\star}$ |  [R⊙] |  $U$(0, 100)$\dagger$ |  0.3926$\pm$0.062 |  0.3910$\pm$0.0032 |  0.3948${}^{+0.0064}_{-0.0052}$
Mass, $M_{\star}$ |  [M⊙] |  |  |  0.4103$\pm$0.0045 |  0.390${}^{+0.014}_{-0.023}$
Density, $\rho_{\star}$ |  [$\mathrm{g\;cm^{-3}}$] |  |  |  9.670$\pm$0.180 |  8.920${}^{+0.540}_{-0.800}$
Age | [Gyr] |  |  |  5.3${}^{+3.5}_{-2.4}$ |  0.143${}^{+0.15}_{-0.049}$
Luminosity |  [L⊙] |  |  |  0.02276${}^{+0.00063}_{-0.00050}$ |  0.02261${}^{+0.00066}_{-0.00054}$

  * Notes. $N$($\mu$,$\sigma$): Normal distribution prior with mean $\mu$, and standard deviation $\sigma$. $U$(l,u): Uniform distribution prior in the range [l, u]. $\dagger$ For the BT-Settl analysis only.

Figure 19: Spectral energy distribution of TOI-269. The solid line is the MAP
PHOENIX/BT-Settl interpolated synthetic spectrum, red circles are the absolute
photometric observations, and gray open circles are the result of integrating
the synthetic spectrum in the observed band-passes.