11institutetext:  Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany 22institutetext: Landessternwarte, Zentrum für Astronomie der Universität Heidelberg, Königstuhl 12, 69117 Heidelberg, Germany 33institutetext: Centro de Astrobiología (CSIC-INTA), ESAC, Camino bajo del castillo s/n, 28692 Villanueva de la Cañada, Madrid, Spain 44institutetext: Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain 55institutetext: Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain 66institutetext: Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, United States of America 77institutetext: Space Telescope Science Institute, Baltimore, MD 21218, United States of America 88institutetext: Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía s/n, 18008 Granada, Spain 99institutetext: Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK 1010institutetext: Institut de Ciències de l’Espai (ICE, CSIC), Campus UAB, C/ de Can Magrans s/n, 08193 Cerdanyola del Vallès, Spain 1111institutetext: Institut d’Estudis Espacials de Catalunya (IEEC), C/ Gran Capità 2-4, 08034 Barcelona, Spain 1212institutetext: Proto-Logic LLC, 1718 Euclid Street NW, Washington, DC 20009, United States of America 1313institutetext: Thüringer Landessternwarte Tautenburg, Sternwarte 5, 07778 Tautenburg, Germany 1414institutetext: American Association of Variable Star Observers, 49 Bay State Road, Cambridge, MA 02138, United States of America 1515institutetext: Institut für Astrophysik, Georg-August-Universität, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany 1616institutetext: Centro Astronónomico Hispano Alemán, Observatorio de Calar Alto, Sierra de los Filabres, E-04550 Gérgal, Spain 1717institutetext: Observatori Astronòmic Albanyà, Camí de Bassegoda s/n, Albanyà 17733, Girona, Spain 1818institutetext: Centre for Astrophysics, University of Southern Queensland, Toowoomba, QLD, 4350, Australia 1919institutetext: Astrophysics Group, Keele University, Staffordshire, ST5 5BG, United Kingdom 2020institutetext: NASA Ames Research Center, Moffett Field, CA 94035, United States of America 2121institutetext: Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig Weg 3, 37077 Göttingen, Germany 2222institutetext: Department of Physics & Astronomy, Swarthmore College, Swarthmore PA 19081, United States of America 2323institutetext: Department of Physics and Astronomy, University of Louisville, Louisville, KY 40292, United States of America 2424institutetext: Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America 2525institutetext: Universitäts-Sternwarte, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany 2626institutetext:  Departamento de Física de la Tierra y Astrofísica & IPARCOS-UCM (Instituto de Física de Partículas y del Cosmos de la UCM), Facultad de Ciencias Físicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain 2727institutetext: NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, United States of America 2828institutetext: Centro de Astrobiología (CSIC-INTA), Carretera de Ajalvir km 4, 28850 Torrejón de Ardoz, Madrid, Spain 2929institutetext: Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America 3030institutetext: Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, United States of America 3131institutetext: Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany 3232institutetext: Vereniging Voor Sterrenkunde, Brugge, Belgium & Centre for mathematical Plasma-Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Heverlee, Belgium 3333institutetext: AstroLAB IRIS, Provinciaal Domein “De Palingbeek”, Verbrandemolenstraat 5, 8902 Zillebeke, Ieper, Belgium 3434institutetext: Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, United States of America

# TOI-1201 b: A mini-Neptune transiting
a bright and moderately young M dwarf††thanks: Tables 11 and 12 and additional
data (i.e., stellar activity indicators) are available in electronic form at
the CDS via anonymous ftp to cdsarc.u-strasbg.fr (TBD)

D. Kossakowski${}^{{\ref{inst:mpia}}}$ Fellow of the International Max Planck
Research School for Astronomy and Cosmic Physics at the University of
Heidelberg (IMPRS-HD). J. Kemmer${}^{{\ref{inst:lsw}}}$††footnotemark:  P.
Bluhm${}^{{\ref{inst:lsw}}}$††footnotemark:  S.
Stock${}^{{\ref{inst:lsw}}}$††footnotemark:  J. A.
Caballero${}^{{\ref{inst:cabesac}}}$ V. J. S.
Béjar${}^{{\ref{inst:iac},\ref{inst:ull}}}$ C. Cardona
Guillén${}^{{\ref{inst:iac},\ref{inst:ull}}}$ N.
Lodieu${}^{{\ref{inst:iac},\ref{inst:ull}}}$ K. A.
Collins${}^{{\ref{inst:cfa}}}$ M. Oshagh${}^{{\ref{inst:iac},\ref{inst:ull}}}$
M. Schlecker${}^{{\ref{inst:mpia}}}$††footnotemark:  N.
Espinoza${}^{{\ref{inst:stsci}}}$ E.
Pallé${}^{{\ref{inst:iac},\ref{inst:ull}}}$ Th.
Henning${}^{{\ref{inst:mpia}}}$ L. Kreidberg${}^{{\ref{inst:mpia}}}$ M.
Kürster${}^{{\ref{inst:mpia}}}$ P. J. Amado${}^{{\ref{inst:iaa}}}$ D. R.
Anderson${}^{{\ref{inst:warwick}}}$ J. C.
Morales${}^{{\ref{inst:ice},\ref{inst:ieec}}}$ S.
Cartwright${}^{{\ref{inst:proto}}}$ D. Charbonneau${}^{{\ref{inst:cfa}}}$ P.
Chaturvedi${}^{{\ref{inst:tls}}}$ C. Cifuentes${}^{{\ref{inst:cabesac}}}$ D.
M. Conti${}^{{\ref{inst:aavso}}}$ M. Cortés-
Contreras${}^{{\ref{inst:cabesac}}}$ S. Dreizler${}^{{\ref{inst:iag}}}$ D.
Galadí-Enríquez${}^{{\ref{inst:caha}}}$ P. Guerra${}^{{\ref{inst:oaa}}}$ R.
Hart${}^{{\ref{inst:usq}}}$ C. Hellier${}^{{\ref{inst:keele}}}$ C.
Henze${}^{{\ref{inst:ames}}}$ E.
Herrero${}^{{\ref{inst:ice},\ref{inst:ieec}}}$ S. V.
Jeffers${}^{{\ref{inst:mig}}}$ J. M. Jenkins${}^{{\ref{inst:ames}}}$ E. L. N.
Jensen${}^{{\ref{inst:swarthmore}}}$ A. Kaminski${}^{{\ref{inst:lsw}}}$ J. F.
Kielkopf${}^{{\ref{inst:louisville}}}$ M. Kunimoto${}^{{\ref{inst:mit}}}$ M.
Lafarga${}^{{\ref{inst:ice},\ref{inst:ieec}}}$ D. W.
Latham${}^{{\ref{inst:cfa}}}$ J. Lillo-Box${}^{{\ref{inst:cabesac}}}$ R.
Luque${}^{{\ref{inst:iaa}}}$ K.
Molvaerdikhani${}^{{\ref{inst:lsw},\ref{inst:mpia},\ref{inst:lmu}}}$ D.
Montes${}^{{\ref{inst:ucm}}}$ G. Morello${}^{{\ref{inst:iac},\ref{inst:ull}}}$
E. .H. Morgan${}^{{\ref{inst:mit}}}$ G.
Nowak${}^{{\ref{inst:iac},\ref{inst:ull}}}$ A. Pavlov${}^{{\ref{inst:mpia}}}$
M. Perger${}^{{\ref{inst:ice},\ref{inst:ieec}}}$ E. .V.
Quintana${}^{{\ref{inst:goddard}}}$ A. Quirrenbach${}^{{\ref{inst:lsw}}}$ S.
Reffert${}^{{\ref{inst:lsw}}}$ A. Reiners${}^{{\ref{inst:iag}}}$ G.
Ricker${}^{{\ref{inst:mit}}}$ I. Ribas${}^{{\ref{inst:ice},\ref{inst:ieec}}}$
C. Rodríguez López${}^{{\ref{inst:iaa}}}$ M. R. Zapatero
Osorio${}^{{\ref{inst:cabinta}}}$ S.
Seager${}^{{\ref{inst:mit},\ref{inst:mit_planetarysciences},\ref{inst:mit_aeronautics}}}$
P. Schöfer${}^{{\ref{inst:iag}}}$ A. Schweitzer${}^{{\ref{inst:hamburg}}}$ T.
Trifonov${}^{{\ref{inst:mpia}}}$ S.
Vanaverbeke${}^{{\ref{inst:leuven},\ref{inst:iris}}}$ R.
Vanderspek${}^{{\ref{inst:mit}}}$ R. West${}^{{\ref{inst:warwick}}}$ J.
Winn${}^{{\ref{inst:princeton}}}$ M. Zechmeister${}^{{\ref{inst:iag}}}$

(Received 18 June 2021 / Accepted dd September 2021)

We present the discovery of a transiting mini-Neptune around TOI-1201, a
relatively bright and moderately young early M dwarf ($J\approx$ 9.5 mag,
$\sim$600–800 Myr) in an equal-mass $\sim$8 arcsecond-wide binary system,
using data from the Transiting Exoplanet Survey Satellite (TESS), along with
follow-up transit observations. With an orbital period of 2.49 d, TOI-1201 b
is a warm mini-Neptune with a radius of $R_{\mathrm{b}}=2.415\pm
0.090\,R_{\oplus}$. This signal is also present in the precise radial velocity
measurements from CARMENES, confirming the existence of the planet and
providing a planetary mass of $M_{\mathrm{b}}=6.28\pm 0.88\,M_{\oplus}$ and,
thus, an estimated bulk density of $2.45^{+0.48}_{-0.42}$ g cm-3. The
spectroscopic observations additionally show evidence of a signal with a
period of 19 d and a long periodic variation of undetermined origin. In
combination with ground-based photometric monitoring from WASP-South and ASAS-
SN, we attribute the 19 d signal to the stellar rotation period
($P_{\textnormal{rot}}=$ 19–23 d), although we cannot rule out that the
variation seen in photometry belongs to the visually close binary companion.
We calculate precise stellar parameters for both TOI-1201 and its companion.
The transiting planet is an excellent target for atmosphere characterization
(the transmission spectroscopy metric is $97^{+21}_{-16}$) with the upcoming
James Webb Space Telescope. It is also feasible to measure its spin-orbit
alignment via the Rossiter-McLaughlin effect using current state-of-the-art
spectrographs with submeter per second radial velocity precision.

###### Key Words.:

techniques: photometric – techniques: radial velocities – planetary systems –
stars: individual: TOI-1201, TIC-29960110 – stars: low-mass

##  1 Introduction

Results from the Kepler (Borucki et al., 2010; Mathur et al., 2017) and K2
(Howell et al., 2014) missions have revealed that M dwarfs
($T_{\textnormal{eff}}\lesssim 4\,000$ K) host on average $\sim$2.5 planets
with radii below 4 $R_{\oplus}$ and with periods of less than 200 d (e.g.,
Dressing & Charbonneau, 2013, 2015). The bimodal distribution of radii of
small, close-in planets produces a gap that separates planets with 1–2
$R_{\oplus}$, the so-called super-Earths, and 2–4 $R_{\oplus}$, denominated as
mini-Neptunes. For solar-like stars, this radius gap occurs between 1.7
$R_{\oplus}$ and 2.0 $R_{\oplus}$ (Fulton et al., 2017; Fulton & Petigura,
2018; Van Eylen et al., 2018), and it resides a bit lower for low-mass stars,
between 1.4 $R_{\oplus}$ and 1.7 $R_{\oplus}$ (Cloutier & Menou, 2020; Van
Eylen et al., 2021). This bimodality suggests that mini-Neptunes are mostly
rocky planets that were born with primary atmospheres and were able to retain
them, whereas planets below the radius gap lost their atmospheres and were
stripped to their cores (Bean et al., 2021).

The mechanism that drives atmospheric loss for these planets remains
ambiguous, with the prime candidates being photo-evaporation (e.g., Owen & Wu,
2013, 2017; Lehmer & Catling, 2017; Van Eylen et al., 2018; Mordasini, 2020)
and core-powered mass loss (Ginzburg et al., 2016, 2018; Gupta & Schlichting,
2019, 2021) on timescales of $\sim$100 Myr and $\sim$1 Gyr, respectively. In
both models, the heating of the planet’s upper atmosphere drives a
hydrodynamic outflow. In the case of core-powered mass loss, the planet’s
heating originates from infrared (IR) radiation coming from the cooling
planetary interior, while photo-evaporation is due to extreme ultraviolet
photons from the host star. However, it is not clear which heating mechanism
dominates the mass loss observed for mini-Neptune-sized planets. Thus,
investigating young planets (100 Myr–1 Gyr) and determining accurate masses
for these worlds is critical in constraining the mass loss rate to then learn
how they evolve over time in hopes of better explaining the origin of the
radius gap.

Precise mass and radius measurements alone, however, are not sufficient in
establishing the bulk composition, as there are large degeneracies when
determining the ratio of rock, water, and hydrogen for the interior structure
(Rogers & Seager, 2010; López & Fortney, 2014). Mini-Neptunes are one of the
most commonly detected outcomes of planet formation (Barnes et al., 2009;
Rogers et al., 2011; Marcy et al., 2014; Rogers, 2015), and understanding the
composition of their atmospheres can help reveal the nature, origins, and
evolution of these objects (Miller-Ricci & Fortney, 2010; Benneke & Seager,
2013; Crossfield & Kreidberg, 2017). Luckily, we find ourselves in an era in
which the ongoing Transiting Exoplanet Survey Satellite (TESS; Ricker et al.,
2015) mission is set to find such targets that will be suitable for
transmission spectroscopy using the future James Webb Space Telescope (JWST;
Gardner et al., 2009). TOI-1201 b adds to the growing sample of mini-Neptunes
around M dwarfs that are promising targets for transmission spectroscopy.

Additionally, the stellar M-dwarf host TOI-1201 is found in a wide binary
system. Observations of planets in multiple-star systems can shed light on
stellar and planet formation (see e.g., Goodwin et al., 2007, 2008; Thebault &
Haghighipour, 2015; Monnier et al., 2018). To date, planet discoveries in
binary systems where the primary is an M dwarf are scarce despite them being
the most abundant stars in our Galaxy (Henry et al., 2006; Winters et al.,
2015; Reylé et al., 2021). An M dwarf is the primary in fewer than 10 % of the
known binary systems with planet detections111
https://exoplanetarchive.ipac.caltech.edu/, accessed on 29 March 2021. Such a
low count is not surprising since M-dwarf systems with close visual companions
were typically discarded from dedicated detection surveys due to the lack of
high-resolution near-IR spectrographs and the high risk of potential light
contamination in transits (e.g., Cortés-Contreras et al., 2017, and references
therein).

Nearly half of the solar-like stars in our solar neighborhood are members of
binaries or multiple systems (Duquennoy & Mayor, 1991; Raghavan et al., 2010),
and 25 % of them are found in wide binaries (projected separation $s>100$ au).
It has been shown that the planet occurrence rate for these wide binary
systems is comparable to that around single stars, presumably because the
influence of the stellar companion on the formation of the planet is
negligible (Wang et al., 2014; Deacon et al., 2016). Turning our focus back to
M dwarfs, the stellar multiplicity rate is believed to be $\sim$16–27 %
(Janson et al., 2012, 2014; Cortés-Contreras et al., 2017; Winters et al.,
2019a). However, the planet occurrence rate in low-mass binaries is still
uncertain because these stellar targets have often been neglected in surveys.

More recently, the CARMENES spectrograph and consortium (introduced in Sect.
3.3) has been responsible for increasing the number of detected planets around
M dwarfs in binary systems, particularly around wide separation systems,
namely, HD~180617 (Kaminski et al., 2018), Gl~49 (Perger et al., 2019),
LTT~3780 (Nowak et al., 2020; Cloutier et al., 2020), HD~79211 (GJ 338 B,
González-Álvarez et al., 2020), GJ~3473 (TOI-488, Kemmer et al., 2020), and
HD~238090 (GJ 458 A, Stock et al., 2020b). Precise stellar properties, as well
as radial velocities (RVs), are commonly determined solely for the host; the
details of the companion are often missed, with some exceptions, such as GJ
338 B (González-Álvarez et al., 2020) or GJ~15 A and B (Howard et al., 2014;
Pinamonti et al., 2018; Trifonov et al., 2018). Studying properties such as
metallicity and age can shed light on which environments favor the formation
of particular planets (Johnson & Li, 2012; Hobson et al., 2018; Montes et al.,
2018). Observing more systems would allow for a better grasp on how stellar
multiplicity in M-dwarf systems plays a role in the planet formation process
and in the types of planets that can exist.

In this paper we present the discovery and mass determination of the
transiting mini-Neptune TOI-1201 b. The planet orbits one member of the
M-dwarf wide binary system PM~J02489–1432. We calculate precise stellar
parameters and present RV measurements for both the host and the companion.
The mini-Neptune, with a period of about 2.5 d, was initially discovered as a
transiting planet candidate in TESS data and is confirmed here using ground-
based photometry and CARMENES RV measurements. Future observations with JWST
will be able to precisely constrain the atmospheric compositions of this and
other similar planets and, thus, provide important constraints on mini-Neptune
formation.

The paper is organized as follows. The TESS photometry is introduced in Sect.
2, followed by the various ground-based photometric and spectroscopic
observations in Sect. 3. The stellar properties of both TOI-1201 and its
companion are discussed in Sect. 4. The modeling analysis, which combines all
the available data to produce the final planetary parameters, is presented in
Sect. 5. Finally, in Sect. 7 we unveil the future prospects for TOI-1201 b. We
give our final conclusions in Sect. 8.

##  2 TESS photometry

TOI-1201 (TIC-29960110) was observed by TESS with the short cadence 2-minute
integrations during cycle 1, sector 4 (camera #1, CCD #1) between 18 October
and 15 November 2018, and also during the first year of the extended mission
during cycle 3, sector 31 (camera #1, CCD #3) between 21 October and 19
November 2020. The planetary signature of TOI-1201 b was detected in the
Science Processing Operations Center (SPOC; Jenkins et al., 2016) transit
search pipeline on 16 January 2019 and was issued as an alert by the TESS
Science Office (TSO) on 31 January 2019. The target was not initially
announced as a TESS object of interest (TOI) along with the other TOIs from
sector 4, but rather its companion (TOI-393, TIC-29960109) that fell on the
same pixel was (Sect. 4.2).

Fig. 1 displays a plot of the target pixel file (TPF) and the aperture mask
used to produce the Simple Aperture Photometry (SAP), created using
tpfplotter222https://github.com/jlillo/tpfplotter (Aller et al., 2020). Within
the Tess Follow-up Observing Program (TFOP) “Seeing-limited Photometry” SG1
subgroup333https://tess.mit.edu/followup/, the first follow-up transit
photometric data immediately indicated that TOI-1201 was the correct stellar
host and not TOI-393 (see Sect. 3.1). In this work, we only analyzed the
2-minute integrations. In addition, 20-second integrations are available for
sector 31. However, they do not improve the uncertainty on the model
parameters and rather increase computation time in comparison to the 2-minute
integrations.

Figure 1: TESS TPF plot for TOI-1201 for sectors 4 and 31. The SAP was
computed using the flux counts coming in from the red bordered pixels (mask).
The red circles represent neighboring sources listed in Gaia DR2, where the
size corresponds to the brightness difference with respect to TOI-1201. The
close companion to TOI-1201 is indicated as source #2.

We downloaded the TESS data from the Mikulski Archive for Space
Telescopes444https://mast.stsci.edu. The TESS photometric light curve is
corrected for systematics as usually carried out (Presearch Data Conditioning,
PDC_SAP flux – Smith et al., 2012; Stumpe et al., 2012, 2014) and is presented
in Fig. 2 with the best-fit model (explained in detail in Sect. 5.3).

TOI-1201 and its equally bright companion (0.26 mag fainter in $G_{BP}$) are
just 8 arcsec away from each other (see Sect. 4.2) and, therefore, fall on the
same TESS pixel (21 arcsec). This raised the issue of ensuring that the radius
ratio is correct. This problem was solved since the PDC_SAP flux is corrected
for possible nearby flux contamination. Specifically, the images of the
postage stamps for this target have a flat background with only one other
bright star in the photometric aperture that is already known with no
additional significant crowding, so the sky background bias is expected to be
minimal for the sector 4 data. From sector 27 onward, the sky background
algorithm was modified and improved such that any sky background bias for
sector 31 data is negligible. The transit depth in the sector 4 data is
therefore slightly overestimated by 0.3 %. However, this did not raise a
serious issue for the analysis. Using the keyword CROWDSAP, the correction for
sector 4 and sector 31 data is 0.52 and 0.56, respectively. These values are
in agreement to our calculation for the dilution from converting the TESS
magnitudes into fluxes and following $f_{A}/(f_{A}+f_{B})$ to obtain 0.56,
where $f_{B}$ and $f_{A}$ are the fluxes for TOI-1201 and its companion,
respectively. Therefore, the preliminary parameters provided by the SPOC
presented in the TOI catalog555https://tev.mit.edu/data/collection/193/ are
valid. The transit signal was initially detected to have a period of
2.49198$\pm$0.00032 d and a depth of 2128$\pm$160 parts per million (ppm),
corresponding to an approximate planetary radius of 2.2$\pm$1.3 $R_{\oplus}$
and equilibrium temperature of 640 K. The quoted uncertainty on the radius is
rather large, but this is not important because the value is anyhow updated
after performing a full analysis (Sect. 5.3).

Figure 2: Top panel: Full TESS photometry for TOI-1201 from sectors 4 and 31.
The opaque and black dots are the data binned to 20 minutes in the light curve
time series and phase-folded plots, respectively. The vertical gray lines
represent the transit times, and the black line is the juliet best-fit model
from the joint fit. Middle and bottom panels: Phase-folded transits for
TOI-1201 b for all photometric instruments: TESS sector 4 (middle left) and
sector 31 (middle right), LCO-SAAO $g^{\prime}$ band (bottom left), OAA $V$
band (bottom middle), and LCO-SSO $z_{s}$ band (bottom right). Any GP
components and linear trends were subtracted out before the curves were phase-
folded.

##  3 Ground-based observations

###  3.1 Follow-up seeing-limited transit photometry

Table 1: Logbook of ground-based transit follow-up observations taken for
TOI-1201.

Instrument | Country | Date | Filter | Exposure | Durationaa$a$Time span of the observation. | Pixel scale | N${}_{\textnormal{obs}}$ | 10-min rmsbb$b$Root mean square in parts-per-thousand.
---|---|---|---|---|---|---|---|---
|  |  |  | (s) | (min) | (arcsec) |  | (ppt)
LCO-SSO | Australia | 2019 Aug. 27 | $z_{s}$ | 60 | 331 | 0.389 | 306 | 1.27
MKO CDK700 | Australia | 2019 Sep. 01 | $r^{\prime}$ | 128 | 231 | 0.4 | 74 | 2.73
LCO-SAAO | South Africa | 2019 Sep. 23 | $g^{\prime}$ | 50 | 215 | 0.389 | 170 | 1.99
OAA | Spain | 2019 Sep. 29 | $V$ | 240 | 234 | 1.44 | 56 | 1.57

666

We acquired four sets of full-transit ground-based time-series follow-up
photometry of TOI-393 and TOI-1201 as part of the
TFOP777https://tess.mit.edu/followup to determine the source of the TESS
transit-like signal detection, refine the transit ephemeris, and place
constraints on transit depth across optical filter bands. We used the TESS
Transit Finder, which is a customized version of the Tapir software package
(Jensen, 2013), to schedule our transit observations. The photometric data
were extracted using the AstroImageJ software package (Collins et al., 2017).
The transit observation logbook is presented in Table 1, where technical
details, such as facility, filter, exposure, or duration, are included. The
following paragraphs describe the various data sets obtained from the ground-
based facilities.

#### MKO CDK700.

The first follow-up transit observation submitted to TFOP was from the Mount
Kent Observatory (MKO) CDK700 telescope near Toowoomba, Queensland, Australia.
The CDK700 is a Planewave Corrected Dall-Kirkham 0.7 m telescope equipped with
an Apogee Alta F16 (KAF-16803) detector resulting in a $27\times 27$ arcmin2
field of view. The CDK700 data tentatively ruled out the event on TOI-393 and
were suggestive of a shallow event in TOI-1201. However, the TOI-1201
detection was inconclusive due to the observational systematics when
separating the two stars. For this reason, the MKO data were not included in
our joint system modeling.

#### LCOGT.

We obtained two observations of TOI-393 and its $\sim 8$ arcsec neighbor
TOI-1201 using the Las Cumbres Observatory Global Telescope (LCOGT) 1.0 m
network (Brown et al., 2013). The telescopes are equipped with $4096\times
4096$ pixel Sinistro cameras, resulting in a $26\times 26$ arcmin2 field of
view. The first LCOGT observation was scheduled according to the initial
public TOI-393 ephemeris on 27 August 2019 at the Siding Spring Observatory
(SSO) 1.0 m node in Pan-STARRS $z_{s}$ band (LCO-SSO hereinafter). The stellar
point-spread functions (PSFs) in the images had nominal full width at half
maximum (FWHM) of $\sim 1.7$ arcsec. A photometric aperture with radius of 7
pixels (2.7 arcsec) was selected to separate most of the flux of TOI-393 and
TOI-1201 in two different apertures. A transit-like event consistent with the
TESS detection was ruled out in TOI-393, and a transit-like event arriving
$\sim 40$ minutes early, with depth $\sim 2000$ ppm, was confirmed in
TOI-1201. We revised the follow-up ephemeris according to the LCO-SSO
observation and observed another predicted full-transit observation on 23
September 2019 from the LCOGT 1.0 m node at South Africa Astronomical
Observatory (SAAO) in Sloan $g^{\prime}$. A $\sim 2000$ ppm transit-like event
was detected arriving on-time relative to the revised ephemeris (denoted as
LCO-SAAO). The combination of the $z_{s}$ and $g^{\prime}$ $\sim 2000$ ppm
detections suggests that the transit-like event is achromatic, which reduces
of the chances that the TESS signal had been caused by a false positive
scenario.

#### OAA.

We observed another full transit on 29 September 2019 with the 0.4 m telescope
at the Observatori Astronòmic Albanyà888https://www.observatorialbanya.com/
(OAA) near Girona, Spain, in Johnson $V$ band. The telescope is equipped with
a Moravian G4-9000 camera with a field of view of $36\times 36$ arcmin2 .
TOI-393 and TOI-1201 could not be cleanly separated, so we selected a
photometric aperture with radius 13 arcsec that included most of the flux from
both of the $\sim 8$ arcsecond-wide neighbors. The transit-like event arrived
on-time relative to the revised ephemeris.

###  3.2 Long-term photometric monitoring

We also assembled a list of archival long-time baseline data, namely from the
WASP-South and ASAS-SN surveys.

#### WASP-South.

TOI-1201 was observed with the Wide Angle Search for Planets (WASP) array of
eight cameras at the South African Astronomical Observatory in Sutherland
(WASP-South; Pollacco et al., 2006) over the course of six years from 2008 to
2014, amounting to about 64 000 acquired data points. From 2008 to 2009, the
200 mm lenses were used (camera 222, 13.7 arcsec pixel-1), and from 2012 to
2014, the data were taken with the 85 mm lenses (camera 281, 32 arcsec
pixel-1). The root mean square (rms) across all WASP-South cameras is 0.023
mag. Since the extraction aperture included both stars, it was not possible to
use these data to unequivocally determine which star is producing the
sinusoidal modulation found in the data, as examined in Sect. 4.3.

#### ASAS-SN.

The All-Sky Automated Survey for Supernovae (ASAS-SN) is composed of 24 14 cm
aperture Nikon telephoto lenses, each equipped with a $2048\times 2048$
ProLine CCD camera, at locations distributed worldwide (Shappee et al., 2014;
Kochanek et al., 2017). We input the stellar coordinates for TOI-1201 as
provided in Table 2 to search the ASAS-SN database999https://asas-sn.osu.edu/.
Two sources associated with these coordinates with a separation of $\sim$3.2
arcsec were found, so both light curves are surely contaminating each other
(assuming that the source APJ024859.45–143214.2 corresponds to TOI-1201 and
the other source AP37838964 to the companion). Because the ASAS-SN pixel-scale
is 8 arcsec pixel-1 and the aperture is around 15 arcsec, blending is an
issue. The extracted data consist of a total of 619 points spanning roughly
1600 d from March 2012 to January 2019 in four cameras (ba, bb, be, bf), all
in the $V$ band, with a combined rms of 0.018 mag.

Table 2: Stellar parameters of TOI-1201 and its 8 arcsecond-wide companion.

Parameter | Primary | Secondary | Reference
---|---|---|---
Names and identifiers
Name | PM J02489–1432W | PM J02489–1432E | LG11
Karmn | J02489–145W | J02489–145E | Cab16
Gaia EDR3 ID | 5157183324996790272 | 5157183324996789760 |  Gaia EDR3
TOI | 1201 | 393 | ExoFOP-TESS
TIC | 29960110 | 29960109 | Sta18
Coordinates and spectral types
$\alpha$ (J2000) | 02:48:59.27 | 02:48:59.83 |  Gaia EDR3
$\delta$ (J2000) | –14:32:14.9 | –14:32:16.2 |  Gaia EDR3
Sp. typeaa$a$Photometrically derived spectral types. |  M$2.0\pm 0.5$ V |  M$2.5\pm 0.5$ V | This work
Magnitudes
$NUV$ (mag) |  21.664 $\pm$ 0.337 |  21.923 $\pm$ 0.491 | GALEX
$B$ (mag) | … |  14.111 $\pm$ 0.030 | UCAC4
$g^{\prime}$ (mag) |  13.7285 $\pm$ 0.0028 |  13.334 $\pm$ 0.020 | Pan-STARRS1/UCAC4
$G_{BP}$ (mag) |  13.344 $\pm$ 0.025 |  13.694$\pm$ 0.014 |  Gaia EDR3
$V$ (mag) | … |  12.706 $\pm$ 0.020 | UCAC4
$r^{\prime}$ (mag) |  12.5537 $\pm$ 0.0010 |  12.110 $\pm$ 0.080 | Pan-STARRS1/UCAC4
$G$ (mag) |  12.0888 $\pm$ 0.0072 |  12.3710 $\pm$ 0.0052 |  Gaia EDR3
$i^{\prime}$ (mag) |  11.4326 $\pm$ 0.038 |  10.900 $\pm$ 0.010 | Pan-STARRS1/UCAC4
$G_{RP}$ (mag) |  10.9748 $\pm$ 0.0092 |  11.2333 $\pm$ 0.0061 |  Gaia EDR3
$J$ (mag) |  9.528 $\pm$ 0.042 |  9.733 $\pm$ 0.024 | 2MASS
$H$ (mag) |  8.876 $\pm$ 0.057 |  9.125 $\pm$ 0.027 | 2MASS
$K_{s}$ (mag) |  8.646 $\pm$ 0.029 |  8.875 $\pm$ 0.021 | 2MASS
$W1$ (mag) |  7.721 $\pm$ 0.014 |  7.731 $\pm$ 0.011 | AllWISE/WISE
$W2$ (mag) |  7.693 $\pm$ 0.013 |  7.670 $\pm$ 0.012 | AllWISE/WISE
$W3$ (mag) |  7.918 $\pm$ 0.020 |  8.063 $\pm$ 0.019 | AllWISE/WISE
$W4$ (mag) |  7.709 $\pm$ 0.129 |  7.794 $\pm$ 0.120 | AllWISE/WISE
Parallax and kinematics
$\pi$ (mas) |  26.571 $\pm$ 0.022 |  26.539 $\pm$ 0.023 |  Gaia EDR3
$d$ (pc) |  37.636 $\pm$ 0.032 |  37.680 $\pm$ 0.033 |  Gaia EDR3
$\mu_{\alpha}\cos\delta$ (mas yr-1) |  +164.069 $\pm$ 0.025 |  +174.433 $\pm$ 0.033 |  Gaia EDR3
$\mu_{\delta}$ (mas yr-1) |  +46.549 $\pm$ 0.027 |  +45.465 $\pm$ 0.029 |  Gaia EDR3
$V_{r}$bb$b$RAVE DR4 Kordopatis et al. (2013) tabulated $\gamma$ = +6.6$\pm$6.1 km s-1 and $T_{\textnormal{eff}}$ = 3600$\pm$310 K for the primary and $\gamma$ = +31.7$\pm$1.4 km s-1 and $T_{\textnormal{eff}}$ = 3840$\pm$70 K for the secondary. The RAVE spectrum of the primary had a very poor signal-to-noise ratio (S/N = 4.2), which led to wrong $V_{r}$ and stellar parameter determination (e.g., $\log{g}$ = 1.5$\pm$1.0, inconsistent with the star’s main-sequence nature). (km s-1) |  +31.771 $\pm$ 0.018 |  +31.868 $\pm$ 0.018 | This work
$U$ (km s-1) |  –38.495 $\pm$ 0.018 |  –39.577 $\pm$ 0.020 | This work
$V$ (km s-1) |  –17.125 $\pm$ 0.018 |  –18.521 $\pm$ 0.019 | This work
$W$ (km s-1) |  –12.652 $\pm$ 0.019 |  –11.956 $\pm$ 0.020 | This work
Galactic population | Young disk | This work
Stellar kinematic group | Hyades Supercluster | This work
Photospheric parameters
$T_{\textnormal{eff}}$ (K) | $3476\pm 51$ | $3437\pm 51$ | This work
$\log g_{\star}$ (cgs) | $4.80\pm 0.04$ | $4.80\pm 0.04$ | This work
[Fe/H] (dex) | $0.05\pm 0.16$ | $0.05\pm 0.16$ | This work
$v\sin{i}$ (km s-1) |  $<$2 |  $<$2 | This work
H$\alpha$ index |  0.931$\pm$0.025 |  0.913$\pm$0.023 | This work
pEW(H$\alpha$) |  $-$0.437$\pm$0.053 |  $-$0.419$\pm$0.050 | This work
$P_{\textnormal{rot}}$ (d) | 19–23 | $\dots$ | This work
Physical parameters
$L_{\star}$ ($10^{-5}\ L_{\odot}$) |  3400 $\pm$ 57 |  2683 $\pm$ 25 | Cif20
$R_{\star}$ ($R_{\odot}$) |  0.508 $\pm$ 0.016 |  0.462 $\pm$ 0.014 | This work
$M_{\star}$ ($M_{\odot}$) |  0.512 $\pm$ 0.020 |  0.463 $\pm$ 0.018 | This work
$\rho_{\star}$ (g cm-3) | $5.50^{+0.58}_{-0.49}$ | $6.40^{+0.75}_{-0.68}$ | This work
101010

Cab16: Caballero et al. (2016a); Gaia EDR3: Gaia Collaboration et al. (2021);
GALEX: Bianchi et al. (2011); Sta18: Stassun et al. (2018); UCAC4: Zacharias
et al. (2012); 2MASS: Skrutskie et al. (2006); Cif20: Cifuentes et al. (2020);
LG11: Lépine & Gaidos (2011); Pan-STARRS1: Kaiser et al. (2010); WISE/AllWISE:
Cutri & et al. (2012, 2014).

###  3.3 High-resolution spectroscopy with CARMENES

Table 3: CARMENES spectroscopic observations for TOI-1201 and its companion.

Target | Start date | End date | $N_{\textnormal{obs}}$ |  $\sigma_{\textnormal{RV}}$(a)(a)footnotemark: $(a)$ |  rms(b)(b)footnotemark: $(b)$
---|---|---|---|---|---
|  |  |  |  (m s-1) |  (m s-1)
TOI-1201 | Nov. 2019 | Feb. 2020 | 33 | 2.22 | 7.95
PM J02489–-1432E | Nov. 2019 | Jan. 2020 | 23 | 2.18 | 3.33
111111 $a$$a$footnotetext: Median value for the uncertainty of the RV
measurement. $b$$b$footnotetext: Root mean square.

We obtained 34 high-resolution spectra for the transit host TOI-1201 with the
CARMENES121212Calar Alto high-Resolution search for M dwarfs with Exo-earths
with Near-infrared and optical Échelle Spectrographs, http://carmenes.caha.es
instrument located at the 3.5 m telescope at the Calar Alto Observatory in
Almería, Spain. We used only the data collected with the VIS channel, which
covers the spectral range 520–960 nm with a spectral resolution of
$\mathcal{R}$ = 94 600 (Quirrenbach et al., 2014, 2018). One of the
measurements was missing a drift correction and was therefore discarded, which
resulted in 33 observations that were used for the analysis. The companion at
about 8 arcsec (see Sect. 4.2) was also observed by CARMENES 23 times from
November 2019 to January 2020. Details on the quality of the CARMENES
spectroscopic data are given in Table 3. The simultaneously collected spectra
from the near-IR channel (960–1710 nm, $\mathcal{R}$ = 80 400) had an rms of
25 m s-1 and do not show any significant signals, and were, thus, not
considered in the analysis as in other CARMENES works (e.g., Bauer et al.,
2020).

The data are pipelined through the standard guaranteed time observations data
flow (Caballero et al., 2016b), and the resulting are measured using
serval131313https://github.com/mzechmeister/serval (Zechmeister et al., 2018).
They are corrected for barycentric motion, secular acceleration, instrumental
drift, and nightly zero-points using our standard approach (Zechmeister et
al., 2018; Trifonov et al., 2020). The RVs with their uncertainties for
TOI-1201 and its companion are tabulated in Tables 11 and 12, respectively.
Additionally, serval provides a list of stellar activity indicators, namely
the chromatic index (CRX), differential line width (dLW), H$\alpha$ index, and
the Ca ii IR triplet (IRT). Following Lafarga et al. (2020), we applied binary
masks to the spectra and computed the cross-correlation function (CCF) and its
FWHM, contrast (CTR), and bisector velocity span (BVS) values. The pseudo-
equivalent width (pEW), as defined in and provided by Schöfer et al. (2019),
of the photospheric lines TiO $\lambda\ 7050\,\AA$, TiO $\lambda\ 8430\,\AA$,
and TiO $\lambda\ 8860\,\AA$ were also derived from the CARMENES spectra.

##  4 Stellar properties

Figure 3: Top panel: $UVW$ velocities of TOI-1201 (red dot) and PM
J02489–1432E (blue dot) compared against members of young moving groups from
Montes et al. (2001), namely Castor (blue), the Hyades Supercluster (HS,
orange), the IC 2391 Supercluster (green), the Local Association (LA, red),
and Ursa Major (UMa, purple). The ellipses represent the 2$\sigma$ value of
the $UVW$ for each group. The two targets agree with the Hyades Supercluster.
Bottom panel: Rotational period of TOI-1201 alongside members of the Pleiades
(in red) and Praesepe (in green) open clusters from Curtis et al. (2019) and
references therein.

###  4.1 Basic astrophysical parameters

Table 2 summarizes the stellar parameters of TOI-1201 and its companion. Both
stars are poorly investigated late-type dwarfs (e.g., Lépine & Gaidos, 2011;
Frith et al., 2013). We first got the equatorial coordinates, parallaxes, and
proper motions of the two stars from Gaia Early Data Release 3 (EDR3; Gaia
Collaboration et al., 2021) and the blue-optical to mid-IR photometry already
compiled by Cifuentes et al. (2020). Next, we integrated the spectral energy
distributions as the latter authors for computing the bolometric luminosities,
$L_{\star}$. Following the $\chi^{2}$ stellar synthesis of Passegger et al.
(2019) and using only the CARMENES VIS channel spectra, we derived the
photospheric parameters $T_{\textnormal{eff}}$, $\log{g}$, and [Fe/H]. From
them, with the Stefan-Boltzman law and the mass-radius relation of Schweitzer
et al. (2019), we obtained the stellar radii and masses, from which we
determined the stellar bulk density. The mass-radius relation of Schweitzer et
al. (2019) is valid only for objects older than a few hundred megayears,
though it is applicable for the age of this system as we currently infer it
(see below). Another systematic uncertainty might have originated from the
accuracy of the models used for the determination of the photospheric
parameters (Passegger et al., 2020). The presented relative uncertainties of
3–4% in the radius and mass of the two M dwarfs stem from the measurement
uncertainties of 1–2% for the effective temperature and photometry of the
stars, and, thus, were carried over accordingly.

We also used the same CCF methodology with the weighted binary masks of
Lafarga et al. (2020) for computing the stellar RVs, $V_{r}$, on the CARMENES
spectra. Using this value and the Gaia astrometry, we calculate the $UVW$
galactocentric space velocities as in Johnson & Soderblom (1987). The $UVW$
values (see Fig. 3) for the two stars indicate that this system belongs to the
young disk (Cortés-Contreras 2021, in prep.) and suggest a membership to the
Hyades Supercluster (Eggen, 1958, 1984) when compared to the kinematics of
other members of this young moving group from Montes et al. (2001).

The rotational period of 19–23 d for TOI-1201 (see Sect. 4.3) matches other
members of the Praesepe open cluster (600–750 Myr; Douglas et al., 2019, and
references therein) with similar effective temperature as TOI-1201 (Curtis et
al., 2019, Fig. 3 in this paper). Furthermore, the H$\alpha$ feature in faint
emission (Jeffers et al., 2018; Schöfer et al., 2019) is also compatible with
members of the Praesepe and the Hyades open cluster ($\sim$600–800 Myr –
Martín et al., 2018; Lodieu et al., 2018; Douglas et al., 2019; Lodieu et al.,
2019a, b, and references therein) with $T_{\textnormal{eff}}$ $\sim$3500 K
(Fang et al., 2018), which supports the membership of this system to the
Hyades Supercluster and, thus, implies its age of $\sim$600–800 Myr.

We also computed projected rotation velocities, $v\sin i$, on the CARMENES
spectra as Reiners et al. (2018) and estimated spectral types M2.0 V and M2.5
V for the primary and secondary, respectively, from absolute magnitudes and
colors as Cifuentes et al. (2020), consistent with the effective temperatures.

###  4.2 The stellar host and its companion

The earliest name in the literature of TOI-1201 is PM~J02489–1432W. At only
about 8 arcsec to the east, Lépine & Gaidos (2011) tabulated a second star,
PM~J02489–1432E, slightly fainter (by 0.28 mag and 0.20 mag in the $G$ and $J$
bands, respectively) and redder (by 0.08 mag in $G-J$ color). While both stars
are located at the same Gaia parallactic distance ($\Delta\pi=0.032\pm 0.032$
mas) and have the same RVs ($\Delta V_{r}=0.097\pm 0.025$ km s-1), their
proper motions are similar but not identical
($\Delta\mu_{\alpha}\cos{\delta}=10.340\pm 0.041$ mas yr-1,
$\Delta\mu_{\delta}=1.084\pm 0.040$ mas yr-1). Despite the total proper motion
difference of only 6 %, the pair would pass any kinematic and astrometric
binarity criterion (e.g., Montes et al., 2018), but such a difference may be
indicative of a relative orbital motion as shown by, for example, Makarov &
Kaplan (2005).

The Washington Double Star catalog (WDS; Mason et al., 2001) tabulates the
pair as WDS J02490–1432 (KPP 2871). Although first reported by Lépine & Gaidos
(2011) and next tabulated by El-Badry & Rix (2018), it was Knapp & Nanson
(2019) who performed the first multi-epoch astrometric analysis and gave the
WDS discovery designation (KPP 2871). However, as of 19 April 2021, WDS listed
only five independent epochs between 1998.6 and 2015.5. For complementing
those data, we retrieved SuperCOSMOS (Hambly et al., 2001) digitizations of
First Palomar Observatory Sky Survey (POSS-I) and United Kingdom Schmidt
Telescope (UKST) photographic plates taken between December 1955 and September
1989, and measured angular separation $\rho$ and position angle $\theta$
between the primary and secondary as in Caballero (2010). Besides, we
recomputed the angular separation $\rho$ and position angle $\theta$ for the
2MASS (Skrutskie et al., 2006), DENIS (Epchtein et al., 1997), and Gaia DR1,
DR2, and EDR3 (Gaia Collaboration et al., 2016, 2018, 2021) observations. The
11 resulting astrometric epochs, which cover 61.97 yr, are displayed in Table
13. The pair was not resolved, though, by a number of all-sky surveys:
GSC2.3/USNO-A2/USNO-B1, SDSS, UKIDSS LAS, WISE (e.g., Monet et al., 2003;
Lawrence et al., 2007; Alam et al., 2015; Marocco et al., 2021).

In the six decades of astrometric observations of the binary, there has been
an appreciable increase in $\rho$ from 7.2 arcsec to 8.4 arcsec.
Unfortunately, any variation in $\theta$ has been masked by the uncertainty of
the individual observations, typically larger than 1 deg. Taking the Gaia EDR3
value as the minimum angular separation of the pair, and at the stars
heliocentric distance, we obtain $s$ = 316.4$\pm$1.3 au, which is also the
minimum semimajor axis, $a$, of the binary. Assuming a circular orbit,
together with the individual masses of the primary and secondary in Table 2
and Kepler’s third law, the minimum orbital period $P_{\textnormal{orb}}$ of
the binary would be 5709$\pm$86 yr. The astrometric monitoring of 61.97 yr,
thus, represents only $\sim$1 % of the orbit in time. Certainly, a
prohibitively long astrometric and RV follow-up will be needed to dynamically
characterize the system in detail, but a physical separation of about 320 au
between the two nearly identical stars (mass ratio $0.904\pm 0.027$) may
impose restrictions on the original protoplanetary disk size and planet
stability in the system.

###  4.3 Rotation period

To determine the stellar rotation period, we considered the available
photometric data in the archive from the WASP and ASAS-SN catalogs, as well as
various stellar activity indicators provided by the spectra.

#### Long-term photometry.

Solely focusing on the WASP data first, we found a signal of 21 days in the
periodogram. We confirmed this periodicity by implementing in juliet
(described in Sect. 5.1) a rotation term analog to the one in
celerite2141414https://celerite2.readthedocs.io/en/latest/ (Foreman-Mackey,
2018), which is the sum of two stochastically driven, damped harmonic
oscillator (SHO) terms. The power spectrum of each SHO term was given by
Anderson et al. (1990),

$\displaystyle\textnormal{SHO}_{1}(\omega_{\textnormal{GP}})=\sqrt{\frac{2}{\pi}}\frac{S_{0}\omega_{1}^{4}}{(\omega^{2}_{\textnormal{GP}}-\omega^{2}_{1})^{2}+\omega^{2}_{1}\omega_{\textnormal{GP}}^{2}/Q^{2}_{1}}$
(1a) and
$\displaystyle\textnormal{SHO}_{2}(\omega_{\textnormal{GP}})=\sqrt{\frac{2}{\pi}}\frac{S_{0}\omega_{2}^{4}}{(\omega^{2}_{\textnormal{GP}}-\omega^{2}_{2})^{2}+\omega^{2}_{2}\omega_{\textnormal{GP}}^{2}/Q^{2}_{2}},$
(1b) for which we applied the reparametrization using the hyperparameters
$\displaystyle Q_{1}$ $\displaystyle=0.5+Q_{0}+\delta Q$ (1c)
$\displaystyle\omega_{1}$ $\displaystyle=\frac{4\pi
Q_{1}}{P_{\textnormal{rot}}\sqrt{4Q_{1}^{2}-1}}$ (1d) $\displaystyle S_{1}$
$\displaystyle=\frac{\sigma_{\textnormal{GP}}^{2}}{(1+f)\omega_{1}Q_{1}}$ (1e)
$\displaystyle Q_{2}$ $\displaystyle=0.5+Q_{0}$ (1f) $\displaystyle\omega_{2}$
$\displaystyle=2\omega_{1}=\frac{8\pi
Q_{1}}{P_{\textnormal{rot}}\sqrt{4Q_{1}^{2}-1}}$ (1g) $\displaystyle S_{2}$
$\displaystyle=\frac{f\sigma_{\textnormal{GP}}^{2}}{(1+f)\omega_{2}Q_{2}},$
(1h)

and where $\sigma_{\textnormal{GP}}$ is the amplitude of the Gaussian process
(GP) kernel, $P_{\textnormal{rot}}$, is the primary period of the variability,
$Q_{0}$ is the quality factor for the secondary oscillation, $\delta Q$ is the
difference between the quality factors of the first and second oscillations,
and $f$ represents the fractional amplitude of the secondary oscillation with
respect to the primary one. These stated hyperparameters were used in the
analysis and are listed in Table 7. Such a kernel choice is well suited to
represent stellar signals modulated by the rotation period of the star because
of its flexible nature and smooth variations (e.g., Medina et al., 2020). We
adopted the double SHO (dSHO) because the SHO alone lacks the ability to model
the presence of more than one stellar spot (Jeffers & Keller, 2009).

The WASP data set consists of 11 seasons of data, where each was considered to
be an independent instrument with its own instrumental offset and jitter term.
The data of each instrument were nightly binned in order to cut down on
computational time, which does not create any problems because we are
searching for signals on the order of a few days. From the posterior results
(Fig. 4), we obtained a photometric stellar rotation period of
$P_{\textnormal{rot}}=21.37\pm 0.46$ d. However, as already mentioned in Sect.
3.2, both stars fall on the same pixel making it impossible to distinguish
whether the signal belongs to TOI-1201 or its companion, or even a combination
of both. However, the posterior distributions from the RVs suggest it to be an
individual signal originating from TOI-1201.

Figure 4: Probability density of the posterior samples for the estimated
rotational period of the star ($P_{\textnormal{rot}}$) when using a dSHO-GP to
fit the WASP (gray, 2008–2014) and ASAS-SN (blue, 2012–2019) data. The
posterior distributions for the RVs (orange, 2019–2020) come from the dSHO-GP
component in the final joint fit (Sect. 5.3).

Moving on, we followed the same analysis as on the WASP data set for the ASAS-
SN data. There were four different cameras (ba, bb, be, bf), which we treated
each as individual instruments with their own offsets and jitter terms, and
the GP hyperparameters were shared. The fit produces a GP rotational period of
$P_{\textnormal{rot}}=20.951\pm 0.025$ d. The quoted uncertainty is likely
much less than the true error given that star-spot patterns evolve over time
and, therefore, the rotational modulation is not coherent. Like before, the
data support a signal at 21 d but that cannot be attributed to one of the two
objects. In addition, the periodogram shows a sharp peak at $\sim$400 d that
might be attributed to a magnetic cycle of the star, though this was not
further investigated.

We also considered the TESS light curve before being corrected for systematics
(SAP flux) and simply divided the TESS sector 4 light curve into three chunks,
which we shifted using a sinusoidal signal with a period of 20.5$\pm$0.5 d and
amplitude variations of $\sim$6.7 ppt (Fig. 14). These data also support the
21 d signal, though yet again, the TESS pixel (21 arcsec) contains both
objects.

#### Spectroscopy.

We additionally inspected the various activity indicators from the
spectroscopic observations to further affirm the stellar activity presence.
TOI-1201 is a weakly H$\alpha$ active star (see Table 2), but only shows a
very moderate level of activity that appears to be relatively stable.

Correlations between the RVs and all activity indicators were computed using
Pearson’s p-probability and no strong or moderate correlations were found.
Notably, the chromospheric indicators (H$\alpha$ index, Ca ii IRT have the
tendency to show similar periods. The periodicities in the generalized Lomb-
Scargle (GLS) periodograms show power ranging from 19 d to 23 d (Fig. 5),
hinting toward the 21 d signal found in the photometry. The CRX, dLW,
H$\alpha$ index, Ca ii IRT, FWHM, TiO $\lambda\ 7050\,\AA$, and TiO $\lambda\
8430\,\AA$ all indicate some power in the range 19–23 d, with power of
sometimes $>$1 % false alarm probability (FAP), or broadly around $\sim$35–40
d, corresponding to an alias of the $\sim$21 d signal due to the sampling
frequency of 41 d found in the window function. The FAP levels were computed
following the theoretical levels (Eq. 24 in Zechmeister & Kürster, 2009). The
remaining activity indicators do not show any peaks of interest. This is
consistent with the results of Lafarga et al. (2021), who found that
periodicities from activity indices depend on the mass and activity level of
the star. They reported that, for less active stars, chromospheric lines are
more likely to indicate the true rotation period.

Additionally, the RVs themselves exhibit a peak at around 19 d (Fig. 6), which
is coincident with the CRX periodicity. When constructing our final model
described in Sect. 5.2, we took all the mentioned evidence above into
consideration to assume this signal to have quasi-periodic behavior. This
produced a periodicity of $P_{\textnormal{rot,\ RV}}=19.62^{+1.10}_{-0.81}$ d
and is plotted in comparison to the long-term photometric results in Fig. 4.

Figure 5:  GLS periodograms of the various stellar activity indicators from
the CARMENES spectroscopic data for TOI-1201. The vertical solid blue line
corresponds to the transiting planet (2.49 d) and the green one to the long-
term signal ($\sim$102 d) found in the RVs (Sect. 5.2). The vertical dashed
and dotted orange lines correspond to the rotational period present in the RVs
($\sim$19 d) and its alias ($\sim$35 d), respectively. The horizontal dotted,
dot-dashed, and dashed lines represent the 10 %, 1 %, and 0.1 % FAP levels.
The window function for the data set is displayed in Fig. 6.

To summarize, we see a $\sim$21 d signal in the photometry, a corresponding 19
d signal in the RVs, and a number of activity indicators peaking between 19–23
d. We, therefore, establish the rotational period of TOI-1201 to be 19–23 d.

##  5 Determination of planetary parameters for TOI-1201 b

###  5.1 Transit-only modeling

To first obtain refined values for the orbital period and transit time of the
transiting planet, we performed fits on just the given transit photometry
mentioned earlier in Sects. 2 and 3.1.

All modeling fits for this paper were done using
juliet151515https://juliet.readthedocs.io/en/latest/ (Espinoza et al., 2019a),
a python fitting package for joint-modeling (transit and RV) that uses nested
samplers to explore the prior volume in order to efficiently compute the
Bayesian model log evidence, $\ln\mathcal{Z}$. Though there are a variety of
nested samplers, we employed the dynamic nested sampling algorithm provided by
dynesty161616https://github.com/joshspeagle/dynesty (Speagle & Barbary, 2018;
Speagle, 2020) due to the large parameter space of our models. The juliet tool
makes use of the established python packages
radvel171717https://radvel.readthedocs.io/en/latest/ (Fulton et al., 2018) and
batman181818https://www.cfa.harvard.edu/~lkreidberg/batman/ (Kreidberg, 2015)
to model the RVs and transits, respectively. The GP kernels are implemented
via george191919https://george.readthedocs.io/en/latest/ (Ambikasaran et al.,
2015) and celerite202020https://celerite.readthedocs.io/en/stable/ (Foreman-
Mackey et al., 2017). For model comparison, we followed the general rule that
if $\Delta\ln\mathcal{Z}$ $\lesssim$ 2.5, then the two models are
indistinguishable and neither is preferred so the simpler model would then be
chosen (e.g., Trotta, 2008; Feroz et al., 2011). For any
$\Delta\ln\mathcal{Z}$ that is greater than 2.5, the one with the larger
Bayesian log evidence is moderately favored. Values greater than 5 indicate an
even stronger evidence advocating for the winning model.

For the transit model, we applied the following parameter transformations.
Instead of fitting directly for the planet-to-star radius ratio, $p\equiv
R_{p}/R_{\star}$, and the impact parameter of the orbit, $b$, we fit for the
parameters $r_{1}$ and $r_{2}$ (introduced by Espinoza, 2018) to ensure
uniform sampling of the $b$-$p$ plane. Additionally, we took advantage of our
derived stellar parameters coming from newer and more precise data (i.e., from
Gaia EDR3) to better constrain $a/R_{\star}$ from the transiting light curve.
Therefore, the scaled semimajor axis, $a/R_{\star}$, was replaced and re-
transformed by the stellar density, $\rho_{\star}$, as given in Table 2. The
TESS data were modeled jointly with a quadratic limb-darkening law (i.e., the
$q_{1}$ and $q_{2}$ parameters were shared among both TESS sectors), while the
ground-based instruments were assigned linear limb-darkening laws, both
parametrized with the uniform sampling scheme of Kipping (2013). The decision
to use a two-parameter law for TESS and a linear one for the ground-based
instruments was based on the work of Espinoza & Jordán (2016). While other
studies recommended the use of alternative limb-darkening laws, especially for
M dwarfs (Morello et al., 2017; Maxted, 2018), we performed some numerical
tests showing that the choice of law has a negligible impact relative to the
parameters precision ($<$0.2 $\sigma$). Instrumental offsets were considered,
as well as instrumental jitter terms, which were added in quadrature to the
given instrumental measurement uncertainty. The dilution factor, or the amount
that a light curve is diluted due to neighboring light pollution, was fixed to
one (i.e., no significant flux contamination) for each instrument. The TESS
light curve provided by the SPOC pipeline (Sect. 2) already takes this factor
into account and the apertures of the ground-based instruments were not
affected substantially by the neighboring bright companion. We performed fits
with a free dilution factor to verify this assumption
($\Delta\ln{\mathcal{Z}}=\ln{\mathcal{Z}}_{D=1.0}-\ln{\mathcal{Z}}_{D\neq
1.0}>6$).

To detrend time-correlated noise in the TESS sector 31 data, we adopted the
squared-exponential GP kernel

$k_{i,j}(\tau)=\sigma^{2}_{\textnormal{GP}}\exp\left(-\frac{\tau}{T_{\textnormal{GP}}}\right)$

where $\tau=|t_{i}-t_{j}|$ is the temporal distance between two points,
$\sigma_{\textnormal{GP}}$ is the amplitude of the GP modulation, and
$T_{\textnormal{GP}}$ is the characteristic timescale. This kernel is
characterized as being smooth since it is infinitely differentiable, which is
sufficient for the TESS sector 31 data but not for the data from TESS sector
4. To account for the roughness in the TESS sector 4 data, we applied the
(approximated) Mátern-3/2 kernel provided by celerite

$k_{i,j}(\tau)=\sigma^{2}_{\textnormal{GP}}\left(1+\frac{\sqrt{3}\tau}{\rho_{\textnormal{GP}}}\right)\exp\left(-\frac{\sqrt{3}\tau}{\rho_{\textnormal{GP}}}\right),$

where $\tau=|t_{i}-t_{j}|$ is again the temporal distance between two points
and $\sigma_{\textnormal{GP}}$ is the amplitude of the GP, but now
$\rho_{\textnormal{GP}}$ is the length scale of the GP modulations to vary the
smoothness of the return functions. Both TESS sectors had their own respective
GP amplitude ($\sigma_{\textnormal{GP}}$). As for the ground-based transit
photometry, we detrended the LCO-SAAO and LCO-SSO light curves with airmass
using a linear term. Based on the peaks using the transit-least-
squares212121https://github.com/hippke/tls method (Hippke & Heller, 2019), we
set up the prior on the period to be uniform, $\mathcal{U}(2.45,2.55)$, and
the ephemeris to be focused on the last transit in the data,
$\mathcal{U}(2459169.2,2459169.3)$. When combining all the transit
observations, we determined $P_{b}=2.49198582\pm 0.0000029$ d and $t_{0,b}$
(BJD-TDB) $=2459169.23219^{+0.00049}_{-0.00047}$ (barycentric Julian date-
temps dynamique barycentrique). These posterior values then served as a guide
for the priors for the final joint fit in Sect. 5.3.

###  5.2 RV-only modeling

To search for signals within the RV data, we first calculated the GLS
periodograms (Zechmeister & Kürster, 2009), approaching the data as if we had
no prior information on the transiting planet. We initially employed the Exo-
Striker222222https://github.com/3fon3fonov/exostriker (Trifonov, 2019) to
identify potential combinations of the signals present in the GLS that
describe the data appropriately. We used this information to build the priors
for our RV-only juliet runs. Fig. 6 shows a sequence of these GLS periodograms
after subtracting an increasing number of sinusoidal signals.

The 2.5 d signal only significantly appears after subtracting out the
dominating long-term signal at around $\sim$102 d (Fig. 6 b). The residuals
from simultaneously fitting two sinusoids for the 2.5 d and $\sim$102 d
signals then show two prominent, although not significant, peaks at 19 d and
35 d, which are aliases of one another (induced by a peak at 41 d found in the
window function). We attempted to determine which one of the two is the true
signal using AliasFinder232323https://github.com/JonasKemmer/AliasFinder
(Stock & Kemmer, 2020; Stock et al., 2020a). The algorithm follows the alias-
testing method described by Dawson & Fabrycky (2010), in which the
periodograms of simulated time series, injecting either of the two aliasing
signals, are compared to the periodogram of the original data set. The
injected signal that can best reproduce the data is deemed as the true period.
Still, it was not conclusive which one was the correct signal. Additionally,
we performed some juliet runs using both 19 d or 35 d as the true period, but
these were also inconclusive, as expected. Nonetheless, as was already
presented in Sect. 4.3, the 19 d signal is consistent with the rotational
period of the star based on ground-based photometry, as well as other stellar
activity indicators. After removing this 19 d signal with a sinusoid fit, the
resulting residuals show no further peaks in the GLS periodogram that would
indicate the presence of additional signals (Fig. 6).

To sum up, the CARMENES RV data show three significant signals: the transiting
planet (2.5 d), the stellar rotation period ($\sim$19 d), and a long-term
signal ($\sim$102 d). The next step was to compare various models to test
whether circular or eccentric Keplerian orbits were preferred, if the stellar
activity indicators (e.g., CRX, dLW) should be included as linear terms or
not, and to check what kind of impact a GP kernel may have. The runs are
listed in Table 4 and the priors in Table 7.

#### Transiting mini-Neptune.

For the transiting planet, TOI-1201 b, we fixed the priors for the period and
the transit time to the median values based on the posteriors from the
transit-only fits (Sect. 5.1) since the transit data provide us with very
well-determined values, such that the precision of the RV data would not be
able to. An eccentric orbit was indistinguishable from a circular one, where
most of the posterior samples were consistent with a zero eccentricity.
Therefore, we continued to model the transiting planet with a circular
Keplerian. Nevertheless, the current phase coverage (see Fig. 7) might not be
able to adequately recognize an eccentricity, which could affect certain
parameters (e.g., the semi-amplitude $K_{b}$, and subsequently, the planetary
mass). Filling in the phase coverage gaps with future, carefully planned RV
measurements will help constrain the eccentricity, though a circular orbit is
currently a reasonable assumption, given the short orbital period.

#### Stellar rotation period.

We tested fitting the stellar rotation signal at 19 d with a sinusoid and a
dSHO-GP kernel. The dSHO-GP kernel used was the same one as when determining
$P_{\textnormal{rot}}$ (Sect. 4.3) and introduced in Eq. 1. We implemented a
narrow prior for the period, $\mathcal{U}(15\,d,25\,d)$, which we named
GP${}_{\textnormal{19d}}$. The motivation for the narrow prior centered around
19 d was to avoid picking up periods (i.e., the alias at 35 d) not associated
with the stellar rotation.

The models between using a sinusoid and a GP were indistinguishable
($\Delta\ln{\mathcal{Z}}\sim 2$). Therefore, we decided to use the GP to
describe the nature of the 19 d signal. Given our prior knowledge that this
signal is physically produced by the stellar rotation period, the quasi-
periodic behavior of the GP better explains the underlying incoherent behavior
of a stellar activity signal that may not be exhibited with the current data
given the relatively short time span. Even if we choose to model the stellar
rotation period with a sinusoid, the minimum mass of the transiting planet is
not drastically affected, though the uncertainties are slightly enlarged (Fig.
15, specifically focusing on 1 Kep + 1 Sin + GP${}_{\textnormal{19d}}$ versus
1 Kep + 2 Sin).

In addition to the dSHO-GP, we also experimented with the quasi-periodic GP
kernel (QP-GP), as introduced in george and presented in Appendix A. Both GP
kernels were indistinguishable in their log evidence, so we chose the dSHO-GP,
as it serves our purpose to fit the quasi-periodic stellar activity signal
very well and, at the same time, is computationally much faster compared to
the QP-GP.

#### Long-term signal.

To account for the $\sim$102 d signal, we experimented with a quadratic trend,
a sinusoidal signal, and, for completeness, also a Keplerian model. We used a
wide, uniform prior for the period,
$\mathcal{U}(60\,\textnormal{d},150\,\textnormal{d})$, in all our models. For
the sinusoidal and the Keplerian model, the time of transit center was
additionally set uniform, $\mathcal{U}(2458730,2458840)$. Though the prior was
kept consistent for all attempted models, the median value of the posterior
distribution for the period varied to some extent due to different models,
finding slightly distinct optimized configurations depending on how the other
parameters were adjusted (Table 4). Compared to the quadratic model, the
sinusoidal signal is preferred
($\Delta\ln{\mathcal{Z}}=\ln{\mathcal{Z}}_{\textnormal{sinusoid}}-\ln{\mathcal{Z}}_{\textnormal{quadratic}}\sim
19$). The Keplerian model, with eccentricity varying freely, has a comparable
evidence to the purely sinusoidal signal. However, the posteriors favor in
this case a periodicity at $\sim$80 d with a relatively high eccentricity of
$\sim$0.5–0.6. The suggested high eccentricity is likely a result of only one
cycle or less being observed and the phase not being completely sampled (Fig.
7). With the current baseline, it is no longer possible to distinguish between
80 d and 102 d considering that 400 d of observations would be necessary
(i.e., $\Delta t_{\textnormal{baseline}}=$ (1/80 d – 1/102 d)-1). Therefore,
we continued to model the $\sim$102 d signal with the simplest, and better
constrained, model of a sinusoidal variation.

#### Final model choice.

We had the prior physical knowledge that there is a transiting planet at 2.5 d
and a stellar rotation signal at $\sim$19 d. For this reason, we expected
these two signals to appear in the RVs for which we modeled them with a
Keplerian and a GP, respectively. The most prominent signal in the data was,
however, the $\sim$102 d signal, which we could not ignore. To acknowledge the
signal, we modeled it with a sinusoid. Moreover, we did experiment what
happens if we were to apply a QP-GP with a wider prior for
$P_{\textnormal{rot}}$ (detailed in Appendix. A).

Nonetheless, to ensure that the parameters of the transiting planet were not
drastically affected by our model choice, we examined the minimum mass derived
from the RV-only fits (see Fig. 15). All considered models agree within their
uncertainties. Furthermore, no stellar activity indicator is significant in
power at the frequencies of the transiting planet ($\sim$2.5 d) or of the
$\sim$102 d signal (Fig. 5). Based on these results, we continued the analysis
with the 1 circular Kep (2.5 d) + 1 Sin ($\sim$102 d) + dSHO-
GP${}_{\textnormal{19d}}$ as the favored model. The final model choice
consists of 13 free parameters to the 33 RV data points. The transiting planet
follows a circular Keplerian model, the stellar rotation period is represented
with a dSHO-GP centered around the period of interest, and the most
significant signal at $\sim$102 d is modeled as a sinusoidal variation. We
emphasize that we do not claim the 102 d signal to be a planet candidate or a
photometric variability cycle. Considering that we only observed about one
period or less, we cannot elaborate on the nature of this signal and further
monitoring is needed in order to determine its origin.

Table 4: RV-only model comparison using the Bayesian log evidence for
TOI-1201.

Model |  $P$ (d) | $\ln{\mathcal{Z}}$ | $\Delta\ln{\mathcal{Z}}$
---|---|---|---
Flat | … | $-116.70$ | $-18.31$
1 Kep + 1 Sin + dSHO-GP${}_{\textnormal{19d}}$ | $\mathbf{2.5,102}$ | $\mathbf{-98.39}$ | $\mathbf{0.0}$
1 Kep + 1 Sin + dSHO-GP19d |  2.5**$*$An eccentric orbit was used., 102 | $-99.38$ | $-0.99$
2 Kep + dSHO-GP19d |  2.5, 88**$*$An eccentric orbit was used. | $-98.55$ | $-0.16$
1 Kep + Quad + dSHO-GP19d | 2.5 | $-116.99$ | $-18.61$
1 Kep + 2 Sin | 2.5, 19, 104 | $-100.24$ | $-1.85$
242424A larger, positive $\Delta\ln{\mathcal{Z}}$ indicates a better model. In
the model names, “Kep” refers to a Keplerian orbit and “Sin” to a sinusoidal
signal. The model that we used for the final joint fit was the 1 Kep (2.5 d) +
1 Sin (102 d) + dSHO-GP${}_{\textnormal{19d}}$, indicated by the bold-faced
row. The model names correspond to those in Fig. 15.

Figure 6:  GLS periodograms of the RV residuals after subtracting different
models for TOI-1201. The vertical solid blue line corresponds to the
transiting planet (2.5 d) and the green one to the long-term signal ($\sim$102
d). The vertical dashed and dotted orange lines correspond to the rotational
period picked up in the RVs ($\sim$19 d) and its alias ($\sim$35 d),
respectively. Panel (a): Window function of the data set. Panel (b): No signal
fitted, just the original RVs. Panel (c): Residuals after subtracting the
long-term signal at $\sim$102 d. Panel (d): Residuals after subtracting a
simultaneous model fit of two signals at 102 d and 2.5 d. Panel (e): Residuals
after subtracting a simultaneous model fit of three signals at 102 d, 19 d,
and 2.5 d. The horizontal dashed gray lines represent the FAP levels of 10 %,
1 %, and 0.1 % (from bottom to top).

###  5.3 Joint modeling

We finally combined all the data from the TESS observations, the ground-based
transit follow-ups, and the CARMENES RV data to produce the most precise
planetary parameters. Our final model comprises the 2.5 d transiting planet, a
stellar rotational period component at 19 d, and a long-term 102 d signal,
respectively modeled as a circular Keplerian, with a dSHO-GP centered on 19 d,
and a sinusoid (Sect. 5.2). We used the results from the posteriors of the
transit-only and RV-only fits to set up the priors for the final joint fit, as
discussed in detail and justified by Kemmer et al. (2020). These priors can be
found in Table 8.

Our findings from the joint fit, including the derived planetary parameters,
are presented in Table 5. The best model fits for the transit photometry and
the RVs are shown in Figs. 2 and 7, respectively. Table 9 is a comprehensive
posterior summary including all of the model parameters, where the posterior
probability densities are presented in Figs. 11, 12, and 13.

Table 5: Derived planetary parameters for TOI-1201 b. Parameter | Posterior | Unit
---|---|---
| TOI-1201 b |
$P_{p}$ | $2.4919863^{+0.0000030}_{-0.0000031}$ | d
$t_{0,p}$ (BJD) | $2459169.23222^{+0.00052}_{-0.00054}$ | d
$r_{1,p}$ | $0.603^{+0.048}_{-0.055}$ | $\dots$
$r_{2,p}$ | $0.04383^{+0.00096}_{-0.00110}$ | $\dots$
$K_{p}$ | $4.65^{+0.60}_{-0.64}$ | m s-1
$e_{p}$ |  $0.0$ (fixed) | $\dots$
$\omega_{p}$ |  $90.0$ (fixed) | $\dots$
$p=R_{p}/R_{\star}$ | $0.04383^{+0.00096}_{-0.00110}$ | $\dots$
$b=(a_{p}/R_{\star})\cos(i_{p})$ | $0.404^{+0.071}_{-0.082}$ | $\dots$
$a_{p}/R_{\star}$ | $12.23^{+0.36}_{-0.36}$ | $\dots$
$i_{p}$ | $88.11^{+0.42}_{-0.40}$ | deg
$t_{T}$ | $1.747^{+0.096}_{-0.091}$ | h
$M_{p}$ | $6.28^{+0.84}_{-0.88}$ | $M_{\oplus}$
$R_{p}$ | $2.415^{+0.091}_{-0.090}$ | $R_{\oplus}$
$\rho_{p}$ | $2.45^{+0.48}_{-0.42}$ | g cm-3
$g_{p}$ | $10.5^{+1.8}_{-1.6}$ | m s-2
$a_{p}$ | $0.0287^{+0.0012}_{-0.0012}$ | au
$T_{\textnormal{eq}}$ | $703^{+15}_{-14}$ | K
$S_{p}$ | $40.6^{+3.6}_{-3.2}$ | $S_{\oplus}$

##  6 Radial velocities of PM J02489–1432E

Most observations for the 8 arcsecond-wide companion of TOI-1201 were acquired
on the same nights as for the host star. As a result, with the high-resolution
spectra from CARMENES, we were able to compute very precise stellar parameters
for both stars in the binary system (Sect. 4). We then performed a
complementary analysis on the RVs and various stellar activity indicators of
the companion to search for potentially interesting signals. The GLS
periodogram of the RVs (second panel of Fig. 16) shows a significant peak at
27 d (above 10 % FAP level). Doing juliet runs, we compared the Bayesian log
evidence of a flat model, linear model, and a sinusoidal (i.e., circular
Keplerian) model. We found the best one to be the sinusoidal model at 28.5 d
with a semi-amplitude of $K$ = 3.42$\pm$0.89 m s-1 (see Table 6 for the
results and Fig. 17 for the RVs themselves). To investigate the nature of the
signal, we considered the same stellar activity indicators as mentioned in
Sect. 4.3. While no signals are significant, some power excess at $\sim$16 d
and $\sim$30 d, which are the 41 d aliases of one another, hint that the 28.5
d signal in the RVs might be somehow related to stellar activity (Fig. 16).
Given the similarity between the two stars, one would expect similar
$P_{\textnormal{rot}}$, too. However, given the small number of data points,
its origin remains inconclusive. Thus given the current data at hand,
additional RV data would be necessary for the companion of TOI-1201 to
determine the origin of this signal. Additionally, to test whether we could
detect a similar planet to TOI-1201 b orbiting PM J02489–1432E, we first
subtracted the 28 d periodicity and then followed the procedure as outlined by
Bonfils et al. (2013). We estimate that we can exclude planets above $\sim$6
$M_{\oplus}$ orbiting the companion with a period shorter than 10 d (Fig. 18).

Table 6: RV-only model comparison using the Bayesian log evidence for PM J02489–1432E (TOI-393). Model | $\ln{\mathcal{Z}}$ | $\Delta\ln{\mathcal{Z}}$
---|---|---
Flat | $-63.40$ | $-4.13$
Linear | $-71.38$ | $-12.11$
1 Sin (28.5 d) | $\mathbf{-59.27}$ | $\mathbf{0.0}$

Figure 7:  CARMENES RV data for TOI-1201 with the best-fit model from the
joint fit overplotted (dark gray), the dSHO-GP component (orange), and the
long-term signal (green). Top panel: RV time series. The light gray band
represents the 68 % credibility interval. Bottom panels: RVs phase-folded to
the periods of the transiting planet (left) and long-term signal (right). The
bottom panel of each plot shows the residuals after the model is subtracted.

##  7 Discussion and future prospects

We validate and characterize the exoplanet TOI-1201 b. The relatively hot
mini-Neptune orbits its host star every 2.49 d, has a radius of
$2.415^{+0.091}_{-0.090}\,R_{\oplus}$, a mass of
$6.28^{+0.84}_{-0.88}\,M_{\oplus}$, and a bulk density of
$2.45^{+0.48}_{-0.42}$ g cm-3. A summary of all derived planetary parameters
and their uncertainties can be found in Table 5. An additional signal at 102 d
is revealed in the RV data, whose origin is still unknown. If we were to
assume that it has a planetary origin, we would then obtain a period of
$P=102^{+21}_{-15}$ d and a semi-amplitude of $K=5.84^{+0.91}_{-0.87}$ m s-1
such that the minimum mass would be $27.0^{+5.6}_{-4.5}\,M_{\oplus}$. TOI-1201
could thus be a multi-planetary system (see Appendix C), making further
monitoring quite appealing. Additionally, the RV data show a 19 d signal
corresponding to the $\sim$21 d rotational period of the star as inferred by
photometry. Below we discuss the plentiful potential that TOI-1201 b has for
future follow-up observations and characterizations of the system.

#### Spin-orbit alignment.

Following Boué et al. (2013), the expected Rossiter-McLaughlin (RM; Rossiter,
1924; McLaughlin, 1924) amplitude is in the range $K_{RM}\sim$ 1.5–3.0 m s-1,
since the $v\sin i$ of the star (¡ 2 km s-1) and the spin-orbit angle are not
exactly defined. Collecting roughly ten data points within the transit
(duration of $1.8\pm 0.1$ h) to achieve a precision better than the RM
amplitude is well within reach for the current state-of-the-art spectrographs
with sub-m s-1 precision such as ESPRESSO (Pepe et al., 2021), MAROON-X
(Seifahrt et al., 2018), or EXPRES (Jurgenson et al., 2016).

For this reason, the mini-Neptune TOI-1201 b presents itself as a promising
candidate for measuring the spin-orbit angle between the stellar spin axis and
orbit of the transiting planet, which can be determined by the RM effect.
Studying this effect can shed light on orbital architectures of planetary
systems specifically around low-mass stars. It is expected that close-orbiting
giant planets around such stars are aligned (Gaudi & Winn, 2007; Winn et al.,
2010; Muñoz & Perets, 2018; Louden et al., 2021) because of strong tidal
interactions with the stellar convective envelope. To date, there are only six
other planets around M dwarfs with measured obliquities, namely GJ~436 b
(Bourrier et al., 2018), TRAPPIST-1 b, e, f (Hirano et al., 2020a), AU~Mic b
(Addison et al., 2020; Hirano et al., 2020b; Palle et al., 2020), and K2-25 b
(Stefansson et al., 2020). Determining the spin-orbit angle of TOI-1201 b is
especially interesting in the context of the companion (320 au away) because
it could hint possible interaction.

#### Transmission spectroscopy.

All the currently known transiting exoplanets with a measured mass (with
precision better than 20 %) are displayed in Fig. 8. TOI-1201 b falls in the
realm of Neptune-sized planets above the M-dwarf radius valley (Fig. 7 in Van
Eylen et al., 2021, $R$ = 1.4–1.7 $R_{\oplus}$). In this regard, the density
of $\rho_{b}=2.45^{+0.48}_{-0.42}$ g cm-3 suggests that its composition is in
line with an Earth-like rocky core with an H-He envelope of 0.3 % by mass,
following the theoretical composition models from Zeng et al.
(2019)252525https://lweb.cfa.harvard.edu/~lzeng/planetmodels.html. Likewise,
it is consistent with being a water world, signifying that its internal
composition is rather dominated with H2O in the form of ices and fluids, which
is also a very plausible scenario in the realm of planet formation (e.g.,
Bitsch et al., 2019; Venturini et al., 2020). Atmosphere characterization via
transmission spectroscopy paired with precise mass and radius determinations
and a good set of interior models could aid in breaking this ambiguity of its
interior architecture.

Figure 8: Mass-radius diagram based on the TEPcat catalog (Southworth, 2011,
visited on 10 August 2021). TOI-1201 b is indicated as a red star outlined in
black. The gray points represent the other planets ($R<3\,R_{\oplus}$ and
$M<12\,M_{\oplus}$) with masses and radii measured to precision better than 20
%. The red points are those planets around M dwarfs
($T_{\textnormal{eff}}<4000$ K). All theoretical composition models are taken
from Zeng et al. (2019). The lines represent models for cores composed of pure
iron (100 % Fe), Earth-like composition (32.5 % Fe + 67.5 % MgSiO3), pure rock
(100 % MgSiO3), and pure water (100 % H2O at 700 K). The area between the
solid and dash-dotted lines of the same color represent the theoretical
composition models for Earth-like rocky cores with varying sizes of H-He
envelopes (0.1 %, 0.3 %, 1 %) for equilibrium temperatures of 700 K and 1000
K, respectively. The plot is inspired by Van Eylen et al. (2021), though
presented here in linear scale to emphasize the mini-Neptune population.

Following Kempton et al. (2018), the transmission spectroscopy metric (TSM) of
TOI-1201 b turns out to be $97^{+21}_{-16}$, which is slightly above the
cutoff of 92 with the JWST/NIRISS bandpass (for planet radii of 1.5
$R_{\oplus}$ ¡ $R_{p}$ ¡ 2.75 $R_{\oplus}$). Among other transiting planets
with masses measured via RVs or transit time variations around M dwarfs
(Trifonov et al., 2021)262626Using the continuously updated table:
https://carmenes.caha.es/ext/tmp/. Last updated on 09 April 2021., TOI-1201 b
is ranked high and one of just a few suitable targets known thus far (Fig. 9).
It is besides an intriguing candidate for comparison with GJ 1214 b, which has
similar mass and radius but a slightly lower equilibrium temperature ($8.17\pm
0.43$$M_{\oplus}$, $2.742\pm 0.053$$R_{\oplus}$, $596\pm 19$ K; Cloutier et
al., 2021). GJ 1214 b is known to have high-altitude clouds or haze (Kreidberg
et al., 2014), but the higher temperatures of TOI-1201 b may lead to less
cloudy or hazy atmospheres (Crossfield & Kreidberg, 2017). In preparation for
the presumed launch of JWST in late 2021, our transit ephemeris from the joint
fit (see Table 5) results in an uncertainty of $\sim$60 s toward the beginning
of 2022. The uncertainty then increases to $\sim$100 s and $\sim$140 s for the
beginning of 2023 and 2024, respectively. Further ground-based observations
could help refine the ephemeris and further improve the planet radius.
Moreover, TOI-1201 is a viable target for space-based follow-up observations
with CHEOPS (Benz et al., 2021). The visibility is good given its ecliptic
latitude, allowing it to be observed for an accumulated time of 60 days in one
year. Blending is expected because the size of the PSF of CHEOPS is
approximately 16 arcsec. Using the typical aperture radius of 20–25 arcsec for
a star with the brightness of TOI-1201, however, the final extracted flux
would simply be the added flux of both stars and can be easily mediated with a
dilution factor taken into account when using juliet (Espinoza et al., 2019a).

Likewise, TOI-1201 b is ideal for low-to-mid-resolution ground-based transit
spectroscopy covering the optical regime, serving as a great complement to the
expected near- and mid-IR wavelength range measurements from JWST. These
ground-based observations are typically challenging due to strong atmospheric
and instrumental variations (e.g., Nikolov et al., 2016; Huitson et al., 2017;
Diamond-Lowe et al., 2018; Espinoza et al., 2019b; Wilson et al., 2021; Chen
et al., 2021). Companion stars that are close in brightness and space to the
target star help mitigate these effects since both stars experience a similar
path through the Earth’s atmosphere and the instrument, allowing the effects
from the target star to be monitored and removed. In this regard, the binary
companion PM~J02489–1432E, which has very similar stellar properties (see
Table 2), is a perfect star to detrend atmospheric and instrumental effects
from TOI-1201’s light curve.

Furthermore, the relatively young age of the system (600–800 Myr) makes
TOI-1201 b an intriguing object for studying the future preservation or
evaporation of the atmosphere. Planets found above the radius gap are in the
process of losing their atmospheres through two conceivable mechanisms with
corresponding timescales of $\sim$1 Gyr due to core-powered mass loss (Gupta &
Schlichting, 2020) or of $\sim$100 Myr due to photoevaporation (Owen & Wu,
2017). Other currently known transiting mini-Neptunes planets with mass
determinations in young systems orbit stellar hosts are too faint for
atmospheric characterization ($J>$ 11 mag), for example, K2-25 (Mann et al.,
2016; Stefansson et al., 2020; Thao et al., 2020), EPIC-247589423 (Mann et
al., 2018), K2-264 (Rizzuto et al., 2018; Livingston et al., 2019), and
K2-101, K2-101, K2-103, K2-104, EPIC-211901114, and K2-95 (Mann et al., 2017).
The only suitable candidate orbiting a sufficiently bright host star for this
selective target sample is K2-100 b (Barragán et al., 2019; Gaidos et al.,
2020). Thus, the relative brightness ($J\approx$ 9.5 mag) and intermediate age
of the TOI-1201 system can help constrain the empirical timescale for
evaporation and provide a test case for the two possible theories.

TOI-1201 b is, therefore, a very compelling candidate for atmospheric
characterization using transmission spectroscopy. Determining the atmospheric
compositions will allow for a better understanding of the formation histories
of mini-Neptunes and aid in characterizing them.

Figure 9: Transmission spectroscopy metric (TSM) as a function of $J$
magnitude for currently known transiting Neptune-sized planets around M dwarfs
with a measured mass. The color of each point corresponds to its respective
radius bin as defined by Kempton et al. (2018). Furthermore, promising targets
that are above their respective radius-bin cutoff are labeled and marked with
a circle, and those below the cutoff are represented with an upsidedown
triangle. The uncertainties are only computed for TOI-1201 b.

#### Planet occurrence rates around M-dwarf binary systems.

Most surveys are strongly biased against stars in known binary or multiple
systems, introducing a selection bias against them. As already mentioned in
Sect. 1, many planets discovered around M-dwarf binary systems are in systems
with a wide separation. The same is true for TOI-1201 ($s\sim$ 320 au).
Therefore, the TOI-1201 system most likely does not face significant
gravitational interactions with its companion to hinder planet formation. In
this respect, it is essentially identical to a system around a single star
(Desidera & Barbieri, 2007; Roell et al., 2012). Interestingly enough, in all
of these systems, the stars are quite different in spectral type, with the
exception of GJ 338 ABb (M0 V+M0 V; González-Álvarez et al., 2020), TOI-1201
(M2.0 V+M2.5 V; this paper), and LTT 1445 AbBC (M-dwarf trio of similar
masses; Winters et al., 2019b).

Unlike most other systems, where spectroscopic measurements and precise
stellar parameters are available only for the primary, PM J02489–-1432E, the
stellar companion of TOI-1201 has also been well characterized in this paper.
No signal indicative of a planet was found for this star (Sect. 6). For
comparison, this is also the case for the stellar companion of GJ 338 B. Even
though the two stars in each system are very similar in mass (and age), they
have different planetary architecture. As for the LTT~1445 system, RV
measurements were carried out only for the host star providing an upper mass
limit for the planet, though further observations are underway in determining
its mass.

##  8 Conclusions

In this paper we presented TESS and ground-based photometric observations,
together with CARMENES spectroscopic measurements, of the early M dwarf
TOI-1201. We confirmed the transiting planet with a period of about 2.5 d and
provided a mass determination using RV follow-up to obtain the following
derived planetary parameters: $2.415^{+0.091}_{-0.090}\,R_{\oplus}$ for the
radius and $6.28^{+0.84}_{-0.88}\,M_{\oplus}$ for the mass. This transiting
planet then carries a density of $2.45^{+0.48}_{-0.42}$ g cm-3, classifying it
as a mini-Neptune. The planet is a favorable target for further studies,
namely: (i) spin-orbit alignment using the RM effect, which is achievable with
the current spectroscopic instruments, and (ii) atmospheric studies using
transmission spectroscopy with ground-based facilities (which is possible
thanks to its nearly identical, close-by companion) and with upcoming space-
based missions, such as JWST. The relatively young age of the system
($\sim$600–800 Myr) gives it the additional advantage of potentially
constraining the timescales of currently accepted atmospheric mass-loss
mechanisms.

The RVs also exhibited a long-term signal with a high semi-amplitude at
$\sim$102 d. If the signal is due to an additional planet in the system, then
its minimum mass would be $27.0^{+5.6}_{-4.5}\,M_{\oplus}$. Such system
architectures are commonly reproduced in core accretion formation models (see
Appendix C and Schlecker et al., 2020). Further RV measurements are, however,
necessary to falsify or to prove a planetary origin of the signal, which could
provide more insight into the architecture of multi-planetary systems.

We were able to narrow down the stellar rotation period for TOI-1201 to 19–23
d using archival long-term photometry and stellar activity indicators provided
by the spectral information. The signature of the stellar rotation period also
presented itself in the RVs, which we take into account in our final model.
The stellar host is the primary of a wide ($s\sim$ 320 au) binary system of
two nearly identical M2.0–2.5 dwarfs. We obtained CARMENES RV measurements for
the secondary as well, providing precise stellar parameters. One significant
signal at around 27 d, most likely related to the stellar rotation period, was
detected around the companion.

All things considered, the TOI-1201 system contains two low-mass stars at
relatively short separation, and around one of them there is at least one
transiting mini-Neptune with a precise mass determination and with favorable
opportunities for atmospheric characterization. However, despite the high
quality data on hand and the comprehensive analyses performed, there remain
unanswered questions, the answers to which require further monitoring.

###### Acknowledgements.

Part of this work was supported by the German Deutsche Forschungsgemeinschaft
(DFG) project number Ts 17/2–1. CARMENES is an instrument at the Centro
Astronómico Hispano-Alemán (CAHA) at Calar Alto (Almería, Spain), operated
jointly by the Junta de Andalucía and the Instituto de Astrofísica de
Andalucía (CSIC). CARMENES was funded by the Max-Planck-Gesellschaft (MPG),
the Consejo Superior de Investigaciones Científicas (CSIC), the Ministerio de
Economía y Competitividad (MINECO) and the European Regional Development Fund
(ERDF) through projects FICTS-2011-02, ICTS-2017-07-CAHA-4, and
CAHA16-CE-3978, and the members of the CARMENES Consortium (Max-Planck-
Institut für Astronomie, Instituto de Astrofísica de Andalucía,
Landessternwarte Königstuhl, Institut de Ciències de l’Espai, Institut für
Astrophysik Göttingen, Universidad Complutense de Madrid, Thüringer
Landessternwarte Tautenburg, Instituto de Astrofísica de Canarias, Hamburger
Sternwarte, Centro de Astrobiología and Centro Astronómico Hispano-Alemán),
with additional contributions by the MINECO, the Deutsche
Forschungsgemeinschaft through the Major Research Instrumentation Programme
and Research Unit FOR2544 “Blue Planets around Red Stars”, the Klaus Tschira
Stiftung, the states of Baden-Württemberg and Niedersachsen, and by the Junta
de Andalucía. This work was based on data from the CARMENES data archive at
CAB (CSIC-INTA). We acknowledge financial support from the Agencia Estatal de
Investigación of the Ministerio de Ciencia, Innovación y Universidades and the
ERDF through projects PID2019-109522GB-C5[1:4]/AEI/10.13039/501100011033 and
the Centre of Excellence “Severo Ochoa” and “María de Maeztu” awards to the
Instituto de Astrofísica de Canarias (SEV-2015-0548), Instituto de Astrofísica
de Andalucía (SEV-2017-0709), and Centro de Astrobiología (MDM-2017-0737), the
European Research Council under the Horizon 2020 Framework Program (ERC
Advanced Grant Origins 83 24 28), the Generalitat de Catalunya/CERCA
programme, the DFG priority program SPP 1992 “Exploring the Diversity of
Extrasolar Planets (JE 701/5-1)”, the European Research Council under the
Horizon 2020 Framework Program via ERC Advanced Grant Origins 832428 and under
Marie Skłodowska-Curie grant 895525. Funding for the TESS mission is provided
by NASA’s Science Mission Directorate. This paper includes data collected by
the TESS mission that are publicly available from the Mikulski Archive for
Space Telescopes (MAST). We acknowledge the use of public TESS data from
pipelines at the TESS Science Office and at the TESS Science Processing
Operations Center. Resources supporting this work were provided by the NASA
High-End Computing (HEC) Program through the NASA Advanced Supercomputing
(NAS) Division at Ames Research Center for the production of the SPOC data
products. This work makes use of observations from the LCOGT network. Part of
the LCOGT telescope time was granted by NOIRLab through the Mid-Scale
Innovations Program (MSIP). MSIP is funded by NSF. We thank Brian Mason for
providing us WDS data.

## References

  * Addison et al. (2020) Addison, B. C., Horner, J., Wittenmyer, R. A., et al. 2020, arXiv e-prints, arXiv:2006.13675
  * Alam et al. (2015) Alam, S., Albareti, F. D., Allende Prieto, C., et al. 2015, ApJS, 219, 12
  * 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
  * Anderson et al. (1990) Anderson, E. R., Duvall, Thomas L., J., & Jefferies, S. M. 1990, ApJ, 364, 699
  * Barnes et al. (2009) Barnes, R., Jackson, B., Raymond, S. N., West, A. A., & Greenberg, R. 2009, ApJ, 695, 1006
  * Barragán et al. (2019) Barragán, O., Aigrain, S., Kubyshkina, D., et al. 2019, MNRAS, 490, 698
  * Bauer et al. (2020) Bauer, F. F., Zechmeister, M., Kaminski, A., et al. 2020, A&A, 640, A50
  * Bean et al. (2021) Bean, J. L., Raymond, S. N., & Owen, J. E. 2021, JGR (Planets), 126, e06639
  * Benneke & Seager (2013) Benneke, B. & Seager, S. 2013, ApJ, 778, 153
  * Benz et al. (2021) Benz, W., Broeg, C., Fortier, A., et al. 2021, Experimental Astronomy, 51, 109
  * Bianchi et al. (2011) Bianchi, L., Herald, J., Efremova, B., et al. 2011, Ap&SS, 335, 161
  * Bitsch et al. (2019) Bitsch, B., Raymond, S. N., & Izidoro, A. 2019, A&A, 624, A109
  * Bonfils et al. (2013) Bonfils, X., Delfosse, X., Udry, S., et al. 2013, A&A, 549, A109
  * Borucki et al. (2010) Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, 327, 977
  * Boué et al. (2013) Boué, G., Montalto, M., Boisse, I., Oshagh, M., & Santos, N. C. 2013, A&A, 550, A53
  * Bourrier et al. (2018) Bourrier, V., Lovis, C., Beust, H., et al. 2018, Nature, 553, 477
  * Brown et al. (2013) Brown, T. M., Baliber, N., Bianco, F. B., et al. 2013, PASP, 125, 1031
  * Burn et al. (2021) Burn, R., Schlecker, M., Mordasini, C., et al. 2021, arXiv e-prints, arXiv:2105.04596
  * Caballero (2010) Caballero, J. A. 2010, A&A, 514, A18
  * Caballero et al. (2016a) Caballero, J. A., Cortés-Contreras, M., Alonso-Floriano, F. J., et al. 2016a, in 19th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun (CS19), 148
  * Caballero et al. (2016b) Caballero, J. A., Guàrdia, J., López del Fresno, M., et al. 2016b, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9910, Observatory Operations: Strategies, Processes, and Systems VI, ed. A. B. Peck, R. L. Seaman, & C. R. Benn, 99100E
  * Chen et al. (2021) Chen, G., Pallé, E., Parviainen, H., et al. 2021, MNRAS, 500, 5420
  * Cifuentes et al. (2020) Cifuentes, C., Caballero, J. A., Cortés-Contreras, M., et al. 2020, A&A, 642, A115
  * Cloutier et al. (2021) Cloutier, R., Charbonneau, D., Deming, D., Bonfils, X., & Astudillo-Defru, N. 2021, arXiv e-prints, arXiv:2107.14732
  * 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
  * Cortés-Contreras et al. (2017) Cortés-Contreras, M., Béjar, V. J. S., Caballero, J. A., et al. 2017, A&A, 597, A47
  * Crossfield & Kreidberg (2017) Crossfield, I. J. M. & Kreidberg, L. 2017, AJ, 154, 261
  * Curtis et al. (2019) Curtis, J. L., Agüeros, M. A., Mamajek, E. E., Wright, J. T., & Cummings, J. D. 2019, AJ, 158, 77
  * Cutri & et al. (2012) Cutri, R. M. & et al. 2012, VizieR Online Data Catalog, 2311
  * Cutri & et al. (2014) Cutri, R. M. & et al. 2014, VizieR Online Data Catalog, 2328
  * Dawson & Fabrycky (2010) Dawson, R. I. & Fabrycky, D. C. 2010, ApJ, 722, 937
  * Deacon et al. (2016) Deacon, N. R., Kraus, A. L., Mann, A. W., et al. 2016, MNRAS, 455, 4212
  * Desidera & Barbieri (2007) Desidera, S. & Barbieri, M. 2007, A&A, 462, 345
  * Diamond-Lowe et al. (2018) Diamond-Lowe, H., Berta-Thompson, Z., Charbonneau, D., & Kempton, E. M.-R. 2018, The Astronomical Journal, 156, 42
  * Douglas et al. (2019) Douglas, S. T., Curtis, J. L., Agüeros, M. A., et al. 2019, ApJ, 879, 100
  * Dressing & Charbonneau (2013) Dressing, C. D. & Charbonneau, D. 2013, ApJ, 767, 95
  * Dressing & Charbonneau (2015) Dressing, C. D. & Charbonneau, D. 2015, ApJ, 807, 45
  * Duquennoy & Mayor (1991) Duquennoy, A. & Mayor, M. 1991, A&A, 500, 337
  * Eggen (1958) Eggen, O. J. 1958, MNRAS, 118, 65
  * Eggen (1984) Eggen, O. J. 1984, AJ, 89, 1358
  * El-Badry & Rix (2018) El-Badry, K. & Rix, H.-W. 2018, MNRAS, 480, 4884
  * Emsenhuber et al. (2020) Emsenhuber, A., Mordasini, C., Burn, R., et al. 2020 [arXiv:2007.05561]
  * Epchtein et al. (1997) Epchtein, N., de Batz, B., Capoani, L., et al. 1997, The Messenger, 87, 27
  * Espinoza (2018) Espinoza, N. 2018, Research Notes of the AAS, 2, 209
  * Espinoza & Jordán (2016) Espinoza, N. & Jordán, A. 2016, MNRAS, 457, 3573
  * Espinoza et al. (2019a) Espinoza, N., Kossakowski, D., & Brahm, R. 2019a, MNRAS, 490, 2262
  * Espinoza et al. (2019b) Espinoza, N., Rackham, B. V., Jordán, A., et al. 2019b, MNRAS, 482, 2065
  * Fang et al. (2018) Fang, X.-S., Zhao, G., Zhao, J.-K., & Bharat Kumar, Y. 2018, MNRAS, 476, 908
  * Feroz et al. (2011) Feroz, F., Balan, S. T., & Hobson, M. P. 2011, MNRAS, 415, 3462
  * Foreman-Mackey (2018) Foreman-Mackey, D. 2018, RNAAS, 2, 31
  * Foreman-Mackey et al. (2017) Foreman-Mackey, D., Agol, E., Ambikasaran, S., & Angus, R. 2017, AJ, 154, 220
  * Frith et al. (2013) Frith, J., Pinfield, D. J., Jones, H. R. A., et al. 2013, MNRAS, 435, 2161
  * Fulton & Petigura (2018) Fulton, B. J. & Petigura, E. A. 2018, AJ, 156, 264
  * 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
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Smart, R. L., Sarro, L. M., et al. 2021, A&A, 649, A6
  * Gaidos et al. (2020) Gaidos, E., Hirano, T., Mann, A. W., et al. 2020, MNRAS, 495, 650
  * Gardner et al. (2009) Gardner, J. P., Mather, J. C., Clampin, M., et al. 2009, Astrophysics and Space Science Proceedings, 10, 1
  * Gaudi & Winn (2007) Gaudi, B. S. & Winn, J. N. 2007, ApJ, 655, 550
  * Ginzburg et al. (2016) Ginzburg, S., Schlichting, H. E., & Sari, R. 2016, ApJ, 825, 29
  * Ginzburg et al. (2018) Ginzburg, S., Schlichting, H. E., & Sari, R. 2018, MNRAS, 476, 759
  * González-Álvarez et al. (2020) González-Álvarez, E., Zapatero Osorio, M. R., Caballero, J. A., et al. 2020, A&A, 637, A93
  * Goodwin et al. (2007) Goodwin, S. P., Kroupa, P., Goodman, A., & Burkert, A. 2007, in Protostars and Planets V, ed. B. Reipurth, D. Jewitt, & K. Keil, 133
  * Goodwin et al. (2008) Goodwin, S. P., Nutter, D., Kroupa, P., Ward-Thompson, D., & Whitworth, A. P. 2008, A&A, 477, 823
  * Gupta & Schlichting (2019) Gupta, A. & Schlichting, H. E. 2019, MNRAS, 487, 24
  * Gupta & Schlichting (2020) Gupta, A. & Schlichting, H. E. 2020, MNRAS, 493, 792
  * Gupta & Schlichting (2021) Gupta, A. & Schlichting, H. E. 2021, MNRAS, 504, 4634
  * Hambly et al. (2001) Hambly, N. C., MacGillivray, H. T., Read, M. A., et al. 2001, MNRAS, 326, 1279
  * Henry et al. (2006) Henry, T. J., Jao, W.-C., Subasavage, J. P., et al. 2006, AJ, 132, 2360
  * Hippke & Heller (2019) Hippke, M. & Heller, R. 2019, A&A, 623, A39
  * Hirano et al. (2020a) Hirano, T., Gaidos, E., Winn, J. N., et al. 2020a, ApJ, 890, L27
  * Hirano et al. (2020b) Hirano, T., Krishnamurthy, V., Gaidos, E., et al. 2020b, ApJ, 899, L13
  * Hobson et al. (2018) Hobson, M. J., Jofré, E., García, L., Petrucci, R., & Gómez, M. 2018, RMxAA, 54, 65
  * Howard et al. (2014) Howard, A. W., Marcy, G. W., Fischer, D. A., et al. 2014, ApJ, 794, 51
  * Howell et al. (2014) Howell, S. B., Sobeck, C., Haas, M., et al. 2014, PASP, 126, 398
  * Huitson et al. (2017) Huitson, C. M., Désert, J. M., Bean, J. L., et al. 2017, AJ, 154, 95
  * Janson et al. (2014) Janson, M., Bergfors, C., Brandner, W., et al. 2014, ApJ, 789, 102
  * Janson et al. (2012) Janson, M., Hormuth, F., Bergfors, C., et al. 2012, ApJ, 754, 44
  * Jeffers & Keller (2009) Jeffers, S. V. & Keller, C. U. 2009, in American Institute of Physics Conference Series, Vol. 1094, 15th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, ed. E. Stempels, 664–667
  * Jeffers et al. (2018) Jeffers, S. V., Schöfer, P., Lamert, A., et al. 2018, A&A, 614, A76
  * 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, ed. G. Chiozzi & J. C. Guzman, 99133E
  * Jensen (2013) Jensen, E. 2013, Tapir: A web interface for transit/eclipse observability, Astrophysics Source Code Library
  * Johnson & Soderblom (1987) Johnson, D. R. H. & Soderblom, D. R. 1987, AJ, 93, 864
  * Johnson & Li (2012) Johnson, J. L. & Li, H. 2012, ApJ, 751, 81
  * Jurgenson et al. (2016) Jurgenson, C., Fischer, D., McCracken, T., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9908, Ground-based and Airborne Instrumentation for Astronomy VI, ed. C. J. Evans, L. Simard, & H. Takami, 99086T
  * Kaiser et al. (2010) Kaiser, N., Burgett, W., Chambers, K., et al. 2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7733, Ground-based and Airborne Telescopes III, ed. L. M. Stepp, R. Gilmozzi, & H. J. Hall, 77330E
  * Kaminski et al. (2018) Kaminski, A., Trifonov, T., Caballero, J. A., et al. 2018, A&A, 618, A115
  * Kemmer et al. (2020) Kemmer, J., Stock, S., Kossakowski, D., et al. 2020, A&A, 642, A236
  * Kempton et al. (2018) Kempton, E. M. R., Bean, J. L., Louie, D. R., et al. 2018, PASP, 130, 114401
  * Kipping (2013) Kipping, D. M. 2013, MNRAS, 435, 2152
  * Knapp & Nanson (2019) Knapp, W. & Nanson, J. 2019, Journal of Double Star Observations, 15, 21
  * Kochanek et al. (2017) Kochanek, C. S., Shappee, B. J., Stanek, K. Z., et al. 2017, PASP, 129, 104502
  * Kordopatis et al. (2013) Kordopatis, G., Gilmore, G., Steinmetz, M., et al. 2013, AJ, 146, 134
  * 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
  * Lafarga et al. (2020) Lafarga, M., Ribas, I., Lovis, C., et al. 2020, A&A, 636, A36
  * Lafarga et al. (2021) Lafarga, M., Ribas, I., Reiners, A., et al. 2021, A&A, 652, A28
  * Lawrence et al. (2007) Lawrence, A., Warren, S. J., Almaini, O., et al. 2007, MNRAS, 379, 1599
  * Lehmer & Catling (2017) Lehmer, O. R. & Catling, D. C. 2017, ApJ, 845, 130
  * Lépine & Gaidos (2011) Lépine, S. & Gaidos, E. 2011, AJ, 142, 138
  * Livingston et al. (2019) Livingston, J. H., Dai, F., Hirano, T., et al. 2019, MNRAS, 484, 8
  * Lodieu et al. (2019a) Lodieu, N., Pérez-Garrido, A., Smart, R. L., & Silvotti, R. 2019a, 628, A66
  * Lodieu et al. (2018) Lodieu, N., Rebolo, R., & Pérez-Garrido, A. 2018, 615, L12
  * Lodieu et al. (2019b) Lodieu, N., Smart, R. L., Pérez-Garrido, A., & Silvotti, R. 2019b, 623, A35
  * López & Fortney (2014) López, E. D. & Fortney, J. J. 2014, ApJ, 792, 1
  * Louden et al. (2021) Louden, E. M., Winn, J. N., Petigura, E. A., et al. 2021, AJ, 161, 68
  * Makarov & Kaplan (2005) Makarov, V. V. & Kaplan, G. H. 2005, AJ, 129, 2420
  * Mann et al. (2016) Mann, A. W., Gaidos, E., Mace, G. N., et al. 2016, ApJ, 818, 46
  * Mann et al. (2017) Mann, A. W., Gaidos, E., Vanderburg, A., et al. 2017, AJ, 153, 64
  * Mann et al. (2018) Mann, A. W., Vanderburg, A., Rizzuto, A. C., et al. 2018, AJ, 155, 4
  * Marcy et al. (2014) Marcy, G. W., Weiss, L. M., Petigura, E. A., et al. 2014, PNAS, 111, 12655
  * Marocco et al. (2021) Marocco, F., Eisenhardt, P. R. M., Fowler, J. W., et al. 2021, ApJS, 253, 8
  * Martín et al. (2018) Martín, E. L., Lodieu, N., Pavlenko, Y., & Béjar, V. J. S. 2018, ApJ, 856, 40
  * Mason et al. (2001) Mason, B. D., Wycoff, G. L., Hartkopf, W. I., Douglass, G. G., & Worley, C. E. 2001, AJ, 122, 3466
  * Mathur et al. (2017) Mathur, S., Huber, D., Batalha, N. M., et al. 2017, ApJS, 229, 30
  * Maxted (2018) Maxted, P. F. L. 2018, A&A, 616, A39
  * McLaughlin (1924) McLaughlin, D. B. 1924, ApJ, 60, 22
  * Medina et al. (2020) Medina, A. A., Winters, J. G., Irwin, J. M., & Charbonneau, D. 2020, ApJ, 905, 107
  * Miller-Ricci & Fortney (2010) Miller-Ricci, E. & Fortney, J. J. 2010, ApJ, 716, L74
  * Monet et al. (2003) Monet, D. G., Levine, S. E., Canzian, B., et al. 2003, AJ, 125, 984
  * Monnier et al. (2018) Monnier, J. D., Kraus, S., Ireland, M. J., et al. 2018, Experimental Astronomy, 46, 517
  * Montes et al. (2018) Montes, D., González-Peinado, R., Tabernero, H. M., et al. 2018, MNRAS, 479, 1332
  * Montes et al. (2001) Montes, D., López-Santiago, J., Gálvez, M. C., et al. 2001, MNRAS, 328, 45
  * Mordasini (2020) Mordasini, C. 2020, A&A, 638, A52
  * Morello et al. (2017) Morello, G., Tsiaras, A., Howarth, I. D., & Homeier, D. 2017, AJ, 154, 111
  * Muñoz & Perets (2018) Muñoz, D. J. & Perets, H. B. 2018, AJ, 156, 253
  * Nikolov et al. (2016) Nikolov, N., Sing, D. K., Gibson, N. P., et al. 2016, ApJ, 832, 191
  * Nowak et al. (2020) Nowak, G., Luque, R., Parviainen, H., et al. 2020, A&A, 642, A173
  * Owen & Jackson (2012) Owen, J. E. & Jackson, A. P. 2012, MNRAS, 425, 2931
  * Owen & Wu (2013) Owen, J. E. & Wu, Y. 2013, ApJ, 775, 105
  * Owen & Wu (2017) Owen, J. E. & Wu, Y. 2017, ApJ, 847, 29
  * Palle et al. (2020) Palle, E., Oshagh, M., Casasayas-Barris, N., et al. 2020, A&A, 643, A25
  * Passegger et al. (2020) Passegger, V. M., Bello-García, A., Ordieres-Meré, J., et al. 2020, A&A, 642, A22
  * Passegger et al. (2019) Passegger, V. M., Schweitzer, A., Shulyak, D., et al. 2019, A&A, 627, A161
  * Pepe et al. (2021) Pepe, F., Cristiani, S., Rebolo, R., et al. 2021, A&A, 645, A96
  * Perger et al. (2019) Perger, M., Scandariato, G., Ribas, I., et al. 2019, A&A, 624, A123
  * Pinamonti et al. (2018) Pinamonti, M., Damasso, M., Marzari, F., et al. 2018, A&A, 617, A104
  * Pollacco et al. (2006) Pollacco, D. L., Skillen, I., Collier Cameron, A., et al. 2006, PASP, 118, 1407
  * Quirrenbach et al. (2014) Quirrenbach, A., Amado, P. J., Caballero, J. A., et al. 2014, in Proc. SPIE, Vol. 9147, Ground-based and Airborne Instrumentation for Astronomy V, 91471F
  * Quirrenbach et al. (2018) Quirrenbach, A., Amado, P. J., Ribas, I., et al. 2018, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 10702, Ground-based and Airborne Instrumentation for Astronomy VII, 107020W
  * Raghavan et al. (2010) Raghavan, D., McAlister, H. A., Henry, T. J., et al. 2010, ApJS, 190, 1
  * Reiners et al. (2018) Reiners, A., Zechmeister, M., Caballero, J. A., et al. 2018, A&A, 612, A49
  * Reylé et al. (2021) Reylé, C., Jardine, K., Fouqué, P., et al. 2021, A&A, 650, A201
  * Ricker et al. (2015) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, JATIS, 1, 014003
  * Rizzuto et al. (2018) Rizzuto, A. C., Vanderburg, A., Mann, A. W., et al. 2018, AJ, 156, 195
  * Roell et al. (2012) Roell, T., Neuhäuser, R., Seifahrt, A., & Mugrauer, M. 2012, A&A, 542, A92
  * Rogers (2015) Rogers, L. A. 2015, ApJ, 801, 41
  * Rogers et al. (2011) Rogers, L. A., Bodenheimer, P., Lissauer, J. J., & Seager, S. 2011, ApJ, 738, 59
  * Rogers & Seager (2010) Rogers, L. A. & Seager, S. 2010, ApJ, 712, 974
  * Rossiter (1924) Rossiter, R. A. 1924, ApJ, 60, 15
  * Schlecker et al. (2020) Schlecker, M., Mordasini, C., Emsenhuber, A., et al. 2020, arXiv e-prints, arXiv:2007.05563
  * Schöfer et al. (2019) Schöfer, P., Jeffers, S. V., Reiners, A., et al. 2019, A&A, 623, A44
  * Schweitzer et al. (2019) Schweitzer, A., Passegger, V. M., Cifuentes, C., et al. 2019, A&A, 625, A68
  * Seifahrt et al. (2018) Seifahrt, A., Stürmer, J., Bean, J. L., & Schwab, C. 2018, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 10702, Ground-based and Airborne Instrumentation for Astronomy VII, ed. C. J. Evans, L. Simard, & H. Takami, 107026D
  * Shappee et al. (2014) Shappee, B. J., Prieto, J. L., Grupe, D., et al. 2014, ApJ, 788, 48
  * 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
  * Southworth (2011) Southworth, J. 2011, MNRAS, 417, 2166
  * Speagle & Barbary (2018) Speagle, J. & Barbary, K. 2018, dynesty: Dynamic Nested Sampling package, Astrophysics Source Code Library
  * Speagle (2020) Speagle, J. S. 2020, MNRAS, 493, 3132
  * Stassun et al. (2018) Stassun, K. G., Oelkers, R. J., Pepper, J., et al. 2018, AJ, 156, 102
  * Stefansson et al. (2020) Stefansson, G., Mahadevan, S., Maney, M., et al. 2020, AJ, 160, 192
  * Stock & Kemmer (2020) Stock, S. & Kemmer, J. 2020, Journal of Open Source Software, 5(45), 1771
  * Stock et al. (2020a) Stock, S., Kemmer, J., Reffert, S., et al. 2020a, A&A, 636, A119
  * Stock et al. (2020b) Stock, S., Nagel, E., Kemmer, J., et al. 2020b, A&A, 643, A112
  * 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
  * Thao et al. (2020) Thao, P. C., Mann, A. W., Johnson, M. C., et al. 2020, AJ, 159, 32
  * Thebault & Haghighipour (2015) Thebault, P. & Haghighipour, N. 2015, Planet Formation in Binaries, 309–340
  * Trifonov (2019) Trifonov, T. 2019, The Exo-Striker: Transit and radial velocity interactive fitting tool for orbital analysis and N-body simulations
  * Trifonov et al. (2021) Trifonov, T., Caballero, J. A., Morales, J. C., et al. 2021, Science, 371, 1038
  * Trifonov et al. (2018) Trifonov, T., Kürster, M., Zechmeister, M., et al. 2018, A&A, 609, A117
  * Trifonov et al. (2020) Trifonov, T., Tal-Or, L., Zechmeister, M., et al. 2020, A&A, 636, A74
  * Trotta (2008) Trotta, R. 2008, Contemporary Physics, 49, 71
  * Van Eylen et al. (2018) Van Eylen, V., Agentoft, C., Lundkvist, M. S., et al. 2018, MNRAS, 479, 4786
  * Van Eylen et al. (2021) Van Eylen, V., Astudillo-Defru, N., Bonfils, X., et al. 2021, MNRAS, 507, 2154
  * Venturini et al. (2020) Venturini, J., Guilera, O. M., Haldemann, J., Ronco, M. P., & Mordasini, C. 2020, A&A, 643, L1
  * Wang et al. (2014) Wang, J., Fischer, D. A., Xie, J.-W., & Ciardi, D. R. 2014, ApJ, 791, 111
  * Wilson et al. (2021) Wilson, J., Gibson, N. P., Lothringer, J. D., et al. 2021, MNRAS, 503, 4787
  * Winn et al. (2010) Winn, J. N., Fabrycky, D., Albrecht, S., & Johnson, J. A. 2010, ApJ, 718, L145
  * Winters et al. (2019a) Winters, J. G., Henry, T. J., Jao, W.-C., et al. 2019a, AJ, 157, 216
  * Winters et al. (2015) Winters, J. G., Henry, T. J., Lurie, J. C., et al. 2015, AJ, 149, 5
  * Winters et al. (2019b) Winters, J. G., Medina, A. A., Irwin, J. M., et al. 2019b, AJ, 158, 152
  * Zacharias et al. (2012) Zacharias, N., Finch, C. T., Girard, T. M., et al. 2012, VizieR Online Data Catalog, I/322A
  * Zechmeister & Kürster (2009) Zechmeister, M. & Kürster, M. 2009, A&A, 496, 577
  * Zechmeister et al. (2018) Zechmeister, M., Reiners, A., Amado, P. J., et al. 2018, A&A, 609, A12
  * Zeng et al. (2019) Zeng, L., Jacobsen, S. B., Sasselov, D. D., et al. 2019, PNAS, 116, 9723

##  Appendix A Further RV-only investigation

For the main RV-only analysis (Sect. 5.2), we decided to use the dSHO-GP
kernel (Eq. 1) for its computationally faster capabilities in comparison to
the QP-GP kernel, as presented in george,

$k_{i,j}(\tau)=\sigma^{2}_{\textnormal{GP}}\exp\left(-\alpha\tau^{2}-\Gamma\sin^{2}\left(\frac{\pi\tau}{P_{\textnormal{rot}}}\right)\right),$

where $\tau=|t_{i}-t_{j}|$ is the temporal distance between two points,
$\sigma_{\textnormal{GP}}$ is the amplitude of the GP modulation, $\alpha$ is
the inverse length-scale of the GP exponential component, $\Gamma$ is the
amplitude of the GP sine-squared component, and $P_{\textnormal{rot}}$ is the
rotational modulation of the GP quasi-periodic component. We followed the
approach as discussed by Stock et al. (2020b) in order to set up the priors
and thus constrained $\alpha$ to refrain from including the samples that
exhibit a “plateau-like” behavior (see Fig. 6 in Stock et al. 2020b). Upon
visual inspection of the $\alpha$-versus-$P_{\textnormal{rot}}$ correlation
plot when keeping $\alpha$ unconstrained (Fig. 10), we found that the $\alpha$
prior values for this analysis should be log-uniform from $10^{-8}$ to
$10^{-4}$, corresponding to timescales272727$\alpha=1/l^{2}$, where $l$ is the
timescale for the GP variations. In the original juliet paper (Espinoza et al.
2019a), $\alpha$ was defined as $\alpha=1/2l^{2}$. However, this has since
been corrected. of 100 to 10 000 days and we set $\Gamma$ to be log-uniform
from $10^{-2}$ to $10^{1}$. These constraints ensured that truly (decaying)
periodic-like signals were picked up by the GP, rather than allowing the
exponentially decaying component to be the dominant term, and thus acting as a
white-noise filter. As already stated in Sect. 5.2, using either of the two
kernels resulted in indistinguishable differences in their Bayesian log
evidence.

We further experimented with the two GP kernels by applying a wider prior for
$P_{\textnormal{rot}}$, $\mathcal{U}(10\,\textnormal{d},150\,\textnormal{d})$.
We denote this with GP${}_{\textnormal{wide}}$. The motivation for the wider
period prior is to evaluate whether the GP is flexible enough and can account
for both the stellar activity and the longer-term signal at the same time, in
other words, how the statistical metric that we use (i.e., the Bayesian log
evidence) compares to that of the sinusoidal variation. The
GP${}_{\textnormal{wide}}$ often picked up signals at 80 d, 35 d (the alias of
the stellar rotation period), and also 102 d, but the 19 d signal attributed
to the true stellar rotation period seemed to be dominated by the others. In
fact, the 1 circular Kep (2.5 d) + GP${}_{\textnormal{wide}}$ model had a
slightly favorable log evidence ($\Delta\ln{\mathcal{Z}}\sim 2$) when compared
to our final model choice of 1 circular Kep (2.5 d) + 1 Sin ($\sim$102 d) +
dSHO-GP${}_{\textnormal{19d}}$. This is intriguing, because based on the log
evidence alone, the statistically better model is the one including the
GP${}_{\textnormal{wide}}$ component, which is indeed able to account for both
signals. One reason for this behavior can be that we do not have enough of
time baseline coverage to truly constrain the long-term trend. Hence, this
could be used as a word of caution for when performing a “blind search” for
signals by applying a wide period prior for the GP because it could be that it
does statistically have an improved value and its flexibility can account for
the signals. Though, this model is not physically motivated considering that
we know the rotation period of the star and this should be taken into account.
One should thus take care when implementing a GP into the model and should ask
for what purpose it is trying to achieve.

Figure 10: Posterior distribution of the GP parameters for $\alpha$ and
$P_{\textnormal{rot}}$ for an RV-only run, including a QP-GP centered on the
rotational period $\sim$19 d and using an unconstrained prior on $\alpha$.
Samples are color-coded in accordance to their log-likelihood values, where
those with a $\Delta\ln L>10$ compared to the best solution are colored gray.
The horizontal dashed line represents the maximum value at which we
constrained the $\alpha$ parameter in order to exclude the plateau-like
behavior. The plot is inspired by Stock et al. (2020b).

##  Appendix B Priors and posteriors

Table 7: Priors for the RV-only fits for TOI-1201 with juliet in Sect. 5.2. Parameter | Prior | Unit | Description
---|---|---|---
Parameters for transiting planet b
$P_{b}$ | $\mathcal{F}(2.4919858227 )$ | d | Period
$t_{0,b}$ (BJD) | $\mathcal{F}(2459169.2321864809)$ | d | Time of transit center
$K_{b}$ | $\mathcal{U}(0.0,20)$ |  m s-1 | RV semi-amplitude
$S_{1,b}=\sqrt{e_{c}}\sin\omega_{c}$ |  $\mathcal{F}{(0.0)}$ (circular) | $\dots$ |  Parametrization for $e$ and $\omega$
|  $\mathcal{U}{(-1,1)}$ (eccentric) | $\dots$ |  Parametrization for $e$ and $\omega$
$S_{2,b}=\sqrt{e_{b}}\cos\omega_{b}$ |  $\mathcal{F}{(0.0)}$ (circular) | $\dots$ |  Parametrization for $e$ and $\omega$
|  $\mathcal{U}{(-1,1)}$ (eccentric) | $\dots$ |  Parametrization for $e$ and $\omega$
Parameters for long-term signal in RVs
$P_{[c]}$ | $\mathcal{U}(60.0,150.0)$ | d | Period
$t_{0,[c]}$ | $\mathcal{U}(2458730.0,2458840.0)$ | d | Time of transit center
$K_{[c]}$ | $\mathcal{U}(0.0,20.0)$ |  m s-1 | RV semi-amplitude
$S_{1,[c]}=\sqrt{e_{[c]}}\sin\omega_{[c]}$ |  $\mathcal{F}{(0.0)}$ (circular) | $\dots$ |  Parametrization for $e$ and $\omega$
|  $\mathcal{U}{(-1,1)}$ (eccentric) | $\dots$ |  Parametrization for $e$ and $\omega$
$S_{2,[c]}=\sqrt{e_{[c]}}\cos\omega_{[c]}$ |  $\mathcal{F}{(0.0)}$ (circular) | $\dots$ |  Parametrization for $e$ and $\omega$
|  $\mathcal{U}{(-1,1)}$ (eccentric) | $\dots$ |  Parametrization for $e$ and $\omega$
RV instrumental parameters
$\gamma_{\textnormal{CARMENES-VIS}}$ | $\mathcal{U}(-10.0,10.0)$ |  m s-1 | Systemic velocity for CARMENES-VIS
$\sigma_{\textnormal{CARMENES-VIS}}$ | $\mathcal{J}(0.01,100.0)$ |  m s-1 | Extra jitter term for CARMENES-VIS
dSHO-GP parameters
$\sigma_{\textnormal{GP,\ CARMENES-VIS}}$ | $\mathcal{U}(0.0,10.0)$ |  m s-1 | Amplitude of the dSHO-GP
$Q_{0\ \textnormal{GP,\ CARMENES-VIS}}$ | $\mathcal{J}(1.0,100000.0)$ | $\dots$ | Quality factor for the secondary oscillation of the dSHO-GP
$f_{\textnormal{GP,\ CARMENES-VIS}}$ | $\mathcal{U}(0.1,1.0)$ | $\dots$ | Fractional amplitude of the secondary oscillation of the dSHO-GP
$\delta Q_{\textnormal{GP,\ CARMENES-VIS}}$ | $\mathcal{J}(1.0,100000.0)$ | $\dots$ | Quality factor difference between the first
|  |  | and second oscillations of the dSHO-GP
$P_{\textnormal{rot,\ GP,\ CARMENES-VIS}}$ | $\mathcal{U}(15.0,25.0)$ | d | Primary period of the dSHO-GP
|  $\mathcal{U}(10.0,150.0)$ (wide) | d | Primary period of the dSHO-GP
QP-GP parameters
$\sigma_{\textnormal{GP,\ CARMENES-VIS}}$ | $\mathcal{U}(0.0,10.0)$ |  m s-1 | Amplitude of the QP-GP
$\Gamma_{\textnormal{GP,\ CARMENES-VIS}}$ | $\mathcal{J}(0.01,10.0)$ | $\dots$ | Amplitude of the sine-squared component of the QP-GP
$\alpha_{\textnormal{GP,\ CARMENES-VIS}}$ | $\mathcal{J}(10^{-8},0.001)$ |  d-2 | Inverse length-scale of the exponential component of the QP-GP
$P_{\textnormal{rot,\ GP,\ CARMENES-VIS}}$ | $\mathcal{U}(15.0,25.0)$ | d | Rotational period of the quasi-periodic component of the QP-GP
|  $\mathcal{U}(10.0,150.0)$ (wide) | d | Rotational period of the quasi-periodic component of the QP-GP
Table 8: Priors for the final joint transit and RV fit for TOI-1201 with juliet in Sect. 5.3. Parameter | Prior | Unit | Description
---|---|---|---
Stellar parameters
$\rho_{*}$ | $\mathcal{N}(5.40,.60)$ |  g cm-3 | Stellar density
Parameters for transiting planet b
$P_{b}$ | $\mathcal{N}(2.4919858227,0.0001)$ | d | Period
$t_{0,b}$ (BJD) | $\mathcal{N}(2459169.232186481,0.05)$ | d | Time of transit center.
$r_{1,b}$ | $\mathcal{U}(0.0,1.0)$ | $\dots$ | Parametrization for p and b
$r_{2,b}$ | $\mathcal{U}(0.0,1.0)$ | $\dots$ | Parametrization for p and b
$K_{b}$ | $\mathcal{U}(0.0,20)$ |  m s-1 | RV semi-amplitude
$S_{1,b}=\sqrt{e_{b}}\sin\omega_{b}$ | 0.0 (fixed) | $\dots$ |  Parametrization for $e$ and $\omega$
$S_{2,b}=\sqrt{e_{b}}\cos\omega_{b}$ | 0.0 (fixed) | $\dots$ |  Parametrization for $e$ and $\omega$
Parameters for long-term RV signal
$P_{[c]}$ | $\mathcal{U}(60.0,150.0)$ | d | Period
$t_{0,[c]}$ | $\mathcal{U}(2458730.0,2458840.0)$ | d | Time of transit center
$K_{[c]}$ | $\mathcal{U}(0.0,20.0)$ |  m s-1 | RV semi-amplitude
$S_{1,[c]}=\sqrt{e_{[c]}}\sin\omega_{[c]}$ | 0.0 (fixed) | $\dots$ |  Parametrization for $e$ and $\omega$
$S_{2,[c]}=\sqrt{e_{[c]}}\cos\omega_{[c]}$ | 0.0 (fixed) | $\dots$ |  Parametrization for $e$ and $\omega$
RV instrumental parameters
$\gamma_{\textnormal{CARMENES-VIS}}$ | $\mathcal{U}(-10.0,10.0)$ |  m s-1 | Systemic velocity for CARMENES-VIS
$\sigma_{\textnormal{CARMENES-VIS}}$ | $\mathcal{J}(0.01,100.0)$ |  m s-1 | Extra jitter term for CARMENES-VIS
$\sigma_{\textnormal{GP,\ CARMENES-VIS}}$ | $\mathcal{U}(0.0,10.0)$ |  m s-1 | Amplitude of the dSHO-GP
$Q_{0\ \textnormal{GP,\ CARMENES-VIS}}$ | $\mathcal{J}(1.0,100000.0)$ | $\dots$ | Quality factor for the secondary oscillation of the dSHO-GP
$f_{\textnormal{GP,\ CARMENES-VIS}}$ | $\mathcal{U}(0.1,1.0)$ | $\dots$ | Fractional amplitude of the secondary oscillation of the dSHO-GP
$\delta Q_{\textnormal{GP,\ CARMENES-VIS}}$ | $\mathcal{J}(1.0,100000.0)$ | $\dots$ | Quality factor difference between the first
|  |  | and second oscillations of the dSHO-GP
$P_{\textnormal{rot,\ GP,\ CARMENES-VIS}}$ | $\mathcal{U}(15.0,25.0)$ | d | Primary period of the dSHO-GP
Photometry instrumental parameters
$D_{\textnormal{TESS4}}$ | 1.0 (fixed) | $\dots$ | Dilution factor for TESS4
$M_{\textnormal{TESS4}}$ | $\mathcal{U}(-0.1,0.1)$ |  $10^{6}$ ppm | Relative flux offset for TESS4
$\sigma_{\textnormal{TESS4}}$ | $\mathcal{J}(10^{-7},100000.0)$ | ppm | Extra jitter term for TESS4
$\sigma_{\textnormal{GP,\ TESS4}}$ | $\mathcal{J}(10^{-5},100.0)$ | ppm | Amplitude of the Matern-3/2-GP for TESS4
$\rho_{\textnormal{GP,\ TESS4}}$ | $\mathcal{J}(0.001,100.0)$ | d | Length scale of the Matern-3/2-GP for TESS4
$D_{\textnormal{TESS31}}$ | 1.0 (fixed) | $\dots$ | Dilution factor for TESS31
$M_{\textnormal{TESS31}}$ | $\mathcal{U}(-0.1,0.1)$ |  $10^{6}$ ppm | Relative flux offset for TESS31
$\sigma_{\textnormal{TESS31}}$ | $\mathcal{J}(10^{-7},100000.0)$ | ppm | Extra jitter term for TESS31
$\sigma_{\textnormal{GP,\ TESS31}}$ | $\mathcal{J}(10^{-8},0.0001)$ | ppm | Amplitude of the exp-GP for TESS31
$T_{\textnormal{GP},\textnormal{TESS31}}$ | $\mathcal{J}(10^{-5},100.0)$ | d | Characteristic timescale of the exp-GP for TESS31
$q_{1,\textnormal{TESS4+TESS31}}$ | $\mathcal{U}(0.0,1.0)$ | $\dots$ | Quadratic limb-darkening parametrization for TESS4 and TESS31
$q_{2,\textnormal{TESS4+TESS31}}$ | $\mathcal{U}(0.0,1.0)$ | $\dots$ | Quadratic limb-darkening parametrization for TESS4 and TESS31
$D_{\textnormal{OAA}}$ | 1.0 (fixed) | $\dots$ | Dilution factor for OAA
$M_{\textnormal{OAA}}$ | $\mathcal{U}(-0.1,0.1)$ |  $10^{6}$ ppm | Relative flux offset for OAA
$\sigma_{\textnormal{OAA}}$ | $\mathcal{J}(10^{-7},100000.0)$ | ppm | Extra jitter term for OAA
$q_{1,\textnormal{OAA}}$ | $\mathcal{U}(0.0,1.0)$ | $\dots$ | Linear limb-darkening parametrization for OAA
$D_{\textnormal{LCO-SSO}}$ | 1.0 (fixed) | $\dots$ | Dilution factor for LCO-SSO
$M_{\textnormal{LCO-SSO}}$ | $\mathcal{U}(-0.1,0.1)$ |  $10^{6}$ ppm | Relative flux offset for LCO-SSO
$\sigma_{\textnormal{LCO-SSO}}$ | $\mathcal{J}(10^{-7},100000.0)$ | ppm | Extra jitter term for LCO-SSO
$q_{1,\textnormal{LCO-SSO}}$ | $\mathcal{U}(0.0,1.0)$ | $\dots$ | Linear limb-darkening parametrization for LCO-SSO
$\theta_{0,\textnormal{LCO-SSO}}$ | $\mathcal{U}(-0.1,0.1)$ |  | Linear term applied to the airmass for LCO-SSO
$D_{\textnormal{LCO-SAAO}}$ | 1.0 (fixed) | $\dots$ | Dilution factor for LCO-SAAO
$M_{\textnormal{LCO-SAAO}}$ | $\mathcal{U}(-0.1,0.1)$ |  $10^{6}$ ppm | Relative flux offset for LCO-SAAO
$\sigma_{\textnormal{LCO-SAAO}}$ | $\mathcal{J}(10^{-7},100000.0)$ | ppm | Extra jitter term for LCO-SAAO
$q_{1,\textnormal{LCO-SAAO}}$ | $\mathcal{U}(0.0,1.0)$ | $\dots$ | Linear limb-darkening parametrization for LCO-SAAO
$\theta_{0,\textnormal{LCO-SAAO}}$ | $\mathcal{U}(-0.1,0.1)$ |  | Linear term applied to the airmass for LCO-SAAO
Table 9: Full set of posterior parameters used in the model for TOI-1201 and described in Sect. 5.3 Parameter | Posterior
---|---
Stellar parameters
$\rho_{*}$ (g cm-3) | $5.57^{+.51}_{-.48}$
Posterior parameters for transiting planet b
$P_{b}$ (d) | $2.4919863^{+0.0000030}_{-0.0000031}$
$t_{0,b}$ (d) | $2459169.23222^{+0.00052}_{-0.00054}$
$r_{1,b}$ | $0.603^{+0.048}_{-0.055}$
$r_{2,b}$ | $0.04383^{+0.00096}_{-0.00110}$
$K_{b}$ (m s-1) | $4.65^{+0.60}_{-0.64}$
Parameters for long-term signal in RVs
$P_{[c]}$ (d) | $102^{+21}_{-15}$
$t_{0,[c]}$ (d) | $2458772^{+12}_{-16}$
$K_{[c]}$ (m s-1) | $5.84^{+0.91}_{-0.87}$
RV instrumental parameters
$\gamma_{\textnormal{CARMENES-VIS}}$ (m s-1) | $-2.91^{+0.74}_{-0.97}$
$\sigma_{\textnormal{CARMENES-VIS}}$ (m s-1) | $0.36^{+0.78}_{-0.29}$
$\sigma_{\textnormal{GP,\ CARMENES-VIS}}$ (m s-1) | $3.7^{+1.7}_{-1.1}$
$Q_{0\ \textnormal{GP,\ CARMENES-VIS}}$ | $5.6^{+41.0}_{-3.8}$
$f_{\textnormal{GP,\ CARMENES-VIS}}$ | $0.57^{+0.25}_{-0.28}$
$\delta Q_{\textnormal{GP,\ CARMENES-VIS}}$ | $179^{+5600}_{-170}$
$P_{\textnormal{rot,\ GP,\ CARMENES-VIS}}$ (d) | $19.62^{+1.10}_{-0.81}$
Photometry instrumental parameters
$M_{\textnormal{TESS4}}$ ($10^{6}$ ppm) | $-0.00003^{+0.00020}_{-0.00021}$
$\sigma_{\textnormal{TESS4}}$ (ppm) | $810^{+44}_{-45}$
$\sigma_{\textnormal{GP,\ TESS4}}$ (ppm) | $0.001455^{+0.000110}_{-0.000098}$
$\rho_{\textnormal{GP,\ TESS4}}$ (d) | $0.255^{+0.027}_{-0.022}$
$M_{\textnormal{TESS31}}$ ($10^{6}$ ppm) | $-0.0003^{+0.0011}_{-0.0018}$
$\sigma_{\textnormal{TESS31}}$ (ppm) | $0.0075^{+3.7000}_{-0.0074}$
$\sigma_{\textnormal{GP,\ TESS31}}$ (ppm) | $0.0000023^{+0.0000170}_{-0.0000019}$
$T_{\textnormal{GP,\ TESS31}}$ (d) | $0.027^{+0.130}_{-0.024}$
$q_{1,\textnormal{TESS4+TESS31}}$ | $0.47^{+0.25}_{-0.22}$
$q_{2,\textnormal{TESS4+TESS31}}$ | $0.33^{+0.28}_{-0.20}$
$M_{\textnormal{OAA}}$ ($10^{6}$ ppm) | $-0.00002^{+0.00019}_{-0.00019}$
$\sigma_{\textnormal{OAA}}$ (ppm) | $0.072^{+32.000}_{-0.072}$
$q_{1,\textnormal{OAA}}$ | $0.46^{+0.30}_{-0.27}$
$M_{\textnormal{LCO-SSO}}$ ($10^{6}$ ppm) | $0.03181^{+0.00041}_{-0.00041}$
$\sigma_{\textnormal{LCO-SSO}}$ (ppm) | $926^{+140}_{-150}$
$q_{1,\textnormal{LCO-SSO}}$ | $0.69^{+0.18}_{-0.23}$
$\theta_{0,\textnormal{LCO-SSO}}$ | $0.0007^{+0.0003}_{-0.0003}$
$M_{\textnormal{LCO-SAAO}}$ ($10^{6}$ ppm) | $0.0383^{+0.0030}_{-0.0031}$
$\sigma_{\textnormal{LCO-SAAO}}$ (ppm) | $112^{+860}_{-110}$
$q_{1,\textnormal{LCO-SAAO}}$ | $0.47^{+0.24}_{-0.24}$
$\theta_{0,\textnormal{LCO-SAAO}}$ | $0.0333^{+0.0026}_{-0.0026}$
Figure 11: Posterior distributions for the transiting planet TOI-1201 b from
the joint fit described in Sect. 5.3.  Figure 12: Posterior distributions for
the dSHO-GP on the CARMENES RVs from the joint fit described in Sect. 5.3.
Figure 13: Posterior distributions for the long-term signal from the joint fit
described in Sect. 5.3.

##  Appendix C Two-planet model

As discussed in Sect. 5.2, a $\sim$102 d signal is the strongest one found in
the RVs. It is favored in the model when included as an additional sinusoidal
component. However, a GP could also model it well (see Appendix A). If
considered to be a planet, it would then have a minimum mass of
$27.0^{+5.6}_{-4.5}$ $M_{\oplus}$ (Table 10, Fig. 13). Thus far, we cannot
immediately rule out a possible planet candidate. Nevertheless, given that the
orbital period is on the order of the time baseline, we do not have sufficient
evidence to unequivocally prove the origin of the signal to be planetary.

From a dynamical point of view, it would be an unproblematic configuration,
since both planets maintain a sufficient spatial separation to preserve long-
term stability. In addition, the longer-period planet candidate, whose
expected bulk mass would require a significant gaseous envelope, is far enough
from the star to avoid significant atmospheric losses due to photoevaporation
(Owen & Jackson 2012). A Neptunian-mass planet at this orbit is, thus,
plausible. In fact, core accretion theory, which is considered the most
promising path of planet formation, routinely predicts planets like those
found in TOI-1201. Global formation models of multi-planetary systems (e.g.,
Emsenhuber et al. 2020) find the tentative two-planet configuration to be a
rather typical outcome (e.g., Schlecker et al. 2020, their Fig. D.3). New
planetary population syntheses specifically tailored to M-dwarf systems also
propose the regular formation of planets in the mass range of TOI-1201 b and
the tentative TOI-1201 [c] (Burn et al. 2021). Therefore, we believe that the
latter is a promising candidate planetary companion. Further observations,
especially with longer ground-based coverage, will be necessary to
unequivocally determine the nature of the signal.

Table 10: Same derived posterior table as Table 5 but assuming the second
signal to be of planetary origin.

Parameter |  Posterior(a)(a)footnotemark: $(a)$ | Unit
---|---|---
| b |  [c](b)(b)footnotemark: $(b)$ |
$P_{p}$ | $2.4919863^{+0.0000030}_{-0.0000031}$ | $102^{+21}_{-15}$ | d
$t_{0,p}$ (BJD) | $2459169.23222^{+0.00052}_{-0.00054}$ | $2458772^{+12}_{-16}$ | d
$r_{1,p}$ | $0.603^{+0.048}_{-0.055}$ | $\dots$ | $\dots$
$r_{2,p}$ | $0.04383^{+0.00096}_{-0.00110}$ | $\dots$ | $\dots$
$K_{p}$ | $4.65^{+0.60}_{-0.64}$ | $5.84^{+0.91}_{-0.87}$ |  m s-1
$e_{p}$ |  $0.0$ (fixed) |  $0.0$ (fixed) | $\dots$
$\omega_{p}$ |  $90.0$ (fixed) |  $90.0$ (fixed) | $\dots$
$p=R_{p}/R_{\star}$ | $0.04383^{+0.00096}_{-0.00110}$ | $\dots$ | $\dots$
$b=(a_{p}/R_{\star})\cos{i_{p}}$ | $0.404^{+0.071}_{-0.082}$ | $\dots$ | $\dots$
$a_{p}/R_{\star}$ | $12.23^{+0.36}_{-0.36}$ | $\dots$ | $\dots$
$i_{p}$ | $88.11^{+0.42}_{-0.40}$ | $\dots$ | deg
$t_{\textnormal{T}}$(c)(c)footnotemark: $(c)$ | $1.747^{+0.096}_{-0.091}$ | $\dots$ | h
$M_{p}$ | $6.28^{+0.84}_{-0.88}$ | $>27.0^{+5.6}_{-4.5}$ | $M_{\oplus}$
$R_{p}$ | $2.415^{+0.091}_{-0.090}$ | $\dots$ | $R_{\oplus}$
$\rho_{p}$ | $2.45^{+0.48}_{-0.42}$ | $\dots$ |  g cm-3
$g_{p}$ | $10.5^{+1.8}_{-1.6}$ | $\dots$ |  m s-2
$a_{p}$ | $0.0287^{+0.0012}_{-0.0012}$ | $0.341^{+0.046}_{-0.034}$ | au
$T_{\textnormal{eq}}$(d)(d)footnotemark: $(d)$ | $703^{+15}_{-14}$ | $204^{+12}_{-13}$ | K
$S_{p}$(e)(e)footnotemark: $(e)$ | $40.6^{+3.6}_{-3.2}$ | $0.287^{+0.072}_{-0.065}$ | $S_{\oplus}$
282828 $a$$a$footnotetext: Parameters obtained with the posterior values from
Table 9. Error bars denote the 68 % posterior credibility intervals.
$b$$b$footnotetext: The square brackets denote the assumption that the long-
term signal is of planetary origin. $c$$c$footnotetext: Transit duration from
first contact to fourth contact. $d$$d$footnotetext: Equilibrium temperature
calculated assuming zero Bond albedo. $e$$e$footnotetext: Insolation.

##  Appendix D Additional figures