# TOI-1452 b: SPIRou and TESS reveal a super-Earth in a temperate orbit
transiting an M4 dwarf

Charles Cadieux Université de Montréal, Département de Physique, IREX,
Montréal, QC H3C 3J7, Canada  René Doyon Université de Montréal, Département
de Physique, IREX, Montréal, QC H3C 3J7, Canada  Observatoire du Mont-
Mégantic, Université de Montréal, Montréal H3C 3J7, Canada  Mykhaylo Plotnykov
Department of Physics, University of Toronto, Toronto, ON M5S 3H4, Canada
Guillaume Hébrard Institut d’astrophysique de Paris, UMR7095 CNRS, Sorbonne
Université, 98 bis bd Arago, 75014 Paris, France  Farbod Jahandar Université
de Montréal, Département de Physique, IREX, Montréal, QC H3C 3J7, Canada
Étienne Artigau Université de Montréal, Département de Physique, IREX,
Montréal, QC H3C 3J7, Canada  Observatoire du Mont-Mégantic, Université de
Montréal, Montréal H3C 3J7, Canada  Diana Valencia Department of Physical &
Environmental Sciences, University of Toronto at Scarborough, Toronto, ON M1C
1A4, Canada  David A. Dunlap Dept. of Astronomy & Astrophysics, University of
Toronto, 50 St. George Street, Toronto, Ontario, M5S 3H4, Canada  Neil J. Cook
Université de Montréal, Département de Physique, IREX, Montréal, QC H3C 3J7,
Canada  Eder Martioli Institut d’astrophysique de Paris, UMR7095 CNRS,
Sorbonne Université, 98 bis bd Arago, 75014 Paris, France  Laboratório
Nacional de Astrofísica, Rua Estados Unidos 154, Itajubá, MG 37504-364, Brazil
Thomas Vandal Université de Montréal, Département de Physique, IREX, Montréal,
QC H3C 3J7, Canada  Jean-François Donati Université de Toulouse, CNRS, IRAP,
14 Avenue Belin, 31400 Toulouse, France  Ryan Cloutier Banting Fellow  Center
for Astrophysics $|{}$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA,
02138, USA  Norio Narita Komaba Institute for Science, The University of
Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan  Astrobiology Center,
2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Instituto de Astrofísica de
Canarias (IAC), 38205 La Laguna, Tenerife, Spain  Akihiko Fukui Komaba
Institute for Science, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo
153-8902, Japan  Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna,
Tenerife, Spain  Teruyuki Hirano Astrobiology Center, 2-21-1 Osawa, Mitaka,
Tokyo 181-8588, Japan  National Astronomical Observatory of Japan, 2-21-1
Osawa, Mitaka, Tokyo 181-8588, Japan  François Bouchy Departement
d’astronomie, Université de Genève, Chemin Pegasi, 51, CH-1290 Versoix,
Switzerland  Nicolas B. Cowan Department of Earth & Planetary Sciences, McGill
University, 3450 rue University, Montréal, QC H3A 0E8, Canada  Department of
Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada
Erica J. Gonzales University of California Santa Cruz, Santa Cruz CA 95065,
USA  David R. Ciardi NASA Exoplanet Science Institute-Caltech/IPAC, Pasadena,
CA 91125 USA  Keivan G. Stassun Department of Physics and Astronomy,
Vanderbilt University, 6301 Stevenson Center Ln., Nashville, TN 37235, USA
Department of Physics, Fisk University, 1000 17th Avenue North, Nashville, TN
37208, USA  Luc Arnold Canada-France-Hawaii Telescope, CNRS, Kamuela, HI
96743, USA  Björn Benneke Université de Montréal, Département de Physique,
IREX, Montréal, QC H3C 3J7, Canada  Isabelle Boisse Aix Marseille Univ, CNRS,
CNES, LAM, Marseille, France  Xavier Bonfils Univ. Grenoble Alpes, CNRS, IPAG,
38000 Grenoble, France  Andrés Carmona Univ. Grenoble Alpes, CNRS, IPAG, 38000
Grenoble, France  Pía Cortés-Zuleta Aix Marseille Univ, CNRS, CNES, LAM,
Marseille, France  Xavier Delfosse Univ. Grenoble Alpes, CNRS, IPAG, 38000
Grenoble, France  Thierry Forveille Univ. Grenoble Alpes, CNRS, IPAG, 38000
Grenoble, France  Pascal Fouqué Canada-France-Hawaii Telescope, CNRS, Kamuela,
HI 96743, USA  Université de Toulouse, CNRS, IRAP, 14 Avenue Belin, 31400
Toulouse, France  João Gomes da Silva Instituto de Astrofísica e Ciências do
Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762, Porto,
Portugal  Jon M. Jenkins NASA Ames Research Center, Moffett Field, CA 94035,
USA  Flavien Kiefer Institut d’astrophysique de Paris, UMR7095 CNRS, Sorbonne
Université, 98 bis bd Arago, 75014 Paris, France  Ágnes Kóspál Konkoly
Observatory, Research Centre for Astronomy and Earth Sciences, Eötvös Loránd
Research Network (ELKH), Konkoly-Thege Miklós út 15-17, 1121 Budapest, Hungary
Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
ELTE Eötvös Loránd University, Institute of Physics, Pázmány Péter sétány 1/A,
1117 Budapest, Hungary  David Lafrenière Université de Montréal, Département
de Physique, IREX, Montréal, QC H3C 3J7, Canada  Jorge H. C. Martins Instituto
de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das
Estrelas, 4150-762, Porto, Portugal  Claire Moutou Université de Toulouse,
CNRS, IRAP, 14 Avenue Belin, 31400 Toulouse, France  J.-D. do Nascimento, Jr.
Universidade Federal do Rio Grande do Norte (UFRN), Departamento de Física,
59078-970, Natal, RN, Brazil  Center for Astrophysics $|{}$ Harvard &
Smithsonian, 60 Garden Street, Cambridge, MA, 02138, USA  Merwan Ould-Elhkim
Université de Toulouse, CNRS, IRAP, 14 Avenue Belin, 31400 Toulouse, France
Stefan Pelletier Université de Montréal, Département de Physique, IREX,
Montréal, QC H3C 3J7, Canada  Joseph D. Twicken SETI Institute, Mountain View,
CA 94043, USA  NASA Ames Research Center, Moffett Field, CA 94035, USA  Luke
G. Bouma Department of Astrophysical Sciences, Princeton University, 4 Ivy
Lane, Princeton, NJ 08544, USA  Scott Cartwright  Proto-Logic Consulting LLC,
Washington DC, 20009 USA  Antoine Darveau-Bernier Université de Montréal,
Département de Physique, IREX, Montréal, QC H3C 3J7, Canada  Konstantin
Grankin Crimean Astrophysical Observatory, Department of Stellar Physics,
Nauchny, 298409, Crimea  Masahiro Ikoma National Astronomical Observatory of
Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Taiki Kagetani Department
of Multi-Disciplinary Sciences, Graduate School of Arts and Sciences, The
University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan  Kiyoe
Kawauchi Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna,
Tenerife, Spain  Departamento de Astrofísica, Universidad de La Laguna (ULL),
38206 La Laguna, Tenerife, Spain  Takanori Kodama Komaba Institute for
Science, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan
Takayuki Kotani Astrobiology Center, 2-21-1 Osawa, Mitaka, Tokyo 181-8588,
Japan  National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan  Department of Astronomy, School of Science, The Graduate
University for Advanced Studies (SOKENDAI), 2-21-1Osawa, Mitaka, Tokyo, Japan
David W. Latham Center for Astrophysics $|{}$ Harvard & Smithsonian, 60 Garden
Street, Cambridge, MA, 02138, USA  Kristen Menou  Department of Physical &
Environmental Sciences, University of Toronto at Scarborough, Toronto, ON M1C
1A4, Canada  David A. Dunlap Dept. of Astronomy & Astrophysics, University of
Toronto, 50 St. George Street, Toronto, Ontario, M5S 3H4, Canada  Department
of Physics, University of Toronto, Toronto, ON M5S 3H4, Canada  George Ricker
MIT Kavli Institute for Astrophysics and Space Research, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  MIT Department of Physics,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Sara Seager
MIT Kavli Institute for Astrophysics and Space Research, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  Earth and Planetary
Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue,
Cambridge, MA 02139, USA  Department of Aeronautics and Astronautics, MIT, 77
Massachusetts Avenue, Cambridge, MA 02139, USA  Motohide Tamura Department of
Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo,
Bunkyo, Tokyo 113-0033, Japan  Astrobiology Center, 2-21-1 Osawa, Mitaka,
Tokyo 181-8588, Japan  National Astronomical Observatory of Japan, 2-21-1
Osawa, Mitaka, Tokyo 181-8588, Japan  Roland Vanderspek MIT Kavli Institute
for Astrophysics and Space Research, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Noriharu Watanabe Department of Multi-Disciplinary
Sciences, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1
Komaba, Meguro, Tokyo 153-8902, Japan

(Received April 25, 2022; Revised June 22, 2022; Accepted June 27, 2022)

###### Abstract

Exploring the properties of exoplanets near or inside the radius valley
provides insights on the transition from the rocky super-Earths to the larger,
hydrogen-rich atmosphere mini-Neptunes. Here, we report the discovery of
TOI-1452 b, a transiting super-Earth ($R_{\rm p}=1.67\pm 0.07$ R⊕) in an
11.1–day temperate orbit ($T_{\rm eq}=326\pm 7$ K) around the primary member
($H=10.0$, $T_{\rm eff}=3185\pm 50$ K) of a nearby visual binary M dwarf. The
transits were first detected by TESS, then successfully isolated between the
two $3\farcs 2$ companions with ground-based photometry from OMM and MuSCAT3.
The planetary nature of TOI-1452 b was established through high-precision
velocimetry with the near-infrared SPIRou spectropolarimeter as part of the
ongoing SPIRou Legacy Survey. The measured planetary mass ($4.8\pm 1.3$ M⊕)
and inferred bulk density ($5.6^{+1.8}_{-1.6}$ g/cm3) is suggestive of a rocky
core surrounded by a volatile-rich envelope. More quantitatively, the mass and
radius of TOI-1452 b, combined with the stellar abundance of refractory
elements (Fe, Mg and Si) measured by SPIRou, is consistent with a core mass
fraction of $18\pm 6$% and a water mass fraction of $22^{+21}_{-13}$%. The
water world candidate TOI-1452 b is a prime target for future atmospheric
characterization with JWST, featuring a Transmission Spectroscopy Metric
similar to other well-known temperate small planets such as LHS 1140 b and
K2-18 b. The system is located near Webb’s northern Continuous Viewing Zone,
implying that is can be followed at almost any moment of the year.

††facilities: TESS, OMM-PESTO, MuSCAT3, KeckII/NIRC2, CFHT/SPIRou,
Subaru/IRD††software: emcee (Foreman-Mackey et al., 2013); Astropy (Astropy
Collaboration et al., 2018); radvel (Fulton et al., 2018); matplotlib (Hunter,
2007); celerite (Foreman-Mackey et al., 2017); celerite2 (Foreman-Mackey et
al. 2017; 2018); juliet (Espinoza et al., 2019); batman (Kreidberg, 2015);
SciPy (Virtanen et al., 2020); NumPy (Harris et al., 2020); photutils (Bradley
et al., 2020); Tapir (Jensen, 2013); AstroImageJ (Collins et al., 2017)

August 12, 2022

##  1 Introduction

Over the past decade, it has become increasingly clear that the typical
extrasolar planetary system is quite different from our Solar System.
Exoplanets are usually found in a much more compact orbital configuration
(Howard et al., 2010) and the majority of systems have at least one planet
with a size intermediate between the Earth and Neptune (Howard et al. 2012;
Fressin et al. 2013). Population studies based on the Kepler sample have shown
that the occurrence rate distribution of close-in ($P<100$ days) exoplanets
displays a valley/gap near 1.5–2.0 R⊕ (Fulton et al. 2017; Fulton & Petigura
2018; Mayo et al. 2018; Hardegree-Ullman et al. 2020). This radius valley most
likely separates scaled-up, rocky versions of the Earth (super-Earths) and
hydrogen-rich planets reminiscent of Neptune, but smaller (mini-Neptunes).
This transition is known to be period-dependent (Van Eylen et al. 2018;
Martinez et al. 2019) and to vary with the host star properties such as
metallicity (Petigura et al. 2018; Owen & Murray-Clay 2018), mass (McDonald et
al. 2019; Cloutier & Menou 2020), and age (Berger et al. 2020; David et al.
2021). The existence of a radius valley was rapidly attributed to total or
partial photoevaporation of the atmosphere by highly energetic photons during
the first 100 Myr, when the host star is more active (Owen & Wu 2013, 2017;
Lopez & Fortney 2014; Lopez & Rice 2018; Wu 2019). However, another
atmospheric erosion mechanism is plausible, involving mass loss caused by the
release of energy from the planet core, accumulated during formation and
slowly cooling down over Gyr timescales (Ginzburg et al. 2018; Gupta &
Schlichting 2019, 2020). More recently, Lee & Connors (2021) have shown that
the radius valley can be sculpted as a feature of formation, involving gas-
poor accretion and supporting the hypothesis of a primordial bimodal
distribution, rather than the result of subsequent atmospheric erosion. In
order to identify which mechanism dominates, Rogers et al. (2021) predict that
the number of well-characterized small exoplanets must reach $\gtrsim 5000$.
Such characterization requires the precise knowledge of planetary radii
($\lesssim 5\%$ uncertainty) and, if possible, the planet mass. The
combination of the two measurements leads to the mean density of the objects,
a way to determine whether their internal structure is compatible with a
rocky, gaseous, or intermediate bulk composition.

Identifying new small planets transiting nearby bright stars is the primary
objective of the ongoing NASA Transiting Exoplanet Survey Satellite (TESS)
mission (Ricker et al., 2015). In operation since 2018, TESS has observed 85%
of the celestial sphere, staring for at least $\sim$27 days at over 50 sectors
covered so far ($24\arcdeg\times 96\arcdeg$ per sector). The TESS survey has
already unveiled more than 5000 candidate exoplanets of which more than two
hundred have been confirmed as new transiting planetary systems, including
small planets around M-dwarf hosts (e.g., TOI-270, Günther et al. 2019; LP
791-18, Crossfield et al. 2019; L 98-59, Cloutier et al. 2019; LTT 1445 A,
Winters et al. 2019; LTT 3780, Cloutier et al. 2020a; TOI-1235, Cloutier et
al. 2020b; TOI-700, Gilbert et al. 2020; TOI-1266, Demory et al. 2020; LP
714-47, Dreizler et al. 2020; TOI-776, Luque et al. 2021).

M dwarfs represent prime targets not only for TESS, but in exoplanetary
science in general. They are the most abundant stars in the solar neighborhood
(Reylé et al., 2021) and host on average 2.5$\pm$0.2 planets per M dwarf with
radii 1–4 R⊕ (Dressing & Charbonneau, 2015). Their smaller size compared to
Sun-like stars facilitate the detection and characterization of new exoplanets
by producing deeper transits for planets of a given size. The larger planet-
to-star mass ratio amplifies the planetary radial velocity (RV) signal,
allowing easier mass determination. Lastly, their lower luminosity results in
a closer-in Habitable Zone (HZ), with orbital periods typically of one or two
weeks adequately sampled by TESS.

The James Webb Space Telescope (JWST) is poised to revolutionize the field of
exoplanet atmospheres (Bean et al., 2018) by offering a collecting area more
than 6 times larger than the Hubble Space Telescope (HST) and spectral
coverage from the visible to the mid-infrared (0.6–28 $\mu$m). JWST will allow
simultaneous identification of many chemical species with large absorption
cross section in the infrared (e.g., H2O, CH4, CO, CO2, NH3), as well as probe
the atmosphere of terrestrial planets with unprecedented sensitivity. One key
objective of TESS is to discover the best transiting exoplanets amenable for
atmospheric characterization with JWST (Kempton et al., 2018).

Here, we report the discovery of a new small exoplanet around the nearby M
dwarf TOI-1452. The planet was first detected by TESS, then characterized via
follow-up efforts including RV monitoring with the SPIRou spectropolarimeter.
The complete set of observations is described in Section 2. The host star
properties and physical parameters are derived in Section 3. Our data analysis
and results are presented in Section 4. The implications of this discovery and
prospects for follow-up characterization are discussed in Section 5, followed
by concluding remarks in Section 6.

##  2 Observations

###  2.1 TESS photometry

TOI-1452 (TIC 420112589) was observed by TESS in sectors 14 through 26 (except
18), thus almost continuously from July 18, 2019 to July 4, 2020, in sectors
40–41 from June 25 to August 20, 2021, and finally in sector 47 from December
31, 2021 to January 27, 2022 (details in Table 1). TOI-1452 was sampled at the
TESS 2-minute “short” cadence, as the star is part of the Cool Dwarf List
(Muirhead et al., 2018), a specially curated list of high-priority late-K and
M dwarfs added to the TESS Input Catalog (TIC, Stassun et al. 2018b, 2019). We
used the publicly available111Mikulski Archive for Space Telescopes (MAST):
archive.stsci.edu/tess/ per-sector light curves produced by the TESS Science
Processing Operations Center (SPOC, Jenkins et al. 2016) at NASA Ames, more
specifically their Presearch Data Conditioning Simple Aperture Photometry
(PDCSAP, Smith et al. 2012; Stumpe et al. 2012, 2014). The PDCSAP light curves
are corrected for both instrumental systematic trends seen across stars in the
same sector/camera/CCD and for flux contamination from nearby stars located
within a few TESS pixels (21$\arcsec$). Flux dilution reduces the observable
transit depth, resulting in an underestimation of the planetary radius if not
accounted for. This was particularly important for TOI-1452 because a
companion star (TIC 420112587, see Sect. 3.2) is separated by only $3\farcs 2$
and has a similar magnitude in the TESS band ($\Delta T=0.204$). A new
background correction was implemented for the TESS extended mission (starting
with sector 27). We followed the procedure outlined in the TESS Data Release
38 notes222archive.stsci.edu/tess/tess_drn.html to correct our PDCSAP fluxes
from the primary mission (sectors 14–26), adjusting the baseline level and
reducing the inferred transit depth by $\sim$1.7%. This ensures that the
primary and extended mission data produce the same estimate of the planetary
radius. Figure 1 shows a 11$\times$11 pixels sub-region around TOI-1452 from
TESS sector 14 and the same region of the sky observed from the ground. This
illustrates how TESS alone cannot resolve the source of a transit between
TOI-1452 and the nearby companion TIC 420112587. The normalized PDCSAP light
curve of TOI-1452 from sectors 14 and 21 is presented in Figure 2, while the
remaining sectors are shown in Figure A.1.

Table 1: TESS observations of TOI-1452

Sector | Camera | CCD | UT Start Date | UT End Date
---|---|---|---|---
14 | 3 | 2 | 2019-07-18 | 2019-08-14
15 | 3 | 2 | 2019-08-15 | 2019-09-10
16 | 2 | 1 | 2019-09-12 | 2019-10-06
17 | 4 | 2 | 2019-10-08 | 2019-11-02
19 | 4 | 1 | 2019-11-28 | 2019-12-23
20 | 4 | 1 | 2019-12-24 | 2019-01-20
21 | 4 | 1 | 2020-01-21 | 2020-02-18
22 | 4 | 4 | 2020-02-19 | 2020-03-17
23 | 4 | 4 | 2020-03-19 | 2020-04-15
24 | 3 | 4 | 2020-04-16 | 2020-05-12
25 | 3 | 3 | 2020-05-14 | 2020-06-08
26 | 3 | 3 | 2020-06-09 | 2020-07-04
40 | 3 | 2 | 2021-06-25 | 2021-07-23
41 | 3 | 2 | 2021-07-24 | 2021-08-20
47 | 4 | 1 | 2021-12-31 | 2022-01-27

A search of the sectors 14–16 with an adaptive, wavelet-based matched filter
(Jenkins 2002; Jenkins et al. 2010, Jenkins et al. 2020) first identified
transit signatures for TOI-1452. The Data Validation Reports (DVR; Twicken et
al. 2018; Li et al. 2019) fitted a limb-darkened transit model with a signal-
to-noise ratio (SNR) of 8.0, a period of 11.06409 days, and an average
uncontaminated transit depth of 3.778 parts per thousand (ppt), corresponding
to a preliminary planetary radius of $1.83\pm 0.30$ R⊕. This led to the
announcement of the planet candidate TOI-1452.01 (Guerrero et al., 2021) by
the TESS Science Office on October 26, 2019. Simultaneously, the TESS mission
announced the candidate TOI-1760.01 around the companion star TIC 420112587
sharing the same ephemeris as TOI-1452.01. Ground-based photometry was able to
isolate the transit signal, originating from TOI-1452 (see Sect. 4.1). The
latest available DVR from sectors 14–41 includes 30 transits and reports a
period of 11.06196 days along with a radius $R_{\rm p}=1.60\pm 0.42$ R⊕. Our
complete reanalysis of the TESS light curve presented in Section 4 has
resulted in a more precise planetary radius, in agreement with previous
estimates. Figure 2 shows the phase-folded 32 transits from currently
available sectors. We note that TESS is expected to continue monitoring
TOI-1452 during 2022.

Figure 1: Upper panel: TESS Target Pixel File of TOI-1452 from sector 14
($11\times 11$ pixels sub-region). The optimal aperture to extract the PDCSAP
photometry is delimited by a black line. Nearby Gaia EDR3 sources are
represented with blue circles. TOI-1452 and its $3\farcs 2$ companion (TIC
420112587) are shown with a red and a cyan circle respectively. Lower panel:
Same region of the sky observed with OMM-PESTO 1.6 m on 2020-02-22 (see Sect.
2.2). The visual binary was partially resolved.

Figure 2: Left panels: Normalized PDCSAP light curve of TOI-1452 from sectors
14 and 21, featuring transits (blue data points), a $\sim$5% stellar flare
event (zoomed in sub-panel), and outliers (red data points) either rejected by
sigma clipping (3.5 $\sigma$ clip) or manually (sector 21). A quasi-periodic
Gaussian Process model is depicted with the green curve (details in Sect.
4.2). The remaining sectors are presented in Fig. A.1. Right panel: TESS
phase-folded corrected transits (32) from sectors 14–26, 40–41, and 47. Binned
photometry (8 min phase bin) is represented with black points. The blue curve
shows the best-fit transit model (described in Sect. 4.3), with the 68%
confidence interval envelope in light blue. The residuals of this fit are
shown below.

###  2.2 OMM-PESTO transit monitoring

Due to the coarse image sampling of TESS (21″ per pixel), the origin of a
transit signal may be ambiguous when several stars are located inside the
aperture (e.g., Fig. 1). For this reason, TESS planet candidates are prone to
false positives, occasionally attributed to a nearby eclipsing binary (NEB)
contaminating the light curve (Sullivan et al., 2015). Ground-based follow-up
with arc-second angular resolution is therefore necessary to validate on-
target transit and reject the NEB scenario. For TOI-1452, a particular
challenge was to determine the signal’s provenance between the target and its
$3\farcs 2$ companion.

Two transit events of TOI-1452.01 were observed using the PESTO camera
installed on the 1.6 m telescope of the Observatoire du Mont-Mégantic (OMM),
Québec, Canada. PESTO features a $1024\times 1024$ pixel EMCCD detector with a
pixel scale of $0\farcs 466$, providing a field of view (FOV) of $7\farcm
95\times 7\farcm 95$. We scheduled the two observing sequences with the TESS
Transit Finder (TTF), a customized version of the Tapir software package
(Jensen, 2013), and have used AstroImageJ (AIJ; Collins et al. 2017) to
perform image calibrations, including bias subtractions and flat field
corrections, and differential aperture photometry.

A first full transit was observed on February 22, 2020 in the $i^{\prime}$
filter with a sequence of 30 s exposure time. As seen in the lower panel of
Figure 1, TOI-1452 and TIC 420112587 were partially resolved. Using a circular
aperture of 7$\farcs$9 containing both stars, the transit was detected 53 min
earlier than predicted by the TTF (2.2$\sigma$ early), causing us to miss
observing a proper pre-ingress baseline (see Fig. 3, upper left). Additional
TESS data later confirmed that the period was slightly overestimated by SPOC
(sectors 14–16 only) at the time of observations, explaining why the transit
arrived “early”. The transit timing was also later confirmed by TESS sector 22
data, which was contemporaneous to this dataset. Even without a proper
baseline, this transit was particularly valuable because it allowed us to
reject the NEB false positive scenario and to determine, using point spread
function (PSF) fitting (see Sect. 4.1), that the signal originated from
TOI-1452.

A second full transit of TOI-1452.01 was observed on March 4, 2021 in
$i^{\prime}$, using a 10 s exposure time sequence. With a combined aperture of
8$\farcs$4, the transit was detected on time according to the TTF. In addition
to a standard airmass linear detrending (also performed for the first
transit), we used the Width (mean of the x- and y-direction FWHM) detrending
option in AIJ. This was necessary to account for flux loss when the seeing was
worse for certain exposures in the sequence, without increasing the aperture
radius and dealing with flux contamination from a third star. This made sure
that the transit depth was consistent with the one derived from the first
PESTO observation, when the overall seeing was better (see Table 2).

The OMM-PESTO observations are summarized in Table 2. The resulting aperture
photometry transits are shown in Figure 3, and were included with the 32 TESS
transits in our joint analysis (transit and RV datasets) presented in Section
4.3.

Figure 3: Ground-based transit monitoring of TOI-1452.01 with the PESTO camera
installed at Observatoire du Mont-Mégantic. Left panels: Individual transit
observations in the $i^{\prime}$ band on 2020 February 22 UT and 2021 March 4
UT. Right panel: Transits from the left panels folded in phase, with black
points representing the binned photometry (8 min phase bin). The red curve
shows the best-fit transit model (described in Sect. 4.3), with the 68%
confidence interval envelope in transparent red. The residuals are shown below
the phase-folded transit.

###  2.3 MuSCAT3 transit monitoring

A full transit of TOI-1452.01 was observed on September 8, 2021 with the
multiband imager MuSCAT3 (Narita et al., 2020) on the 2 m Faulkes Telescope
North (FTN) of Las Cumbres Observatory (LCO) at Haleakala observatory, Hawaii.
MuSCAT3 has four optical channels, each of which is equipped with a 2k
$\times$ 2k CCD camera with a pixel scale of 0$\farcs$266 pixel-1, enabling
$g^{\prime}$-, $r^{\prime}$-, $i^{\prime}$-, and $z_{\rm s}$-band simultaneous
imaging. For transit monitoring, significant chromaticity in the transit
depths could indicate a diluted eclipsing binary. The exposure times were set
at 35, 12, 6, and 3 s for the $g^{\prime}$, $r^{\prime}$, $i^{\prime}$, and
$z_{\rm s}$ bands, respectively. The observations were performed in-focus to
spatially resolve the host star from the nearby companion star at $3\farcs 2$,
resulting in the FWHM of stellar point spread function of 3–8 pixels ($0\farcs
8$–$2\farcs 0$) depending on the airmass and band (see Table 2).

The obtained images were calibrated by the BANZAI pipeline (McCully et al.,
2018). We performed aperture photometry on the calibrated images using a
custom pipeline (Fukui et al., 2011) with aperture radii of 5 pixels, or
$1\farcs 3$, for all bands, which is almost free from flux contamination from
the nearby companion star. For each band, we extracted the light curve using
different sets of comparison stars, but have found that using only the
companion (TIC 420112587) as a reference produced the minimum point-to-point
dispersion. Since both the companion and the target stars have a similar color
and are close to each other, the attenuation by the atmosphere is almost
identical, so that we can safely assume that any second-order extinction
effect (airmass dependent) is almost negligible. We clearly detected the
transit on the target star in all bands, as shown in Figure 4, providing
further unambiguous evidence that TOI-1452 hosts a transiting object. A
summary of this dataset is provided in Table 2.

Figure 4: Ground-based transit follow-up of TOI-1452.01 on 2021 September 8 UT
with the multi-filter ($g^{\prime}$, $r^{\prime}$, $i^{\prime}$, $z_{\rm s}$)
MuSCAT3 instrument installed on LCO-FTN at Haleakala Observatory. For each
corresponding filter, the black points depict the binned photometry (8 min
temporal bin). The color-coded curves correspond to each filter’s best-fit
transit model (described in Sect. 4.3), with their respective 68% confidence
interval envelope in lighter shade. The residuals are shown below each phase-
folded transit. Table 2: Summary of the ground-based transit monitoring of
TOI-1452

UT Date | Camera | Filter | PSF | Aperture
---|---|---|---|---
|  |  | FWHM (′′) | Size (′′)
OMM 1.6 m
2020-02-22 | PESTO | $i^{\prime}$ | 2.9 | 7.9†
2021-03-04 | PESTO | $i^{\prime}$ | 3.9 | 8.4†
LCO-FTN 2 m
2021-09-08 | MuSCAT3 | $g^{\prime}$ | 1.8 | 1.3
2021-09-08 | MuSCAT3 | $r^{\prime}$ | 1.3 | 1.3
2021-09-08 | MuSCAT3 | $i^{\prime}$ | 1.3 | 1.3
2021-09-08 | MuSCAT3 | $z_{\rm s}$ | 1.0 | 1.3

Note. — †Using an aperture containing TOI-1452 and TIC 420112587

###  2.4 Keck II/NIRC2 high-resolution imaging

One or more unresolved sources not in Gaia EDR3 could still be located close
to TOI-1452, whether gravitationally bound or not. A blended eclipsing binary
(BEB) could indicate a false positive detection, and any other flux source
would lead to underestimate the size of the transiting object in the TESS,
PESTO and MuSCAT3 light curves. For these reasons, we searched for sub-
arcsecond sources around TOI-1452 with the NIRC2 adaptive optics imaging
camera installed on the 10 m Keck II telescope. The images were acquired on
May 28, 2020 in the $K$ band with a spatial resolution of 0$\farcs$01 per
pixel, integration time per coadd of 1.6 s, mean PSF FWHM of 0$\farcs$061, and
airmass of 1.69. Figure 5 shows the 5$\sigma$ contrast curve of TOI-1452,
revealing that no additional companion is detected with a contrast ratio
$\Delta K\leq 5.429$ for separation greater than $0\farcs 5$. Although in the
$K$ band, this contrast limit is similar to the difference in magnitude
required ($\Delta T=5.55$) for a 50% depth BEB to mimic a 3 ppt transit in the
TESS light curve. Following the procedure of Lillo-Box et al. (2014), we
calculated the probability of contamination from a blended source due to a
random alignment inside $0\farcs 5$. For this, we simulated the galactic
stellar population in a region near the target with TRILEGAL (Girardi et al.,
2012), using their default bulge, halo, disk (thin and thick) parameters and
the log-normal initial mass function of Chabrier (2001). The probability of an
undetected source with $\Delta K\leq 5.55$ inside $0\farcs 5$ is less than
0.04%, so we can safely assume that the transit signal is not produced by a
BEB or significantly diluted by a background star.

Figure 5: $K$-band 5$\sigma$ contrast curve of TOI-1452 from KeckII/NIRC2
adaptive optics imaging. No close companion is detected.

###  2.5 SPIRou velocimetry

TOI-1452 was observed at 53 epochs from June 4, 2020 to October 8, 2020 with
the near-infrared (0.98–2.5 $\mu$m) SPIRou spectropolarimeter (Donati et al.
2018; 2020) mounted on the 3.6 m Canada-France-Hawaii telescope (CFHT). The
observations were conducted as part of the ongoing SPIRou Legacy Survey (SLS;
Donati et al. 2020), more precisely its Transit Follow-up program (SLS-WP2),
which aims to characterize exoplanets orbiting low mass stars revealed by
photometric surveys such as TESS. SLS-WP2 has thus far allowed the
characterization of the brown dwarf TOI-1278 B (Artigau et al., 2021), the
sub-Neptune TOI-1759 b (Martioli et al., 2022) transiting M dwarfs, and the
studies of the transiting planets HD 189733 b (Moutou et al. 2020; Boucher et
al. 2021) and AU Mic b (Martioli et al., 2020).

SPIRou offers simultaneous high resolution spectroscopy and polarimetry, with
a spectral resolving power $R\sim 70\,000$. Each epoch measurement consisted
of four consecutive 15-min exposures, i.e., a polarimetric sequence, with two
rotating Fresnel rhombs varying positions between the exposures. During such a
sequence, the two science fibers, A and B, each receive orthogonal
polarization states, giving access to the circular polarization and total
intensity of the light beam (Stokes V and I). A total of 212 spectra were
collected, with SNR per spectral element ($\sim$2.2 km/s/pixel for SPIRou)
between 20 and 65 (median of 55) near 1.6 $\mu$m. Four individual spectra were
rejected; one due to loss of guiding, three others because of high extinction
(clouds). A single polarimetric sequence of four 15-min exposures was also
acquired on the $3\farcs 2$ companion (TIC 420112587) on April 22, 2021,
principally to check its rotation profile and magnetic activity level (see
Section 3.5). The diameter of the SPIRou fiber is $1\farcs 33$ and the typical
seeing during the observations of TOI-1452 was $0\farcs 8$. We measure no
correlation between the radial velocity residuals (Keplerian and activity
models described in Sect. 4.3) and the seeing, suggesting that any effect of
contamination from the companion was negligible. Per-epoch RV measurements
consisted of taking the error weighted mean of the individual observations
within a polarimetric sequence. The data analysis presented in Section 4.3 was
performed on the unbinned RVs, but we show the per-epoch average to facilitate
visualization.

The SPIRou data were reduced with APERO v0.7.194 (Cook et al., in prep.). In
brief, APERO starts by correcting known H4RG infrared detector defects
(Artigau et al., 2018), then proceeds to identify bad pixels, locate each
spectral order on the image, calculate the shape of the instrument pupil
slicer (Micheau et al., 2018), and finally determine from nightly calibration
sequences the flat and blaze corrections to apply. Once this preprocessing and
calibration step is completed, APERO performs an optimal flux extraction
(Horne, 1986) in both science channels, separately (fibers A and B) and
together (AB), as well as in the simultaneous calibration channel (fiber C).
The extracted 2D images (49 orders by 4088 pixels) are then spectral flat
fielded, as well as corrected for thermal background and for any leakage from
the calibration channel to the science ones. A nightly pixel-to-wavelength
solution is applied using a combination of a UNe hollow-cathode lamp and a
Fabry-Perot (FP), as described in Hobson et al. (2021). APERO uses the
simultaneous FP measurements from fiber C to calculate drifts between
individual science frames relative to the nightly wavelength solution
(typically below 2 m/s). Finally, a telluric absorption and night-sky emission
correction is applied in a two-step process. The science frames are first pre-
cleaned with a TAPAS (Bertaux et al., 2014) absorption model that leaves
percent-level residuals for deep ($>$50%) H2O and dry absorption features
(e.g., CH4, O2, CO2, N2O and O3). Then, a telluric residuals model with 3
degrees of freedom per pixel (optical depths for the H2O and dry components
and a constant) is fitted to the pre-cleaned spectra. The grid of telluric
models was generated from a set of rapidly rotating hot stars observed with
SPIRou at various airmass, water columns, and dry absorptions, producing
telluric corrected spectra with final residuals at the level of the PCA-based
method of Artigau et al. (2014).

Radial velocity measurements were obtained from the telluric-corrected spectra
using the novel line-by-line (LBL) method (Artigau et al., 2022). The LBL
formalism is based on the Bouchy et al. (2001) framework, in which Doppler
shifts are inferred for individual spectral lines ($\sim$16 000 for an M dwarf
observed with SPIRou) as opposed to a given spectral range. As in Bouchy et
al. (2001), such calculations require a noiseless template since velocities
are derived from the comparison between the residuals (observed spectrum minus
template) and the derivative of the template. For a given observed star, one
uses in practice a high SNR combined spectrum as a template, so that any
remaining noise is small compared to that of an individual spectrum. For
TOI-1452, the combined spectrum produced by APERO did not reach a SNR as high
as other bright standard stars observed in the SLS. Moreover, TOI-1452 is
located near the North ecliptic pole, meaning its yearly Barycentric Earth
Radial Velocity (BERV) variation is small. Our observations with SPIRou
covered BERV excursions between 1.7 and 4.8 km/s, which is not ideal to filter
out tellurics lines (i.e., stellar lines do not move a lot with respect to the
telluric lines), producing a template that still contains some telluric
artefacts. For these reasons, we used the template of Gl 699, a standard star
monitored with SPIRou for 2.5 years with a spectral type (M4V) similar to that
of TOI-1452 (M4$\pm$0.5, see Sect. 3.1) and a good BERV coverage ($\pm 26$
km/s).

For each spectrum, the LBL algorithm combines thousands of per-line velocities
into a single RV measurement, with per-line uncertainties varying from 50 m/s
for the strongest features to tens of km/s for the shallow ones. This is
achieved using a simple mixture model: per-line velocities either originate
from a Gaussian distribution centered on the mean velocity, with a standard
deviation derived from Bouchy et al. (2001), or they arise from another
distribution, namely that of high-sigma outliers, whose plausible causes are
diverse (persisting bad pixels, cosmic rays, telluric residuals, etc.).
Lastly, the LBL RVs are corrected for the instrumental day-to-day drift
measured by the FP and for a long-term zero point obtained with a Gaussian
process regression using the most observed stars in the SLS. This zero point
calibration is similar to Courcol et al. (2015) for the SOPHIE spectrograph,
but will be described in more details in a forthcoming publication (Vandal et
al., in prep.). The comparison between the LBL and other methods such as the
cross-correlation function and template matching is discussed in Martioli et
al. (2022) and in Artigau et al. (2022). The final SPIRou radial velocities of
TOI-1452 are listed in Table D.1, with typical precision of 8.0 m/s per
exposure, or 4.0 m/s per epoch.

###  2.6 IRD velocimetry

Seven high-resolution spectra of TOI-1452 were obtained with the InfraRed
Doppler (IRD) spectrograph on the Subaru 8.2 m telescope (Tamura et al., 2012;
Kotani et al., 2018) between September 26, 2020 and June 25, 2021. IRD covers
the near-infrared wavelengths between 970 nm and 1730 nm, with a spectral
resolution $R\sim 70\,000$. For accurate RV measurements, stellar spectra were
obtained simultaneously with the reference spectra of the laser-frequency comb
(LFC). The integration times were set to 600–1500 sec, depending on the
available observing time slots and sky conditions. The IRD fiber has a
$0\farcs 48$ diameter, so that flux contamination from the companion star is
not an issue.

The raw IRD data were reduced following the standard procedure of Hirano et
al. (2020). We extracted wavelength-calibrated one-dimensional spectra for
TOI-1452, as well as for the simultaneously injected LFC. The typical SNR of
the TOI-1452 extracted spectra was 60–70 per pixel around 1000 nm. To measure
precise RVs for TOI-1452, the reduced spectra were put into the RV analysis
pipeline for IRD (Hirano et al., 2020). This pipeline fits each small spectral
segment of the observed spectra by the forward-modeling technique, taking into
account the instantaneous variations of Earth’s atmospheric features as well
as the instrumental profile of the spectrograph (which is estimated based on
each laser-comb spectrum). The seven IRD RV measurements have an overall
precision of 4.0 m/s and are given in Table D.1.

##  3 Stellar Characterization

###  3.1 TOI-1452 (TIC 420112589)

The star TOI-1452 (TIC 420112589) is a nearby M dwarf at a distance of 30.504
$\pm$ 0.013 pc (Gaia Collaboration et al., 2021). This star does not belong to
any known young stellar moving groups, with a very high probability ($>$99.9%)
of being a field star (Gagné et al., 2018). The presence of flares and short-
period sinusoidal signal in the TESS PDCSAP data (see Fig. 2 and A.1) cannot
be attributed with certainty to TOI-1452, due to flux contamination from
multiple nearby objects. An analysis of the photometric variations is
presented in Section 4.2, but we note that the polarimetric data from SPIRou
reveal no important surface magnetic field variations (see Sect. 3.5),
suggesting that TOI-1452 is relatively quiet, with a rotation period probably
much longer than the modulation seen in the TESS light curve.

As discussed in Section 3.4, we measure an effective temperature of $3185\pm
50$ K for TOI-1452 using the SPIRou combined spectrum, from which a spectral
type (SpT) between M4 and M4.5 is inferred based on Table 5 of Pecaut &
Mamajek (2013). We also considered the Gaia DR2 color to SpT relation of Kiman
et al. (2019), more specifically the $G$ – $G_{\rm RP}$ relationship, for an
independent SpT determination. From this relationship, the Gaia magnitudes and
their respective uncertainties, we obtain a SpT of M$3.7\pm 0.6$. The same M4
spectral type was derived through a visual comparison of the SPIRou combined
spectrum, degraded to a lower resolution ($R\sim 5\,000$), with spectral type
standards of the IRTF spectra library (Cushing et al. 2005; Rayner et al.
2009). Considering all these estimates, we adopt a SpT of M4 $\pm$ 0.5.

The mass of TOI-1452 was inferred from the Mann et al. (2019) absolute $K_{\rm
s}$ magnitude ($M_{K_{\rm s}}$) to $M_{\star}$ relation for M dwarfs. Taking
into consideration the dispersion of this relation, the $K_{\rm s}$ magnitude,
the distance, and their corresponding uncertainties, a mass of $0.249\pm
0.008$ M⊙ is obtained. A similar approach was used to measure the stellar
radius, this time using the $M_{K_{\rm s}}$–$R_{\star}$ relationship of Mann
et al. (2015), from which we derive $R_{\star}=0.275\pm 0.009$ R⊙. Other
physical parameters such as the surface gravity ($\log g$), the mean density
($\rho_{\star}$), and the luminosity ($L_{\star}$) were determined from the
$M_{\star}$, $R_{\star}$, and $T_{\rm eff}$ estimates. The stellar parameters
of TOI-1452 are summarized in Table 3.1.

Table 3: TOI-1452 stellar properties

Parameter | Value | Ref.
---|---|---
Designations
TIC | 420112589 | 1
TOI | 1452 | 1
2MASS | J19204172+7311434 | 2
UCAC4 | 816-023943 | 3
Gaia EDR3 | 2264839957167921024 | 4
Astrometry
RA (J2016.0) | 19:20:41.75 | 4
DEC (J2016.0) | +73:11:42.35 | 4
$\mu_{\alpha}\cos\delta$ (mas/yr) | 7.800 $\pm$ 0.017 | 4
$\mu_{\delta}$ (mas/yr) | -74.076 $\pm$ 0.017 | 4
$\pi$ (mas) | 32.7823 $\pm$ 0.0140 | 4
Distance (pc) | 30.5043 $\pm$ 0.0130 | 4
Stellar parameters
$T_{\rm eff}$ (K) | 3185 $\pm$ 50 | 5
SpT | M4 $\pm$ 0.5 | 5
$\left[{\rm M/H}\right]$ |  $-0.07$ $\pm$ 0.02 | 5
$M_{\star}$ (M⊙) | 0.249 $\pm$ 0.008 | 5
$R_{\star}$ (R⊙) | 0.275 $\pm$ 0.009 | 5
log $g$ (dex) | 4.95 $\pm$ 0.03 | 5
$\rho_{\star}$ (g/cm3) | 16.8 $\pm$ 1.9 | 5
$L_{\star}$ (L⊙) | 0.0070 $\pm$ 0.0006 | 5
Photometry
$B$ | 15.94 $\pm$ 0.03 | 1
$V$ | 14.35 $\pm$ 0.12 | 1
$G_{\rm BP}$ | 15.222 $\pm$ 0.004 | 4
$G$ | 13.598 $\pm$ 0.003 | 4
$G_{\rm RP}$ | 12.362 $\pm$ 0.004 | 4
$T$ | 12.295 $\pm$ 0.007 | 1
$g$ | 15.580 $\pm$ 0.002 | 6
$r$ | 14.383 $\pm$ 0.007 | 6
$i$ | 12.873∗ | 6
$z$ | 12.272∗ | 6
$y$ | 11.875 $\pm$ 0.020 | 6
$J$ | 10.604 $\pm$ 0.058 | 2
$H$ | 10.026 $\pm$ 0.058 | 2
$K_{\rm s}$ | 9.740 $\pm$ 0.046 | 2
$W1$ | 8.938 $\pm$ 0.023† | 7
$W2$ | 8.760 $\pm$ 0.019† | 7
$W3$ | 8.686 $\pm$ 0.023† | 7
$W4$ | 8.46 $\pm$ 0.29† | 7

Note. — ∗The uncertainty was not indicated.

†WISE magnitudes include the flux from TOI-1452 and TIC 420112587.

References. — (1) TIC (Stassun et al., 2019). (2) 2MASS (Skrutskie et al.,
2006). (3) UCAC4 (Zacharias et al., 2013). (4) Gaia EDR3 (Gaia Collaboration
et al., 2021). (5) This work. (6) Pan-STARRS1 DR2 (Chambers et al., 2016). (7)
AllWISE (Wright et al., 2010).

###  3.2 Bound companion (TIC 420112587)

TOI-1452 has a resolved companion (TIC 420112587) with several comparable
photometric and astrometric measurements. The two objects have similar Gaia
EDR3 magnitudes of $G=13.598\pm 0.003$ and $G=13.830\pm 0.003$ for TOI-1452
and TIC 420112587 respectively. Their Gaia EDR3 parallaxes are identical
(within the errors), $32.782\pm 0.014$ mas for TOI-1452 and $32.791\pm 0.014$
mas for TIC 420112587, indicating a very similar distance to these stars.
Their projected angular separation is $3\farcs 182$, which corresponds to a
projected physical separation of $\sim$97 au, using a common approximate
distance of 30.5 pc. The proper motion of TIC 420112587 is similar to that of
TOI-1452, with $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ within 15% for the
two stars (see Tables 3.1 and 3.2). TOI-1452 and TIC 420112587 most likely
form a visual binary, i.e., a resolved gravitationally bound system, which was
previously reported in the TOI visual-binary catalog of Mugrauer & Michel
(2020), as well as in the binary catalog based on Gaia EDR3 of El-Badry et al.
(2021). From our single visit on the companion star with SPIRou, we measure an
RV offset between TOI-1452 and TIC 420112587 of $-6.9$ km/s. The SPIRou
template spectrum of TIC 420112587 combining only four individual spectra at
the same epoch and BERV does not allow for a similar spectral analysis as the
one presented for TOI-1452 in Section 3.4.

Using the empirical relationships of Mann et al. (2015, 2019), we obtain a
mass of 0.226 $\pm$ 0.006 M⊙ and a radius of 0.254 $\pm$ 0.008 R⊙ for TIC
420112587. The mass ratio of the binary system is close to unity ($q=0.91\pm
0.04$), with TOI-1452 as the primary member. The projected physical separation
and masses of the two stars imply an orbital period of about 1400 years. The
radial velocity variation expected from such an orbital motion and for a
circular orbit is under $\sim$1.5 m/s over the span of our SPIRou RV
observations. According to Table 5 of Pecaut & Mamajek (2013) and a $T_{\rm
eff}=3060\pm 50$ K derived from the spectral energy distribution (see analysis
below), TIC 420112587 has an M5 spectral type. The Kiman et al. (2019) $G$ –
$G_{\rm RP}$ relationship yields a SpT of M$4.0\pm 0.6$, so we adopt an
intermediate spectral type of M4.5 $\pm$ 0.5. A summary of the stellar
properties of TIC 420112587 is presented in Table 3.2.

Table 4: TIC 420112587 stellar properties

Parameter | Value | Ref.
---|---|---
Designations
TIC | 420112587 | 1
TOI | 1760 | 1
2MASS | J19204172+7311467 | 2
Gaia EDR3 | 2264839952875245696 | 3
Astrometry
RA (J2016.0) | 19:20:41.76 | 3
DEC (J2016.0) | +73:11:45.53 | 3
$\mu_{\alpha}\cos\delta$ (mas/yr) | 6.845 $\pm$ 0.017 | 3
$\mu_{\delta}$ (mas/yr) | -82.216 $\pm$ 0.017 | 3
$\pi$ (mas) | 32.7913 $\pm$ 0.0141 | 3
Distance (pc) | 30.4959 $\pm$ 0.0131 | 3
Stellar parameters
$T_{\rm eff}$ (K) | 3060 $\pm$ 50 | 4
SpT | M4.5 $\pm$ 0.5 | 4
$M_{\star}$ (M⊙) | 0.226 $\pm$ 0.006 | 4
$R_{\star}$ (R⊙) | 0.254 $\pm$ 0.008 | 4
log $g$ (dex) | 4.98 $\pm$ 0.03 | 4
$\rho_{\star}$ (g/cm3) | 19.5 $\pm$ 1.8 | 4
$L_{\star}$ (L⊙) | 0.0051 $\pm$ 0.0005 | 4
Photometry
$B$ | 15.76 $\pm$ 0.17 | 1
$V$ | 13.99 $\pm$ 0.2 | 1
$G_{\rm BP}$ | 15.512 $\pm$ 0.005 | 3
$G$ | 13.830 $\pm$ 0.003 | 3
$G_{\rm RP}$ | 12.576 $\pm$ 0.004 | 3
$T$ | 12.499 $\pm$ 0.008 | 1
$g$ | 15.890 $\pm$ 0.002 | 5
$r$ | 14.659 $\pm$ 0.003 | 5
$i$ | 13.153 $\pm$ 0.002 | 5
$z$ | 12.456 $\pm$ 0.021 | 5
$y$ | 12.111 $\pm$ 0.007 | 5
$J$ | 10.795 $\pm$ 0.027 | 2
$H$ | 10.257 $\pm$ 0.031 | 2
$K_{\rm s}$ | 9.944 $\pm$ 0.023 | 2

References. — (1) TIC (Stassun et al., 2019). (2) 2MASS (Skrutskie et al.,
2006). (3) Gaia EDR3 (Gaia Collaboration et al., 2021). (4) This work. (5)
Pan-STARRS1 DR2 (Chambers et al., 2016).

###  3.3 Spectral energy distribution fit

As an independent determination of the basic stellar parameters, as well as to
estimate the contaminating flux from the nearby companion star, we performed
an analysis of the broadband spectral energy distribution (SED) of the stars
together with the Gaia EDR3 parallax (with no systematic offset applied; e.g.,
Stassun & Torres, 2021), following the procedures described in Stassun &
Torres (2016) and Stassun et al. (2017, 2018a). For both stars, we pulled the
$JHK_{S}$ magnitudes from 2MASS, the W1–W4 magnitudes from WISE, and the
$grizy$ magnitudes from Pan-STARRS. Together, the available photometry spans
the full stellar SED over the wavelength range 0.4–10 $\mu$m (see Figure 6).
We excluded the WISE photometry from the initial fitting because the two stars
are blended in WISE, such that the catalog photometry in fact represents the
sum of the fluxes of both stars.

Figure 6: Spectral Energy Distributions (SED) of TOI-1452 and TIC 420112587
fitted with a NextGen atmospheric model, respectively depicted with a black
and a cyan line. Photometric measurements are represented with red (TOI-1452)
and blue (TIC 420112587) error bars, where the horizontal bars represent the
effective widths of the bandpasses and the small blue dots represent the model
fluxes of TOI-1452 for comparison to the red symbols. The WISE measurements
(3.4, 4.6, 12, and 22 $\mu$m), excluded from this analysis for including both
star fluxes, agree with the sum of the two SED (green).

For each star, we performed a fit using NextGen stellar atmosphere models
(Hauschildt et al., 1999), with the free parameters being the effective
temperature ($T_{\rm eff}$) and metallicity ([Fe/H]). The remaining free
parameter is the extinction $A_{V}$, which we fixed at zero due to the stars’
proximity. The resulting fit for TOI-1452 (Figure 6) has a reduced $\chi^{2}$
of 1.8 with $T_{\rm eff}=3100\pm 50$ K and [Fe/H] = $0.0\pm 0.5$. Integrating
the model SED gives the bolometric flux at Earth, $F_{\rm bol}=2.34\pm
0.11\times 10^{-11}$ erg s-1 cm-2. Taking the $F_{\rm bol}$ and $T_{\rm eff}$
together with the Gaia parallax, gives the stellar radius, $R_{\star}=0.286\pm
0.011$ R⊙. This independent radius measurement is consistent, although
slightly less precise, with the one derived using Mann et al. 2015
($R_{\star}=0.275\pm 0.009$ R⊙).

Similarly, the resulting parameters for the companion star from the SED fit
are $T_{\rm eff}=3060\pm 50$ K, [Fe/H] $=0.0\pm 0.5$, and $R_{\star}=0.263\pm
0.010$ R⊙. This radius estimate is again fully consistent with the value
derived from empirical relation ($R_{\star}=0.254\pm 0.008$ R⊙). The sum of
the two stellar models is compared to the combined WISE fluxes in Figure 6,
showing good agreement. Integrating the companion SED within the TESS bandpass
yields a flux ratio (companion relative to TOI-1452) of $0.77\pm 0.03$. Note
that the flux ratio derived strictly from the $T$ magnitudes from the TIC is
$0.829\pm 0.002$. In the event that the PDCSAP overestimated the dilution
correction for TIC 420112587, this difference in flux ratio would imply a
$\sim$1.7% overestimation of the planetary radius.

###  3.4 Stellar parameters from SPIRou spectra

The high-resolution combined spectrum of TOI-1452 from SPIRou lets us
determine $T_{\rm eff}$ and the abundance of several elements with relatively
good accuracy. This work follows the methodology of Jahandar et al. (in
prep.), which we briefly summarize here. Because models and observations can
often show significant discrepancies (e.g., continuum mismatch in the $Y$ and
$J$ bands), we only select for the fitting analysis a subset of relatively
strong lines that are matching the models. The selected lines are then divided
into several groups of 15 lines, each analyzed independently through a chi-
squared fitting routine to infer both $T_{\rm eff}$ and [M/H] for all groups.
The spectrum is compared with a grid of ACES models (Allard et al. 2012a;
Husser et al. 2013). The advantage of this method is that it yields several
(typically 15) independent measurements that can be used to characterize the
inherent uncertainties associated with the fitting procedure. This analysis
applied to the TOI-1452 spectrum yields $T_{\rm eff}=3185\pm 50$ K and
[M/H]=$-0.07\pm 0.02$, in good agreement with the parameters derived from the
SED fitting analysis. The quoted uncertainty for $T_{\rm eff}$ is internal to
our fitting methodology and ignore potential systematic differences with
bolometric $T_{\rm eff}$ estimates based on interferometric measurements.
While our $T_{\rm eff}$ estimates have yet to be calibrated with bolometric
$T_{\rm eff}$, it is empirically demonstrated that 50–60 K is a typical
uncertainty derived from atmosphere models (e.g., Mann et al. 2013; 2015). We
thus adopt 50 K for our $T_{\rm eff}$ uncertainty, a conservative value given
that the temperature derived from the SPIRou spectrum is inferred from several
independent measurements. An illustration of the temperature and abundance
sensitivity for an Al I line (at 1675.514 nm) is shown in Figure 7. In
practice, several tens of lines are used to derive $T_{\rm eff}$.

Once $T_{\rm eff}$ is determined, one can then proceed, through a similar
procedure, to determine the abundance of all individual lines of a given
element. The high-resolution near-infrared spectrum of an M dwarf is
characterized by several hundreds of relatively strong OH lines. By selecting
only those that are well isolated, i.e., with no known spectral features
within a few pixels using the PHOENIX/BT-Settl (Allard et al. 2012b; 2013) and
NIST (Ralchenko et al., 2010) line lists, we find 72 OH lines, whose
individual abundance can be used to quantify the inherent, per-line
uncertainty of this method. This uncertainty obviously does not consider any
possible systematic errors associated with the ACES atmosphere models. The 72
independent OH abundance measurements are presented in Figure 8, showing a
good match with a Gaussian distribution with standard deviation 0.13 dex. For
all elements and molecules detected in TOI-1452, we list the average abundance
of all lines in Table 5 (see also Figure 9). For chemical species with only
one line, we adopt an uncertainty of 0.13 dex from the OH distribution. We
report abundances for Fe, Mg and Si that constitute the bulk material of an
exoplanet core and mantle. The overall metallicity ([M/H]) and its
corresponding error are determined by averaging the final abundance of each
element in Table 5, assuming a common uncertainty for all elements taken as
the median of all individual uncertainties. This approach is chosen to avoid
putting too much weight on the oxygen abundance characterized by a small
uncertainty.

Figure 7: SPIRou observation of the Al I line (1675.514 nm) of TOI-1452 (black
dashed line). Top panel: The solid lines represent the ACES models for a fixed
metallicity of 0.1 dex and $T_{\rm eff}$ values of 3060 K, 3160 K, and 3260 K.
Bottom panel: Same as top panel, but the ACES models have a fixed $T_{\rm
eff}=3160$ K and metallicity values of $-0.2$ dex, 0.1 dex and 0.5 dex. These
plots illustrate the good sensitivity of near-IR high-resolution spectroscopy
for constraining both the metallicity and effective temperature of M dwarfs.
Figure 8: Distribution of OH abundance measurements from 72 isolated OH lines
in the SPIRou combined spectrum of TOI-1452. The inherent, per-line
uncertainty (0.13 dex) is inferred from a Gaussian fit of this distribution.
This uncertainty does not take into account possible systematic errors of the
stellar atmosphere models. Figure 9: Chemical abundances of 12 different
elements via line-by-line spectroscopy of 151 spectral features. The dashed
line represents the average metallicity of the star corresponding to the
average of all elements. Table 5: Stellar abundance of TOI-1452 for various
chemical species measured by SPIRou

Element | [X/H] | $\sigma$ | # of lines
---|---|---|---
Fe I | $-0.07$ | 0.03 | 38
Al I | 0.07 | 0.11 | 4
Mg I | $0.02$ | 0.07 | 5
Si I | $0.11$ | 0.13 | 1
Ti I | $-0.31$ | 0.06 | 10
Ca I | $0.01$ | 0.12 | 2
Cr I | $0.04$ | 0.06 | 4
K I | 0.03 | 0.13 | 1
O I∗ | $-0.24$ | 0.02 | 72
C I | $-0.17$ | 0.05 | 11
N I | $-0.12$ | 0.13 | 1
Na I | $-0.22$ | 0.06 | 2
$<>^{{\dagger}}$ | $-0.07$ | 0.02 | –

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

†Average abundance of all elements.

###  3.5 Spectropolarimetry with SPIRou

The combination of the four exposures within a polarimetric sequence obtained
with SPIRou yields the circular polarization profile at the surface of the
star (Donati et al., 2020). The intensity (Stokes I), circular (Stokes V), and
null polarization spectra were generated in APERO following the spirou-
polarimetry code333github.com/edermartioli/spirou-polarimetry. We applied the
Least-Square Deconvolution (LSD) method of Donati et al. (1997), also outlined
in Martioli et al. (2020), to compute the average I and V profiles. We used
the VALD database (Piskunov et al., 1995) and a MARCS atmosphere model
(Gustafsson et al., 2008) with $T_{\rm eff}=3000$ K and log $g$ = 5.0 dex to
search for valid atomic features. Lines deeper than 3 % and with a known Landé
factor were selected to produce a line mask of 955 atomic lines, used in this
LSD analysis of TOI-1452. An estimate of the longitudinal magnetic field
($B_{\ell}$) at the stellar surface can then be obtained using Equation 5 of
Donati et al. (1997), combining the Stokes I and V LSD profiles, the mean
Landé factor of 1.24, and the mean wavelength of 1604.59 nm. By doing this
over multiple epochs, one can monitor the large-scale surface magnetic field,
expected to vary with the rotation of the star. The polarimetric capabilities
of SPIRou can thus serve as a useful activity tracer simultaneous to the RV
measurements, as demonstrated in Martioli et al. (2022), where the rotation
period of the moderately active M0 star TOI-1759 ($P_{\rm
rot}=35.65^{+0.17}_{-0.15}$ days) was determined from the $B_{\ell}$ time
series. We obtained independent and consistent values for the $B_{\ell}$ of
TOI-1452 using the Libre-Esprit pipeline (Donati et al. 1997, Donati et al.
2020), but present below the values from the APERO pipeline.

The $B_{\ell}$ time series of TOI-1452 is presented in Figure 10. A simple
Lomb-Scargle periodogram analysis shows no obvious periodicity. The $B_{\ell}$
data do not favor a sinusoidal model, which could be associated with stellar
rotation, over a constant magnetic field (mean $B_{\ell}=-3.8\pm 1.8$ G). The
small variation of $B_{\ell}$ suggests that the field is intrinsically weak
(quiet star), or that it is strongly axisymmetric with respect to the rotation
axis. Alternatively, the rotation period of TOI-1452 could be longer than the
4-month span of our observations, but this is close to the largest known
period for M dwarfs (Newton et al., 2018).

This LSD analysis was also applied on the companion star TIC 420112587 using
the single polarimetric sequence acquired with SPIRou. We report a
polarimetric signal and a $B_{\ell}$ consistent with a null value, indicating
that the companion is also probably inactive.

Figure 10: Top panel: Monitoring of the longitudinal magnetic field
($B_{\ell}$) of TOI-1452 with SPIRou. Bottom panel: Lomb-Scargle periodogram
of the $B_{\ell}$ time series. No clear periodic signal is detected,
suggesting a relatively quiet star.

##  4 Data Analysis & Results

###  4.1 Determining the transit origin with PSF photometry

The objective of the first OMM-PESTO transit follow-up was to establish the
origin of the TESS signal, particularly between the target (TOI-1452) and its
companion (TIC 420112587). Standard aperture photometry ruled out any NEB in
the FOV, but was unable to isolate the transit between the two stars, as they
were only partially resolved. We therefore had to rely on a different method
using point spread function (PSF) fitting to extract the relative flux of both
stars. We used the photutils (Bradley et al., 2020) package to perform the
DAOPHOT (Stetson, 1987) PSF photometry algorithm. This was achieved by fitting
the PSFs with an effective PSF model (ePSF) generated in photutils using the 6
stars with the highest SNR in the FOV (excluding our targets), then
integrating the best-fit models over pixels containing the stars’ signal.

The intent here was not to produce a precise uncontaminated light curve, but
rather to detect any flux deficit (or excess) that would indicate from which
star the transit originates. We thus inspected the TOI-1452 to TIC 420112587
flux ratio as a function of time, normalized to unity outside of transit. The
resulting relative light curve is presented in Figure 11 and shows a flux
deficit on TOI-1452 during transit. We did not fit a transit model on this
light curve, as it is less precise than the one obtained using a combined
circular aperture (Fig. 3). We nonetheless measure a mean relative flux
deficit of $2.33\pm 0.43$ ppt, which is an approximation of the uncontaminated
transit depth. This flux deficit is comparable in amplitude to the diluted
corrected TESS depth ($3.31\pm 0.19$ ppt) and was detected with a confidence
level sufficiently high ($>$5$\sigma$) to conclude that TOI-1452 was the
source of the transit and justify an RV monitoring campaign on this star,
starting with SPIRou in June 2020. Later, the MuSCAT3 photometry was able to
resolve TOI-1452 and TIC 420112587 and unambiguously identify that the former
star hosts a transiting object.

Figure 11: PSF photometry relative light curve (TOI-1452 to TIC 420112587 flux
ratio) from OMM-PESTO on 2020-02-22. The dotted black lines represent the
ingress and egress of the transit estimated from contemporaneous TESS sector
22 data. The light curve is normalized with the out-of-transit median. A flux
deficit during transit with a depth comparable to TESS is detected on
TOI-1452.

###  4.2 TESS light curve analysis

The TOI-1452 PDCSAP light curve (Fig. 2 and A.1) features stellar flares with
amplitude of a few percents and ppt-level sinusoidal variations. A strong peak
at 0.93 days appears in the Lomb-Scargle periodogram of the multi-year light
curve, as well as in all individual sectors. However, computing the
autocorrelation function, which is more reliable for accurate photometric
rotation period determination (McQuillan et al., 2013), would often find a
period of 1.9 days (2$\times$0.93 days) depending on the sector. Since the
PDCSAP data are corrected for systematic trends, it is unlikely that such
corrections significantly perturb those short-term flares and sinusoids.
Regardless of the origin of these signals (TOI-1452, TIC 420112587, or any
contaminating star), it is crucial to remove the periodic variations to
accurately measure the transit parameters. To accomplish this, we adopted a
sequential approach where we first correct the PDCSAP data using a Gaussian
Process (GP), then fit the 32 corrected transits with a model. The details of
the GP regression are presented below, while the transit modeling is described
in Section 4.3.

We started by masking the epochs of transit and removing outliers from the
PDCSAP light curve with sigma clipping. It was determined that a 3.5 $\sigma$
clipping was robust enough to remove both obvious outliers and stellar flares.
This sigma clipping removed less than 0.2% of the out-of-transit data. Parts
of sectors 21 and 47 coinciding with TESS momentum dump events show large
amplitude variations; those were considered to be non-astrophysical and were
manually rejected. We also rejected data points in sectors 40 and 41, as they
are isolated and have a median considerably different than unity. The data not
considered in this analysis are either displayed in blue (transits) or in red
(rejected) in Figures 2 and A.1. The cleaned out-of-transit PDCSAP dataset was
too large ($N=237\,634$) to be efficiently modeled with a GP. We therefore
binned the data and instead used the corresponding 1-hour effective cadence
light curve ($N=7924$).

The GP regression was done with celerite2 (Foreman-Mackey et al. 2017; 2018).
We selected its RotationTerm kernel because it was specifically designed to
model a range of quasi-periodic variability, from stellar rotation to
pulsations. This kernel is the sum of two stochastically-driven, damped
harmonic oscillator (SHO) terms (SHOTerm) capturing both primary ($P_{\rm
GP}$) and secondary ($P_{\rm GP}/2$) modes in Fourier space. The Fourier
transform of the covariance function, known as the power spectral density
(PSD), takes the following form:

$\begin{split}S(\omega)=\sqrt{\frac{2}{\pi}}&\frac{S_{1}\,\omega_{1}^{4}}{(\omega^{2}-\omega_{1}^{2})^{2}+\omega_{1}^{2}\,\omega^{2}/Q_{1}^{2}}\\\
&+\sqrt{\frac{2}{\pi}}\frac{S_{2}\,\omega_{2}^{4}}{(\omega^{2}-\omega_{2}^{2})^{2}+\omega_{2}^{2}\,\omega^{2}/Q_{2}^{2}}\end{split}$
(1)

where each SHOTerm PSD is described by their respective power $S_{1}$, $S_{2}$
at $\omega=0$, their undamped angular frequency $\omega_{1}$, $\omega_{2}$,
and their own quality factor $Q_{1}$, $Q_{2}$.

Since the periods of the two oscillators are separated by a factor of 2
($\omega_{2}=2\omega_{1}$), the parametrization below reduces by one the
number of free parameters:

$\displaystyle\sigma_{1}=\sqrt{S_{1}\omega_{1}Q_{1}}$ (2)
$\displaystyle\sigma_{2}=\sqrt{S_{2}\omega_{2}Q_{2}}$ (3)
$\displaystyle\tau_{1}=\frac{2Q_{1}}{\omega_{1}}$ (4)
$\displaystyle\tau_{2}=\frac{2Q_{2}}{\omega_{2}}$ (5) $\displaystyle P_{\rm
GP}=\frac{2\pi}{\omega_{1}}=\frac{4\pi}{\omega_{2}}$ (6)

where $\sigma_{1}$, $\sigma_{2}$ are the standard deviations (amplitudes) of
the primary and secondary modes, $\tau_{1}$, $\tau_{2}$ are the damping
timescales of the primary and secondary oscillations, and $P_{\rm GP}$ is the
undamped period of the primary mode. Note that these parameters differ
slightly from the default RotationTerm kernel parametrization by making no
assumptions on the relative amplitudes and quality factors between the two
modes.

Our PDCSAP GP model consisted of the five hyperparameters above, plus an
excess white noise term $s$. We sampled the posterior distributions of the
parameters in their logarithmic form $\\{\ln\sigma_{1}$, $\ln\sigma_{2}$,
$\ln\tau_{1}$, $\ln\tau_{2}$, $\ln P_{\rm GP}$, $\ln s\\}$ using the Markov
chain Monte Carlo (MCMC) package emcee (Foreman-Mackey et al., 2013) and a
Bayesian formalism. We employed 100 walkers and performed 100 000 steps with a
burn-in of 10 000. The number of steps was greater than 50 times the
autocorrelation timescale for each parameter, which usually indicates a
sufficient level of convergence (Sokal 1997; Foreman-Mackey et al. 2019). The
adopted prior distributions and the posteriors median, 16th and 84th
percentiles are reported in Table 6. The resulting mean GP prediction is shown
in Figures 2 and A.1 superimposed on the original PDCSAP cadence. Even though
the sinusoidal variations visually appear to repeat every $\sim$0.93 day, our
model converged to a very well constrained primary oscillation of $1.8680\pm
0.0004$ days, thus indicating significant power at the second harmonic.

Table 6: Prior and posterior distributions of the quasi-periodic GP model of
the TOI-1452 TESS light curve (details in Sect. 4.2)

Parameter | Prior | Posterior
---|---|---
$\ln\sigma_{1}$ | $\mathcal{U}\left(-10,0\right)$ | $-7.5^{+0.5}_{-0.5}$
$\ln\sigma_{2}$ | $\mathcal{U}\left(-10,0\right)$ | $-7.1^{+0.5}_{-0.4}$
$\ln\left[\tau_{1}/\textrm{days}\right]$ | $\mathcal{U}\left(-10,10\right)$ | $-1.42^{+0.13}_{-0.14}$
$\ln\left[\tau_{2}/\textrm{days}\right]$ | $\mathcal{U}\left(-10,10\right)$ | $7.1^{+1.1}_{-0.8}$
$\ln\left[P_{\rm GP}/\textrm{days}\right]$ | $\mathcal{U}\left(-2,5\right)$ | 0.6248${}^{+0.0002}_{-0.0002}$
$\ln s$ | $\mathcal{U}\left(-15,0\right)$ | $-12.7^{+1.6}_{-1.5}$

Note. — $\mathcal{U}\left(a,b\right)$ is the uniform distribution between
value $a$ and $b$.

It is beyond the scope of this study to assess the exact cause of this strong
and persistent signal, but we showed earlier that the SPIRou magnetic field
constraints of TOI-1452 are inconsistent with a fast rotator and active
object. Moreover, a 1.9-day rotation period for TOI-1452 would correspond to a
$v\sin i$ of $\sim$7 km/s, readily detectable in the SPIRou combined spectrum.
Instead, the mean line profile FWHM measured from the cross-correlation
function (CCF) calculated in APERO suggests a slow rotator (i.e., $v\sin i<2$
km/s). We repeated this step for the companion star from the single visit with
SPIRou, and also measured a FWHM consistent with $v\sin i<2$ km/s. Thus, the
rotation of the companion star is also most probably not causing this
photometric signal.

###  4.3 Joint transit-RV fit

In order to constrain the physical and orbital parameters of TOI-1452 b, we
conducted a joint analysis of the transits (TESS, OMM-PESTO, and MuSCAT3) and
the RV data (SPIRou and IRD). The joint fit was performed using the juliet
(Espinoza et al., 2019) package, which utilizes batman (Kreidberg, 2015) to
generate transit models and radvel (Fulton et al., 2018) to compute Keplerian
RV models. The juliet framework implements nested sampling algorithms to
sample posterior distributions, while also enabling model comparison via
evaluations of the Bayesian log-evidence ($\ln Z$). We chose the dynesty
(Speagle, 2020) dynamic nested sampling option in juliet. Standard nested
sampling (Skilling, 2006) was designed to estimate evidences, not posteriors,
and thus struggles with parameter estimation for complex distributions.
Dynamic nested sampling (Higson et al., 2019), on the other hand, adapts the
number of live points based on the structure of the posteriors, providing
parameter estimation comparable to MCMC algorithms.

The transit and RV components of the joint fit have four parameters in common:
the orbital period $P$, the time of inferior conjunction $t_{0}$, the
eccentricity $e$, and the argument of periastron $\omega$. For the transit
modeling, we followed the parametrization from Espinoza (2018) of the impact
parameter $b$ and the planet-to-star radius ratio $p=R_{\rm p}/R_{\star}$ to
efficiently sample physically plausible values in ($b$, $p$) space. Instead of
fitting the scaled semi-major axis $a/R_{\star}$, we used the stellar density
$\rho_{\star}$ parameterization available in juliet. Fitting $\rho_{\star}$
takes into account any prior information on the stellar mass and radius. We
adopted a Gaussian prior on $\rho_{\star}$ using the value and uncertainty in
Table 3.1. Stellar limb-darkening effects in TESS, OMM-PESTO, and MuSCAT3
transits were modeled using per-instrument and per-filter quadratic $q_{1}$
and $q_{2}$ parameters defined in Kipping (2013). For each instrument, we
included in juliet a flux dilution factor $D$, a baseline flux $M$, and an
extra jitter term $\sigma$. We set $D_{\rm TESS}$ to 1 (no dilution), as the
PDCSAP data are already corrected for crowding effects. The OMM-PESTO light
curve combines the flux of TOI-1452 and TIC 420112587, which requires an
adequate $D_{\rm PESTO}$ factor to compensate for contamination. We thus
constructed a Gaussian prior on $D_{\rm PESTO}$ with a mean value calculated
with Equation 6 of Espinoza et al. (2019) and flux ratio derived from TOI-1452
and TIC 420112587 magnitudes in the $i$ band (see Tables 3.1 and 3.2). The
adopted prior on $D_{\rm PESTO}$ was
$\mathcal{N}\left(0.564,0.0564^{2}\right)$, that is with a 10% standard
deviation to account for errors on the magnitudes and deviations between $i$
and $i^{\prime}$. We also explored fixing $D_{\rm PESTO}$ to 0.564, while
letting $D_{\rm TESS}$ vary freely between 0 and 2. Both approaches yielded a
consistent measurement of the planetary radius (within 1-$\sigma$), indicating
that the PDCSAP fluxes were in all likelihood properly corrected for
contamination. The dilution in the MuSCAT3 light curves was a priori unknown.
However, it is expected that the $g^{\prime}$ transit was more affected by
dilution, as the seeing was worse for this filter (see Table 2). We adopted a
conservative approach where a different $D_{\rm MuSCAT3}$ is applied for each
filter, with uniform priors between 0.5 (twice the flux) and 1.

The parameters specific to the RV Keplerian component were the semi-amplitude
$K$, per-instrument offsets $\gamma$ and extra white noise terms $\sigma$. We
explored adding a global GP to model common stellar activity signal in the
SPIRou and IRD data. For this, we used the GP implementation in juliet that
runs celerite (Foreman-Mackey et al., 2017). We chose the Matérn-3/2
approximation kernel, which takes the following form:

$k_{i,j}\left(\tau\right)=A_{\rm
GP}^{2}\left[\left(1+1/\epsilon\right)e^{-\left(1-\epsilon\right)w}\left(1-1/\epsilon\right)e^{-\left(1+\epsilon\right)w}\right]$
(7)

where $\tau=|t_{i}-t_{j}|$ is the time interval between data points $i$ and
$j$, $A_{\rm GP}$ is the amplitude of the GP, $w=\sqrt{3}\tau/\ell_{\rm GP}$,
with $\ell_{\rm GP}$ the timescale of the GP, and $\epsilon$ is set to 0.01
(when $\epsilon\rightarrow 0$, $k_{i,j}$ converges to a Matérn-3/2 kernel). We
did not fit a per-instrument $A_{\rm GP}$ and $\ell_{\rm GP}$ due to the
limited number of RV measurements from IRD. We also considered choosing a
quasi-periodic kernel in celerite instead (Equation 56 of Foreman-Mackey et
al. 2017). Since no clear periodicity was detected in the $B_{\ell}$ time
series, or other activity indicators from the LBL such as the dLW metric
(Zechmeister et al., 2018) or chromatic velocity slope changes, we applied a
uniform prior on the stellar rotation period, namely $\mathcal{U}(0.1,120)$
days. We found that the Matérn-3/2 kernel gave equivalent results with fewer
hyperparameters needed (2 instead of 4) and that the quasi-periodic GP did not
converge to a specific rotation period, showing no preference for a period of
0.93 days (or 2$\times$0.93 days) as seen in TESS photometry. This is another
indication that the sinusoidal signal in the out-of-transit PDCSAP data is
probably not associated with TOI-1452 stellar activity.

We examined the change in Bayesian log-evidence for a suite of joint models
($\mathcal{M}$), all having an identical transit component. The “zero” planet
model ($\mathcal{M}_{\rm 0p}$) has a $K$ fixed to 0 m/s, with only the RV
offsets and extra white noise terms allowed to vary. This model tests whether
the RV dispersion can be fully explained by white noise only, without
questioning the transit detection. Single planet models can either be with
circular ($\mathcal{M}_{\rm 1cp}$; $e=0$, $\omega=90^{\circ}$) or eccentric
orbits ($\mathcal{M}_{\rm 1ep}$; free $e,\omega$). Two additional models
include a global RV activity GP ($\mathcal{M}_{\rm 1cp+GP}$ and
$\mathcal{M}_{\rm 1ep+GP}$). To objectively assess the contribution from the
IRD observations, we decided to apply this framework first on the SPIRou data
individually, then using the full RV dataset (SPIRou + IRD).

For two competing models, the difference in log-evidence ($\Delta\ln Z$)
informs on the probability that one model matches the data better than the
other. To interpret the significance of the $\Delta\ln Z$ and select the
“best” model, we followed the empirical scale introduced in Table 1 of Trotta
(2008). A $\Delta\ln Z>5$ translates into “strong” evidence towards the model
with the highest $\ln Z$. A $2.5<\Delta\ln Z<5$ corresponds to “moderate”
evidence, while $\Delta\ln Z\leq 2.5$ shows “weak” evidence at best, i.e.,
neither model should be favoured in that case.

Figure 12: Bayesian log-evidence ($\ln Z$) for different joint transit-RV
models ($\mathcal{M}$) and RV datasets. The typical uncertainty on the
$\Delta\ln Z$ is $0.7$. The “zero” planet model $\mathcal{M}_{\rm 0p}$ has a
fixed $K=0$ m/s. Single planet models $\mathcal{M}_{\rm 1cp}$ and
$\mathcal{M}_{\rm 1ep}$ correspond to an RV component with a circular ($e=0$,
$\omega=90^{\circ}$) or eccentric (free $e,\omega$) orbits respectively.
Models $\mathcal{M}_{\rm 1cp+GP}$ and $\mathcal{M}_{\rm 1ep+GP}$ add a
Gaussian process to remove correlated noise in the RV data.

Figure 12 shows the Bayesian log-evidence for different joint models and
datasets. Note that the typical errors on the $\ln Z$ computed by dynesty were
0.5, so that the $\Delta\ln Z$ presented in Figure 12 have associated
uncertainties of 0.7. We first observe that all planetary models are strongly
favoured ($\Delta\ln Z>5$) compared to the “zero” planet solution
($\mathcal{M}_{\rm 0p}$), providing quantitative evidence that the TOI-1452 b
Keplerian signal is detected in velocimetry, in phase with transit. There is
also compelling evidence for models with an RV activity GP ($\mathcal{M}_{\rm
1cp+GP}$ and $\mathcal{M}_{\rm 1ep+GP}$), increasing $\ln Z$ by approximately
10 relative to $\mathcal{M}_{\rm 1cp}$ and $\mathcal{M}_{\rm 1ep}$. However,
considering only the SPIRou data yields similar or slightly larger $\Delta\ln
Z$ for all $\mathcal{M}$ compared to joint fits that include the seven IRD RV
measurements. This suggests that the IRD observations do not significantly
contribute to improve the Keplerian solution for TOI-1452 b. The median RV
uncertainty from IRD (4.03 m/s) is nearly identical to SPIRou (4.00 m/s), but
the point-to-point scatter (RMS) is much larger: respectively 12.71 m/s for
IRD and 5.76 m/s for SPIRou. The planetary models fail to capture the extra
RMS in the IRD data, and are instead converging to solutions with white noise
term comparable to the overall scatter (see Table B.1). This is apparent in
Figure 13 showing the RV component of the joint fit (model $\mathcal{M}_{\rm
1cp+GP}$) using the full dataset, with each instrument having their original
error bar plotted. The IRD radial velocities were produced using the template
spectrum of TOI-1452. As previously mentioned, this star has a small BERV
excursion, which is not ideal for filtering out telluric lines. This may
explain the increased dispersion in the resulting RVs, in this case, at a
level much larger than the Keplerian signal. For this reason, we opted to
present below the results using only the SPIRou RVs. We nonetheless provide
all the relevant parameters of the RV modeling for the SPIRou only and
SPIRou+IRD datasets in Table B.1.

The eccentric model $\mathcal{M}_{\rm 1ep+GP}$ produced the highest $\ln Z$
(Fig. 12), but with a Bayesian evidence indistinguishable from the circular
model $\mathcal{M}_{\rm 1cp+GP}$ ($\Delta\ln Z=0.9$). We report an
eccentricity of $0.12^{+0.12}_{-0.08}$, with $e<0.32$ at a 95% confidence, but
argue that the simpler, circular model should be preferred at this point. The
adopted priors and resulting posteriors of the $\mathcal{M}_{\rm 1cp+GP}$ fit
are summarized in Table 7. The MuSCAT3 photometric parameters are given in
another table (Table 8) to facilitate comparison between filters. We measure a
dilution factor $D$ consistent with no dilution for the $i^{\prime}$ transit,
with moderate level of contamination ($\sim$30%) in the $g^{\prime}$ band.
Even if we assume instead that the flux dilution was exactly zero for all
MuSCAT3 filters, the uncorrected transit depths ($\delta_{\rm uncorr.}$)
presented in Table 8 show no sign of strong chromaticity. The best-fit transit
models of the TESS, OMM-PESTO, and MuSCAT3 photometry are shown in Figures 2,
3, and 4 respectively. The best circular ($\mathcal{M}_{\rm 1cp+GP}$) and
eccentric ($\mathcal{M}_{\rm 1ep+GP}$) RV orbital fits of TOI-1452 b are
depicted in Figure 14 in a phase-folded format.

Table 7: Prior and posterior distributions of the joint transit-RV fit for
model $\mathcal{M}_{\rm 1cp+GP}$ (details in Sect. 4.3) using only the SPIRou
radial velocities

Parameter | Priora | Posterior | Description
---|---|---|---
Fitted parameters
$\rho_{\star}$ (g/cm3) | $\mathcal{N}\left(16.8,1.9^{2}\right)$ | 16.8${}^{+1.0}_{-1.4}$ | Stellar density
$P$ (days) | $\mathcal{U}\left(11.0,11.1\right)$ | 11.06201 $\pm$ 0.00002 | Orbital period
$t_{0}$ (BJD - 2 457 000) | $\mathcal{U}\left(1691.4,1691.6\right)$ | 1691.5321 $\pm$ 0.0015 | Time of inferior conjunction
$r_{1}$ | $\mathcal{U}\left(0,1\right)$ | 0.46$\pm$0.08 | Parametrizationb for $R_{\rm p}/R_{\star}$ and $b$
$r_{2}$ | $\mathcal{U}\left(0,1\right)$ | 0.0555 $\pm$ 0.0014 | Parametrizationb for $R_{\rm p}/R_{\star}$ and $b$
$K$ (m/s) | $\mathcal{U}\left(0,10\right)$ | 3.50 $\pm$ 0.94 | RV semi-amplitude
$e$ | 0 (fixed) | 0 | Orbital eccentricity
$\omega$ (∘) | 90 (fixed) | 90 | Argument of periastron
$A_{\rm GP}$ (m/s) | $\mathcal{LU}\left(10^{-2},100\right)$ | 4.5${}^{+2.0}_{-1.2}$ | Amplitude of the GP
$\ell_{\rm GP}$ (days) | $\mathcal{LU}\left(10^{-2},100\right)$ | 11.3${}^{+12.0}_{-6.4}$ | Timescale of the GP
$\gamma_{\rm SPIRou}$ (m/s) | $\mathcal{U}\left(-33995,-33975\right)$ |  $-33985$ $\pm$ 2 | SPIRou RV systemic component
$\sigma_{\rm SPIRou}$ (m/s) | $\mathcal{U}\left(0,10\right)$ | 2.3 $\pm$ 1.3 | SPIRou RV extra white noisec
$q_{\rm 1,TESS}$ | $\mathcal{U}\left(0,1\right)$ | 0.35${}^{+0.27}_{-0.19}$ | TESS limb-darkening parameterd
$q_{\rm 2,TESS}$ | $\mathcal{U}\left(0,1\right)$ | 0.37${}^{+0.33}_{-0.24}$ | TESS limb-darkening parameterd
$D_{\rm TESS}$ | 1.0 (fixed) | 1.0 | TESS dilution factor
$M_{\rm TESS}$ | $\mathcal{N}\left(0,0.1^{2}\right)$ | -0.00032 $\pm$ 0.00010 | TESS baseline flux
$\sigma_{\rm TESS}$ (ppm) | $\mathcal{LU}\left(1,10\,000\right)$ | 15${}^{+70}_{-12}$ | TESS extra white noise
$q_{\rm 1,PESTO}$ | $\mathcal{U}\left(0,1\right)$ | 0.67${}^{+0.21}_{-0.26}$ | PESTO limb-darkening parameterd
$q_{\rm 2,PESTO}$ | $\mathcal{U}\left(0,1\right)$ | 0.46${}^{+0.28}_{-0.25}$ | PESTO limb-darkening parameterd
$D_{\rm PESTO}$ | $\mathcal{N}\left(0.564,0.0564^{2}\right)$ | 0.586 $\pm$ 0.040 | PESTO dilution factor
$M_{\rm PESTO}$ | $\mathcal{N}\left(0,0.1^{2}\right)$ | 0.00013 $\pm$ 0.00018 | PESTO baseline flux
$\sigma_{\rm PESTO}$ (ppm) | $\mathcal{LU}\left(1,10\,000\right)$ | 2287 $\pm$ 67 | PESTO extra white noise
$\mathbf{\vdots}$
MuSCAT3 photometric parameters in Table 8
Derived parameters
$R_{\rm p}$ (R⊕) | — | 1.672 $\pm$ 0.071 | Planetary radius
$M_{\rm p}$ (M⊕) | — | 4.82 $\pm$ 1.30 | Planetary mass
$\rho$ (g/cm3) | — | 5.6${}^{+1.8}_{-1.6}$ | Planetary bulk density
$a$ (au) | — | 0.061 $\pm$ 0.003 | Orbital semi-major axis
$\delta\equiv\left(R_{\rm p}/R_{\star}\right)^{2}$ | — | 3.09 $\pm$ 0.16 | Transit depth
$b$ | — | 0.19 $\pm$ 0.13 | Transit impact parameter
$i$ (∘) | — | 89.77 $\pm$ 0.16 | Orbital inclination
$T_{\rm eq}$ (K) |  |  | Equilibrium temperature
$\left[A_{\rm B}=0\right]$ | — | 326 $\pm$ 7 |
$\left[A_{\rm B}=0.3\right]$ | — | 298 $\pm$ 6 |
$\left[A_{\rm B}=0.77\right]$ | — | 226 $\pm$ 5 |
$S$ (S⊕) | — | 1.8 $\pm$ 0.2 | Insolation

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

bParametrization from Espinoza (2018).

cWhite noise term for single exposures within polarimetric sequences.

${}^{\rm d}\\{q_{1},q_{2}\\}$ are linked to the quadratic limb-darkening
coefficients $\\{u_{1},u_{2}\\}$ through the transformations outlined in
Kipping (2013).

Table 8: Prior and posterior distributions of the MuSCAT3 photometric
parameters for model $\mathcal{M}_{\rm 1cp+GP}$ (details in Sect. 4.3) using
only the SPIRou radial velocities

Parameter | Prior | $g^{\prime}$ | $r^{\prime}$ | $i^{\prime}$ | $z_{\rm s}$
---|---|---|---|---|---
Fitted parameters
$q_{1}$ | $\mathcal{U}\left(0,1\right)$ | 0.60${}^{+0.26}_{-0.31}$ | 0.22${}^{+0.27}_{-0.15}$ | 0.46${}^{+0.32}_{-0.27}$ | 0.24${}^{+0.29}_{-0.16}$
$q_{2}$ | $\mathcal{U}\left(0,1\right)$ | 0.59${}^{+0.27}_{-0.33}$ | 0.37${}^{+0.35}_{-0.24}$ | 0.24${}^{+0.28}_{-0.16}$ | 0.27${}^{+0.33}_{-0.19}$
$D$ | $\mathcal{U}\left(0.5,1\right)$ | 0.71 $\pm$ 0.12 | 0.88${}^{+0.07}_{-0.09}$ | 0.96${}^{+0.03}_{-0.05}$ | 0.85 $\pm$ 0.07
$M$ | $\mathcal{N}\left(0,0.1^{2}\right)$ | -0.00141 $\pm$ 0.00036 | -0.00106 $\pm$ 0.00016 | -0.00130 $\pm$ 0.00014 | -0.00131 $\pm$ 0.00013
$\sigma$ (ppm) | $\mathcal{LU}\left(1,10\,000\right)$ | 2748 $\pm$ 319 | 46${}^{+427}_{-43}$ | 1837${}^{+191}_{-206}$ | 29${}^{+227}_{-26}$
Derived parameters
$\delta_{\rm uncorr.}$ (ppt) | — | 2.18${}^{+0.40}_{-0.36}$ | 2.72${}^{+0.21}_{-0.24}$ | 2.94 $\pm$ 0.17 | 2.64 $\pm$ 0.20

Figure 13: RV time series from SPIRou and IRD with the best-fit Keplerian +
activity GP (orange curve), activity GP only (red dashed curve), and Keplerian
only (blue curve) models overplotted. The residuals below show an overall
agreement between the SPIRou errors and the RV dispersion, which is difficult
to assess for IRD given the limited number of measurements. Figure 14: Phase-
folded SPIRou RV curve, with systemic velocity and activity GP removed. Binned
RV measurements (0.1 phase bin) are marked with black circles. The best-fit
Keplerian models are depicted with a solid (circular orbit) and a dashed
(eccentric orbit) blue curves. The residuals of the circular fit are presented
below. The circular solution yields smaller residuals RMS (3.58 m/s) compared
to the eccentric model (3.66 m/s), yet both Bayesian evidences ($\ln Z$) are
indistinguishable (see Fig. 12).

##  5 Discussion

###  5.1 Planet composition

The analysis of the transit and RV data yields a mass of $4.82\pm 1.30$ M⊕ and
a radius of $1.672\pm 0.071$ R⊕, which together convert into a planetary bulk
density of 5.6${}^{+1.8}_{-1.6}$ g/cm3. A density similar to that of the Earth
(5.5 g/cm3) for a planet that has more mass is indicative of an object
composed of lighter material. We placed these measurements in a mass-radius
diagram (Fig. 15), along with various theoretical composition curves obtained
by the interior structure model of Valencia et al. 2007, 2013; Plotnykov &
Valencia 2020. We populated this diagram, and the figures in the discussion
below, with data from the NASA Exoplanet Archive (Akeson et al., 2013) using
the exofile tool444github.com/AntoineDarveau/exofile.

By comparing the mass and size of TOI-1452 b to theoretical M-R curves in
Figure 15, we see three possibilities for the nature of this planet: (1) an
ocean planet, (2) a bare rock with an iron content less than that of Earth, or
(3) a terrestrial planet with a thin, low molecular weight atmosphere (e.g.,
H-He). The water world hypothesis is supported by a temperate equilibrium
temperature for TOI-1452 b of $298\pm 6$ K assuming an Earth-like Bond albedo
($A_{\rm B}=0.3$), and between 226 and 326 K for extreme $A_{\rm B}$ of 0.77
(Venus-like) and 0 (pure absorber). The insolation level of TOI-1452 b is
about 80% higher than the Earth ($S=1.8\pm 0.2$ S⊕), similar to Venus
($S=1.91$ S⊕).

Focusing on the first two possibilities, we used an MCMC approach (emcee,
Foreman-Mackey et al. 2013) coupled to an interior structure model (Valencia
et al., 2007) to obtain the distribution of mass fractions of iron and water
that are consistent with the data. The details of this modeling can be found
in Plotnykov & Valencia (2020). The H2O layer is described by the equation of
state from Hemley et al. 1987; Stewart & Ahrens 2005. We report below the
16th, 50th, and 84th percentiles of the posterior distributions (available in
Appendix C).

From the chemical analysis of the star (Sect. 3.4), we obtain chemical ratios
relevant to the planetary interior. Notably, TOI-1452 might have a slightly
lower Fe/Mg weight ratio compared to the Sun (see Table 9), but in fair
agreement with that of a sample of $\sim$1000 M dwarfs from the APOGEE (DR16)
catalog (Majewski et al. 2016; Ahumada et al. 2020) with known chemical ratios
(see Fig. 16). The APOGEE abundances are derived from high-resolution near-
infrared spectroscopy ($R\sim 22\,000$), with typical uncertainty on [Fe/H]
and [Mg/H] of 0.02 dex. Obtaining the Si ratios for TOI-1452 was difficult
given the scarcity of spectral lines. In addition, we derive a C/O weight
ratio consistent with the solar value. Our chemical abundance ratios for
TOI-1452 are summarized in Table 9.

To infer the planet’s composition for scenarios 1 and 2, we can either make no
assumptions on the refractory ratios, and thus, obtain all possible
compositions that fit the mass-radius data; or, assume that the refractory
ratios of planet and star are related, and use the star’s ratios as priors in
the Bayesian analysis. Given that the refractory ratios of super-Earths seem
to span a larger range than that of stars (Plotnykov & Valencia, 2020), we
applied both methods here. In both cases, we kept the Mg/Si ratio in the
planetary mantle the same as the star. This assumption should not affect the
results considerably, given that the mantle minerals formed by different Mg/Si
ratios have similar equations of state and thus, the relative content of Mg to
Si is not constrained by planetary mass and radius data (Plotnykov & Valencia,
2020).

In the case where we make no assumptions, we obtain a water-mass fraction
(WMF) of $0.27^{+0.20}_{-0.15}$, and core-mass fraction (CMF) of
$0.30^{+0.20}_{-0.17}$. These values translate to
$\mathrm{Fe/Si}=2.9^{+5.4}_{-1.9}$ and $\mathrm{Fe/Mg}=3.4^{+6.3}_{-2.2}$ by
weight. The planetary refractory ratios are particularly large primarily due
to large uncertainty in planetary mass but also the degeneracy that ensues
when considering water. The tail of the Fe/Mg distribution is long because
this case allows for little to no mantle in the planet (see Fig. C.1). If
instead, we assume the refractory ratios of the star as priors, we obtain a
lower water and core mass fractions: WMF = $0.22^{+0.21}_{-0.13}$, CMF =
$0.18\pm 0.06$, resulting in Fe/Si = $1.3\pm 0.4$ and Fe/Mg = $1.5\pm 0.4$.
Thus, both abundance scenarios yield a non-zero, yet poorly-constrained, WMF.
The large uncertainty on both the CMF and WMF is rooted to the modest mass
constraint (3.7$\sigma$). Better mass measurements are needed to confirm that
TOI-1452 b has a significant WMF.

A different possibility (scenario 2 discussed above) is that this planet is a
bare rock with no significant atmosphere, perhaps because it lost any acquired
water through atmospheric evaporation during the high insolation phase of the
M dwarf host star (Bolmont et al. 2017; Barnes & Heller 2013). In this case,
we constrain the physical model solutions but make no assumptions on the
refractory ratios. The results show a $\mathrm{CMF}=0.19^{+0.18}_{-0.12}$,
with Fe/Si = $1.0^{+1.0}_{-0.5}$ and Fe/Mg = $1.2^{+1.2}_{-0.6}$ by weight.
This CMF indicates a planet not as dense as the Earth, with refractory ratios
still consistent at the 1-$\sigma$ level with those of its host star (see
Table 9 and Fig. 16). However, the maximum a posteriori estimate of Fe/Mg
($\sim$0.8) for this bare rock scenario is lower than that of its host star.
Forming planets that are iron poor with respect to their host star is
difficult (Scora et al., 2020). Therefore, based on our current knowledge of
planet formation and the chemical characteristics of the star, this scenario
is less likely.

A summary of this interior modeling is presented in Table 9 and Figure 16. The
posterior distributions for the three models (no assumptions, stellar priors
and bare rock) are shown in Appendix C.

Outside of these scenarios, our observations do not rule out other structures
with a low molecular weight atmosphere (scenario 3) such as an Earth-like
interior surrounded by an H-He envelope at $T=300\,K$ containing $\sim$0.1% of
the total mass (up to 0.5% H-He at 1-$\sigma$). One way to firmly break the
degeneracy in planetary internal structures would be to characterize the
atmosphere of TOI-1452 b.

Table 9: Chemical ratios by weight for the TOI-1452 system

Chemical | TOI-1452 | Sun${\dagger}$ | TOI-1452 b | TOI-1452 b | TOI-1452 b
---|---|---|---|---|---
Ratios |  |  | No assumptions | Stellar priors | Bare rock
Fe/Mg | $1.48^{+0.36}_{-0.29}$ | 1.83$\pm$0.25 | $3.4^{+6.3}_{-2.2}$ | $1.5^{+0.4}_{-0.4}$ | $1.2^{+1.2}_{-0.6}$
Mg/Si | $0.86^{+0.37}_{-0.26}$ | 1.06$\pm$0.13 | 0.86∗ | 0.86∗ | 0.86∗
C/O | $0.48^{+0.11}_{-0.09}$ | 0.41$\pm$0.07 | ${\hat{}}$ | ${\hat{}}$ | ${\hat{}}$
CMF | – | – | $0.30^{+0.20}_{-0.17}$ | $0.18^{+0.06}_{-0.06}$ | $0.19^{+0.18}_{-0.12}$
WMF | – | – | $0.27^{+0.20}_{-0.15}$ | $0.22^{+0.21}_{-0.13}$ | –

Note. — † Photospheric abundance ratios from Asplund et al. (2009).

∗ Mg/Si ratio of the planets are fixed to the star TOI-1452 ratio.

$\hat{}\ $ The interior models assume no carbon compounds.

Figure 15: Mass–radius diagram of exoplanets (gray points). Only planets with
mass and radius known with precision better than 30% are shown. Various
theoretical composition curves are plotted, using interior structure models
from Valencia et al. 2007, 2013; Guillot & Morel 1995. All models assume no
atmosphere, except the H-He (red dashed lines) models that correspond to
Earth-like interior surrounded by a solar composition envelope at $T=300$ K.
The mass and radius posteriors (green 1 and 2-$\sigma$ contours) of TOI-1452 b
are consistent with either a water-rich interior with $\sim$25% H2O by mass, a
pure rock (rocky threshold radius curve including relevant phase transitions),
or a terrestrial planet with a thin hydrogen envelope of $\sim$0.1% H-He by
mass. Figure 16: Fe/Mg distribution for TOI-1452 b according to different
model assumptions (Table 9) compared to that of its host star (black). We used
kernel density estimate to draw the probabilities from the posteriors. We also
include the M dwarfs distribution of Fe/Mg from the APOGEE database (gray
histogram, sample size of $\sim$1000, Majewski et al. 2016; Ahumada et al.
2020) for comparison.

###  5.2 Atmospheric characterization prospect

TOI-1452 b is a prime target for follow-up transit spectroscopy with JWST. The
system is located near Webb’s Continuous Viewing Zone (CVZ), more precisely at
a few degrees ($\sim$10∘) off the Northern CVZ, which means that it could be
observed most of the year. Moreover, TOI-1452 b is one of the few identified
super-Earths in a temperate regime ($T_{\rm eq}$ between 200 and 400 K)
orbiting a relatively bright star amenable to transmission spectroscopy
observations (see Figure 17 and Table 5.2). The expected strength of the
atmospheric signal is characterized by the Transmission Spectroscopy Metric
(TSM, Kempton et al. 2018), which is proportional to the host star’s $J$
magnitude and the planet’s atmospheric scale height. Figure 17 displays the
TSM as a function of equilibrium temperature for known small exoplanets with
available mass measurements. The sample is restricted to systems with well-
determined masses (relative uncertainty $<30$%) since a constraint on surface
gravity is essential to correctly interpret the transmission spectrum of an
exoplanet (Batalha et al., 2019). The temperate subset of Figure 17 is
detailed in Table 5.2. The TSM of TOI-1452 b (39.9) is similar to well-known
temperate systems such as LHS 1140 b (50.0) and K2-18 b (40.8), while being
60% below the highest listed target in this subset, L231-32 d (TOI-270 d,
104.0). All seven host stars in Table 5.2 have $T_{\rm eff}<4000$ K (or
average $T_{\rm eff}$ of 3225 K), confirming the high interest of M dwarfs for
planetary atmospheric characterization. Note that the high-value target L
98-59 d (TSM above 200, Cloutier et al. 2019; Demangeon et al. 2021) was just
barely excluded from Table 5.2 due to its $T_{\rm eq}$ (409 K) being slightly
above our 400 K cut. Our subset also excludes intriguing planets with
plausible temperate environment, but deprived of mass measurement (or
imprecise mass), such as TOI-700 c (TSM = 79.7, Gilbert et al. 2020), TOI-1266
c (TSM = 48.8, Demory et al. 2020, and K2-3 c (TSM = 25.5, Damasso et al.
2018). The TOI-1452 system is a unique target to explore the atmospheric
properties of temperate planets within the radius valley. This paper provides
the first mass determination needed for the interpretation of future
transmission spectra.

Figure 17: Transmission spectroscopy metric (TSM, Kempton et al. 2018) as a
function of planetary equilibrium temperature for small exoplanets ($R_{\rm
p}<4$ R⊕) with well-established masses (error below 30%). The green region
corresponds to an arbitrary temperate temperature interval (200 K $<T_{\rm
eq}<$ 400 K). TOI-1452 b is among the best temperate targets for follow-up
transit spectroscopy with JWST. Table 10: Transmission Spectroscopy Metric
(TSM) for a subset of well-characterized small exoplanets in a temperate
equilibrium temperature regime (200 K $\leq T_{\rm eq}\leq$ 400 K)

Planet | $P$ | $M_{\rm p}$ | $R_{\rm p}$ |  $T_{\rm eq}$ $[A_{\rm B}=0]$ | $J$ | $T_{\rm eff}$ | $M_{\star}$ | $R_{\star}$ | TSM | Ref.
---|---|---|---|---|---|---|---|---|---|---
| (days) | (M⊕) | (R⊕) | (K) | (mag) | (K) | (M⊙) | (R⊙) |  |
L231-32 d | 11.380 | 4.78 | 2.133 | 388 | 9.10 | 3506 | 0.39 | 0.38 | 104.0 | (1)
TOI-1231 b | 24.246 | 15.4 | 3.65 | 331 | 8.88 | 3553 | 0.48 | 0.48 | 97.6 | (2)
LTT 3780 c | 12.252 | 8.6 | 2.30 | 353 | 9.01 | 3331 | 0.40 | 0.37 | 72.6 | (3)
LHS 1140 b | 24.739 | 6.38 | 1.635 | 214 | 9.61 | 2988 | 0.19 | 0.21 | 50.0 | (4)
K2-18 b | 32.940 | 8.63 | 2.610 | 279 | 9.76 | 3457 | 0.50 | 0.44 | 40.8 | (5)
TOI-1452 b | 11.062 | 4.82 | 1.672 | 326 | 10.60 | 3185 | 0.25 | 0.28 | 39.9 | (6)
TRAPPIST-1 b | 1.511 | 1.374 | 1.116 | 399 | 11.35 | 2566 | 0.09 | 0.12 | 28.6 | (7)
TRAPPIST-1 d | 4.049 | 0.388 | 0.788 | 287 | 11.35 | 2566 | 0.09 | 0.12 | 25.6 | (7)
TRAPPIST-1 c | 2.422 | 1.308 | 1.097 | 341 | 11.35 | 2566 | 0.09 | 0.12 | 24.3 | (7)
TRAPPIST-1 e | 6.101 | 0.692 | 0.920 | 251 | 11.35 | 2566 | 0.09 | 0.12 | 19.9 | (7)
LHS 1140 c | 3.777 | 1.76 | 1.169 | 400 | 9.61 | 2988 | 0.19 | 0.21 | 18.7 | (4)
TRAPPIST-1 f | 9.208 | 1.039 | 1.045 | 218 | 11.35 | 2566 | 0.09 | 0.12 | 17.0 | (7)

References. — (1) Van Eylen et al. (2021). (2) Burt et al. (2021). (3)
Cloutier et al. (2020a). (4) Lillo-Box et al. (2020). (5) Benneke et al.
(2019). (6) This work. (7) Agol et al. (2021).

###  5.3 Implications for the emergence of the M dwarf radius valley

Planets on either side of the radius valley differ by their composition,
typically ‘rocky’ for the smaller super-Earths, and ‘gaseous’ for the larger
mini-Neptunes. This transition occurs as a consequence of a varying envelope
mass fraction: adding an H-He envelope up to a few percents of the total mass
of a planet essentially doubles its observable radius (Lopez & Fortney 2014;
Chen & Rogers 2016). Thermally-driven atmospheric escape processes such as
photoevaporation (Owen & Wu 2013, 2017; Lopez & Fortney 2014; Lopez & Rice
2018; Wu 2019) and core-powered mass loss (Ginzburg et al. 2018; Gupta &
Schlichting 2019, 2020) have been proposed as radius valley emergence
mechanisms. In these models, super-Earths and mini-Neptunes originate from the
same population of planets that form with an extended H-He envelope around
Earth-like core, with the population of rocky super-Earths emerging after
losing their primordial atmospheres to hydrodynamic escape. Another possible
scenario is to assemble rocky super-Earths at late times after most or all of
the gas has been dissipated from the protoplanetary disk (Lee et al. 2014;
Lopez & Rice 2018; Lee & Connors 2021). The two classes of planets would form
on different timescales, resulting in a bimodal distribution without relying
on any subsequent atmospheric escape.

Each of the aforementioned mechanisms predicts that the rocky-to-gaseous
transition ($R_{\rm valley}$) varies with parameters such as orbital period
$P$ and stellar mass $M_{\star}$. Photoevaporation, core-powered mass loss,
and gas-poor accretion models predict a negative slope in $R_{\rm p}$–$P$
space, respectively $R_{\rm valley}\propto P^{-0.25\textendash 0.15}$ (Owen &
Wu 2017; Lopez & Rice 2018; Mordasini 2020), $R_{\rm valley}\propto P^{-0.11}$
(Gupta & Schlichting, 2019), and $R_{\rm valley}\propto P^{-0.08}$ (Lee &
Connors, 2021). Conversely, the formation of super-Earths strictly by the
merging of planetary embryos in a gas-depleted environment, analogous to the
formation of terrestrial planets in the Solar System, would produce a positive
slope ($R_{\rm valley}\propto P^{0.11}$, Lopez & Rice 2018). One way to test
the proposed models is to compare these predictions to the real population of
exoplanets.

From occurrence rate calculations of small close-in planets around Sun-like
stars, Martinez et al. (2019) measured a $d\log R_{\rm valley}/d\log
P=-0.11\pm 0.02$, consistent with thermally-driven mass loss and gas-poor
formation. Using a similar methodology but for planets around low-mass stars
with $T_{\rm eff}<4700$ K, Cloutier & Menou (2020) obtained a $d\log R_{\rm
valley}/d\log P=0.058\pm 0.022$, where the positive sign suggests that the
gas-depleted formation of super-Earths may be dominant around M dwarfs. These
distinct slope measurements carve out regions in the $R_{\rm p}$–$P$ parameter
space where the models make opposing predictions regarding the bulk
composition of a planet (i.e., either rocky or gaseous). This framework to
test radius valley emergence models around M dwarfs was introduced in Cloutier
& Menou (2020) and has since been applied to a number of transiting planets
(TOIs 776 b; Luque et al. 2021, 1235 b; Cloutier et al. 2020b, 1634 b;
Cloutier et al. 2021, 1685 b; Bluhm et al. 2021).

Figure 18 presents the period–radius diagram for exoplanets around M-dwarf
hosts ($T_{\rm eff}<4000$ K). Each planet is color-coded by its bulk density
relative to the Earth-like structure model of Valencia et al. 2007 (see Figure
15). TOI-1452 b sits on or slightly above the empirical valley of Cloutier &
Menou (2020), while being considerably below the slope measured by Martinez et
al. (2019), scaled down to match the median stellar mass of the Cloutier &
Menou (2020) sample (using Equation 11 therein). The locus of TOI-1452 b in
Figure 18, combined with our density estimate, are incompatible with the
photoevaporation and core-powered mass loss models. However, the likely
intermediate nature of TOI-1452 b cannot strongly support the alternative gas-
depleted formation scenario either as the dominant mechanism for the emergence
of the M-dwarf radius valley. A volatile-rich interior for TOI-1452 b could
indicate a different formation pathway, e.g., one without significant gas
accretion during the disk lifetime.

Figure 18 also highlights three other systems presenting similarities with
TOI-1452 b, namely TOI-1235 b (Cloutier et al., 2020b), L 98-59 d (Cloutier et
al. 2019; Demangeon et al. 2021) and LHS 1140 b (Dittmann et al. 2017; Lillo-
Box et al. 2020). All four planets have a similar size, while spanning a large
interval in periods. TOI-1235 b ($P=3.445$ days, $R_{\rm p}=1.738$ R⊕) and LHS
1140 b ($P=24.737$ days, $R_{\rm p}=1.635$ R⊕) have densities compatible with
bona fide super-Earths; their position in Figure 18 indicates that they are
probably examples of the largest terrestrial planets that can be assembled
around M dwarfs without accreting a substantial hydrogen envelope. On the
other hand, L 98-59 d ($P=7.451$ days, $R_{\rm p}=1.521$ R⊕) is a likely
water-rich ($\sim$30%) planet that may be approaching, like TOI-1452 b, the
minimum size for volatile-rich objects around a low-mass star. These four
systems constitute benchmarks for understanding the formation and evolution of
planets within the radius valley.

Figure 18: Period–radius diagram of exoplanets around low-mass stars ($T_{\rm
eff}\leq 4000$ K) with mass and radius known with precision better than 30%.
The TRAPPIST-1 (T-1) planets are represented by triangles. Empirical valley
for low-mass stars from Cloutier & Menou 2020 (CM20), consistent with gas-
depleted formation, and from Martinez et al. 2019 (M19), compatible with
thermally-driven atmospheric mass loss and scaled down to represent the
stellar mass population of CM20. TOI-1452 b lies below M19 and has a small
bulk density compared to a terrestrial planet of the same mass
($\rho/\rho_{\textrm{Earth-like}}\approx 0.76$). This is inconsistent with
photoevaporation and core-powered mass loss predictions.

##  6 Summary & Conclusion

This paper reports the discovery and characterization of the transiting
temperate exoplanet TOI-1452 b. A joint analysis of transit observations from
TESS and other ground-based telescopes combined with radial velocity
measurements from SPIRou and IRD, yields a mass of $4.82\pm 1.30$ M⊕ and a
radius of $1.672\pm 0.071$ R⊕. These physical parameters are consistent with
either a rocky world with a Fe/Mg ratio similar to the host star (Fe/Mg
$=1.2^{+1.2}_{-0.6}$ by weight), a water-rich interior (either
$22^{+21}_{-13}\%$ H2O by weight, if stellar priors are assumed for the
planetary refractory ratios, or $27^{+20}_{-15}\%$ H2O if no assumptions are
made) or a terrestrial planet surrounded by a $\lesssim$1% H-He atmosphere.
Orbiting its M4 host star ($T_{\rm eff}=3185\pm 50$ K) every $11.06201\pm
0.00002$ days, the planet receives about twice as much radiation than the
Earth ($S=1.8\pm 0.2$ S⊕), corresponding to a blackbody temperature of $326\pm
7$ K. The results of our interior modeling and the fact that the planet
receives modest irradiation make TOI-1452 b a good candidate water world.

TOI-1452 b is a prime target for upcoming atmospheric characterization efforts
with JWST, featuring a high Transmission Spectroscopy Metric compared to other
known temperate exoplanets. Transit spectroscopy observations with JWST should
reveal the true nature of this intriguing exoplanet lying within the radius
valley, whether this is a rocky world or one with a volatile envelope. Being
observable with JWST most of the year, TOI-1452 b is a unique system for
studying exoplanets at the transition between super-Earths and mini-Neptunes.

We acknowledge the use of public TESS Alert data from pipelines at the TESS
Science Office and at the TESS Science Processing Operations Center. This
research has made use of the Exoplanet Follow-up Observation Program website,
which is operated by the California Institute of Technology, under contract
with the National Aeronautics and Space Administration under the Exoplanet
Exploration Program. 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 paper includes data collected by the TESS mission that are
publicly available from the Mikulski Archive for Space Telescopes (MAST).
Based on observations obtained at the Canada-France-Hawaii Telescope (CFHT)
which is operated from the summit of Maunakea by the National Research Council
of Canada, the Institut National des Sciences de l’Univers of the Centre
National de la Recherche Scientique of France, and the University of Hawaii.
The observations at the Canada-France-Hawaii Telescope were performed with
care and respect from the summit of Maunakea which is a signicant cultural and
historic site. Based on observations obtained at the Observatoire du Mont-
Mégantic, financed by Université de Montréal, Université Laval, the Canada
Economic Development program and the Ministère de l’Économie et de
l’Innovation. This paper is also based on observations made with the MuSCAT3
instrument, developed by the Astrobiology Center and under financial supports
by JSPS KAKENHI (JP18H05439) and JST PRESTO (JPMJPR1775), at Faulkes Telescope
North on Maui, HI, operated by the Las Cumbres Observatory. This work is
partly supported by the Natural Science and Engineering Research Council of
Canada and the Institute for Research on Exoplanets through the Trottier
Family Foundation This work is partly supported by MEXT/JSPS KAKENHI Grant
Numbers JP22000005, JP15H02063, JP17H04574, JP18H05439, JP18H05442,
JP19K14783, JP21H00035, JP21K13975, JP21K20376, JST CREST Grant Number
JPMJCR1761, and the Astrobiology Center of National Institutes of Natural
Sciences (NINS) (Grant Numbers AB031010, AB031014). We thank Dr. Martin Turbet
for the suggestions to improve the discussion section. We acknowledge very
useful feedback and discussion from Dr. Ansgar Reiners, regarding the
importance to properly check the contamination from the nearby companion in
the SPIRou and IRD spectra and its effect on the final radial velocities. JFD
acknowledges funding from the European Research Council (ERC) under the H2020
research & innovation programme (grant agreement #740651 NewWorlds). This work
has been carried out within the framework of the NCCR PlanetS supported by the
Swiss National Science Foundation. PC thanks the LSSTC Data Science Fellowship
Program, which is funded by LSSTC, NSF Cybertraining Grant #1829740, the
Brinson Foundation, and the Moore Foundation; her participation in the program
has benefited this work. A.C. and X.D. acknowledges funding from the ANR of
France under contract number ANR18CE310019 (SPlaSH). This work is supported by
the French National Research Agency in the framework of the Investissements
d’Avenir program (ANR-15-IDEX-02), through the funding of the “Origin of Life”
project of the Grenoble-Alpes University. F.K. acknowledge the ANR project
[SPlaSH] from the French Agence Nationale de Recherche with reference
ANR-18-CE31-0019-02 J.H.C.M. is supported in the form of a work contract
funded by Fundação para a Ciência e Tecnologia (FCT) with the reference DL
57/2016/CP1364/CT0007; and also supported from FCT through national funds and
by FEDER-Fundo Europeu de Desenvolvimento Regional through COMPETE2020-
Programa Operacional Competitividade e Internacionalização for these grants
UIDB/04434/2020 & UIDP/04434/2020, PTDC/FIS-AST/32113/2017 &
POCI-01-0145-FEDER-032113, PTDC/FIS-AST/28953/2017 &
POCI-01-0145-FEDER-028953, PTDC/FIS-AST/29942/2017. This project has received
funding from the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme under grant agreement No 716155
(SACCRED). KG acknowledges the partial support from the Ministry of Science
and Higher Education of the RF (grant 075-15-2020-780). TV acknowledges
funding from the Fonds de Recherche du Québec - Nature et Technologie (FRQNT).
; TRILEGAL (Girardi et al., 2012).

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