# TOI-1696: a nearby M4 dwarf with a 3$R_{\earth}$ planet in the Neptunian
desert

Mayuko Mori Department of Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan  John H. Livingston 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  Jerome de Leon Department of Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan  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  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  Department of Astronomy, School of Science, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo, Japan  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  Karen A. Collins Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Naho Fujita Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan  Yasunori Hori 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  Hiroyuki Tako Ishikawa 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  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  Keivan G. Stassun Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, 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  Steven Giacalone Department of Astronomy, University of California Berkeley, Berkeley, CA 94720, USA  Rebecca Gore  Department of Astronomy, University of California Berkeley, Berkeley, CA 94720, USA  Ashley Schroeder  Department of Astronomy, University of California Berkeley, Berkeley, CA 94720, USA  Courtney D. Dressing Department of Astronomy, The University of California, Berkeley, CA 94720, USA  Allyson Bieryla Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Eric L. N. Jensen Department of Physics & Astronomy, Swarthmore College, Swarthmore PA 19081, USA  Bob Massey Villa ’39 Observatory, Landers, CA 92285, USA  Avi Shporer Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Masayuki Kuzuhara 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  David Charbonneau Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  David R. Ciardi Caltech/IPAC-NASA Exoplanet Science Institute, 770 S. Wilson Avenue, Pasadena, CA 91106, USA  John P. Doty  Noqsi Aerospace Ltd., 15 Blanchard Avenue, Billerica, MA 01821, USA  Emma Esparza-Borges Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain  Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain  Hiroki Harakawa  Subaru Telescope, 650 N. Aohoku Place, Hilo, HI 96720, USA  Klaus Hodapp University of Hawaii, Institute for Astronomy, 640 N. Aohoku Place, Hilo, HI 96720, USA  Masahiro Ikoma 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), 2-21-1 Osawa, Mitaka, Tokyo, Japan  Kai Ikuta Department of Multi-Disciplinary Sciences, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan  Keisuke Isogai Okayama Observatory, Kyoto University, 3037-5 Honjo, Kamogatacho, Asakuchi, Okayama 719-0232, Japan  Department of Multi-Disciplinary Sciences, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan  Jon M. Jenkins NASA Ames Research Center, Moffett Field, CA 94035, USA  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  Tadahiro Kimura  Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan  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), 2-21-1 Osawa, Mitaka, Tokyo, Japan  Vigneshwaran Krishnamurthy 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  Tomoyuki Kudo Subaru Telescope, 650 N. Aohoku Place, Hilo, HI 96720, USA  Seiya Kurita  Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan  Takashi Kurokawa  Astrobiology Center, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Institute of Engineering, Tokyo University of Agriculture and Technology, 2-24-16, Naka-cho, Koganei, Tokyo, 184-8588, Japan  Nobuhiko Kusakabe 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  David W. Latham Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Brian McLean  Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD, 21218, USA  Felipe Murgas Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain  Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain  Jun Nishikawa 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), 2-21-1 Osawa, Mitaka, Tokyo, Japan  Astrobiology Center, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Taku Nishiumi Department of Astronomy, School of Science, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo, Japan  Astrobiology Center, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Department of Multi-Disciplinary Sciences, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan  Masashi Omiya  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  Hugh P. Osborn Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  NCCR/Planet-S, Universität Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland  Enric Palle Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain  Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain  Hannu Parviainen Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain  Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain  George R. Ricker Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Sara Seager Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Takuma Serizawa  Institute of Engineering, Tokyo University of Agriculture and Technology, 2-24-16, Naka-cho, Koganei, Tokyo, 184-8588, Japan  National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  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  Huan-Yu Teng Department of Earth and Planetary Sciences, School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan  Yuka Terada Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan, R.O.C.  Department of Astrophysics, National Taiwan University, Taipei 10617, Taiwan, R.O.C.  Joseph D. Twicken NASA Ames Research Center, Moffett Field, CA 94035, USA  SETI Institute, Mountain View, CA 94043, USA  Akitoshi Ueda  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), 2-21-1 Osawa, Mitaka, Tokyo, Japan  Roland Vanderspek Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Sébastien Vievard  Subaru Telescope, 650 N. Aohoku Place, Hilo, HI 96720, USA  Astrobiology Center, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Joshua N. Winn Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA  Yujie Zou 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 March 3, 2022)

###### Abstract

We present the discovery and validation of a temperate sub-Neptune around the
nearby mid-M dwarf TIC 470381900 (TOI-1696), with a radius of $3.09\pm 0.11$
$R_{\earth}$ and an orbital period of $2.5$ days, using a combination of TESS
and follow-up observations using ground-based telescopes. Joint analysis of
multi-band photometry from TESS, MuSCAT, MuSCAT3, Sinistro, and KeplerCam
confirmed the transit signal to be achromatic as well as refined the orbital
ephemeris. High-resolution imaging with Gemini/’Alopeke and high-resolution
spectroscopy with the Subaru/IRD confirmed that there are no stellar
companions or background sources to the star. The spectroscopic observations
with IRD and IRTF/SpeX were used to determine the stellar parameters, and
found the host star is an M4 dwarf with an effective temperature of
$T_{\mathrm{eff}}$ $=$ $3185\pm 76$ K and a metallicity of
$[\mbox{Fe}/\mbox{H}]$ $=$ $0.336\pm 0.060$ dex. The radial velocities
measured from IRD set a 2-$\sigma$ upper limit on the planetary mass to be
$48.8$ $M_{\oplus}$. The large radius ratio ($R_{\mathrm{p}}$/$R_{\star}$
$\sim$ 0.1) and the relatively bright NIR magnitude ($J$=12.2 mag) make this
planet an attractive target for further followup observations. TOI-1696 b is
one of the planets belonging to the Neptunian desert with the highest
transmission spectroscopy metric discovered to date, making it an interesting
candidate for atmospheric characterizations with JWST.

Exoplanet astronomy (486) – M dwarf stars (982) – Speckle interferometry
(1552) – Transit photometry (1709) – High resolution spectroscopy (2096)

††journal: ApJ

##  1 Introduction

Exoplanet population statistics from the Kepler mission (Borucki et al., 2010)
revealed that there is a dearth of planets around the size of Neptune
($\sim$3–4$R_{\earth}$) with orbital periods less than 2–4 d. This has been
referred to as the “Neptunian Desert” or “photo-evaporation desert” or simply
“evaporation desert” (Szabó & Kiss, 2011; Mazeh et al., 2016; Lopez, 2017).
The scarcity of planets in this region of parameter space can be explained by
photo-evaporation, that is, atmospheric mass loss due to high-energy
irradiation from the host star (Owen & Wu, 2017). The small number of planets
that have so far been found in the desert (e.g. West et al., 2019; Jenkins et
al., 2020) are believed to retain substantial atmospheres (or are still in the
process of losing them), but the physical mechanisms are not well understood.
Comparing planets that have lost their atmospheres with those that have
retained their atmospheres will be useful to understand the processes such as
photo-evaporation theory. Therefore, it is important to increase the number of
planets in this region and reveal the nature of their atmospheres. TESS
(Ricker et al., 2015), which has identified over 5000 exoplanet candidates so
far111As of 2022 February per https://exoplanetarchive.ipac.caltech.edu/, made
it possible to discover more planets in the Neptunian Desert.

In this paper, we report the validation of a new planet around the mid-M dwarf
TOI-1696, whose transits were identified by the TESS mission. The planet
TOI-1696 b has a sub-Neptune size ($3.09\pm 0.11$ $R_{\earth}$) and an orbital
period of $2.5$ days, which places it within (or near the boundaries of) the
Neptunian desert.

The large radius ratio ($R_{\mathrm{p}}$/$R_{\star}$ $\sim$ 0.1) makes the
planet’s transits deep, and combined with the relatively bright near-IR (NIR)
magnitude (J=12.2 mag) of the star, the planet is one of the best targets for
future atmospheric research via transmission spectroscopy.

The rest of this paper is organized as follows. In Section 2, we present the
observational data and the reduction procedures used for the analyses. In
Section 3, we explain the analyses methods and results. In Section 4, we
discuss the features of the planet and its future observational prospects,
concluding with a summary in Section 5.

##  2 Observations & Data Reduction

###  2.1 Transit photometry - TESS

Figure 1: Archival imaging from POSSII-F survey (taken in 1998; Reid et al.,
1991) with the TESS photometric aperture (black outline) and Gaia sources
(gray circles). The cyan circle indicates the position of TOI-1696; we note
the proper motion is low enough that its current position is not significantly
offset in the archival image.

Figure 2: The upper panels show the TESS PDCSAP lightcurve with Savitzky-Golay
(window=1001) variability model (top), and the flattened lightcurve with TLS
model (bottom). The lower panels show the TLS power spectrum (left), folded
TESS lighturve with TLS model (middle), and individual transit depths from TLS
(right).

TESS observed TOI-1696 with a 2 min cadence in Sector 19 from 2019 Jul 25 to
Aug 22, resulting in photometry spanning approximately 27 days with a gap of
about one day in the middle when the satellite reoriented itself for data
downlink near perigee. Light curves were produced by the Science Processing
Operations Center (SPOC) photometry pipeline (Jenkins, 2002; Jenkins et al.,
2010; Jenkins & et al., 2020) using the aperture shown in Figure 1. We used
the PDCSAP light curves produced by the SPOC pipeline (Stumpe et al., 2012;
Smith et al., 2012; Stumpe et al., 2014) for our transit analyses. TOI-1696 is
located in a fairly crowded field, owing to its low galactic latitude
($b=-0.81^{\circ}$). The SPOC pipeline applies a photometric dilution
correction based on the CROWDSAP metric, which we independently confirmed by
computing dilution values based on Gaia DR2 magnitudes222approximating Gaia
$R_{\mathrm{p}}$ as the TESS bandpass, and assuming a full width at half
maximum (FWHM) of 25 ″.

TOI-1696.01 was detected by the SPOC pipeline in a transiting planet search,
and the candidate was subsequently reported to the community by the TESS
Science Office (TSO) on 2020 January 30 via the TESS Object of Interest (TOI;
Guerrero et al. (2021)) Releases portal333https://tess.mit.edu/toi-releases/.
The candidate passed all data validation diagnostic tests (Twicken et al.,
2018) performed by the SPOC444Full vetting report available for download at
https://exo.mast.stsci.edu/exomast_planet.html?planet=TOI169601. The SPOC
pipeline removed the transit signals of TOI-1696.01 from the light curve and
performed a search for additional planet candidates (Li et al., 2019), but
none were reported.

We independently confirmed the transit signal found by the SPOC. After
removing stellar variability and residual instrumental systematics from the
PDCSAP light curve using a 2$\mathrm{nd}$ order polynomial Savitzy-Golay
filter, we searched for periodic transit-like signals using the transit least-
squares algorithm (TLS; Hippke & Heller,
2019)555https://transitleastsquares.readthedocs.io/en/latest/index.html,
resulting in the detection of TOI-1696.01 with a signal detection efficiency
(SDE) of 11.6, a transit signal-to-noise ratio (SNR) of 7.4, orbital period of
$2.50031\pm 0.00001$ days, and transit depth of 10.6 parts per thousand (ppt),
which is consistent with the values reported by the TESS team on ExoFOP-
TESS666https://exofop.ipac.caltech.edu/tess/. We subtracted this signal and
repeated the transit search, but no additional signals with SDE above 10 were
found. TLS also reports the approximate depths of each individual transit; we
note that these transit depths and uncertainties are useful for diagnostic
purposes only, as they are simplistically determined from the mean and
standard deviation of the in-transit flux. The depths of the odd transits are
within 1.5$\sigma$ of the even transits, suggesting a low probability of
either signal being caused by an eclipsing binary at twice the detected
period. The TLS detection is shown in Figure 2.

###  2.2 Transit photometry - FLWO/KeplerCam

We used KeplerCam, mounted on the 1.2m telescope located at the Fred Lawrence
Whipple Observatory (FLWO) atop Mt. Hopkins, Arizona, to observe a full
transit on 2020 February 17. KeplerCam has a $23^{\prime}.1\times
23^{\prime}.1$ field-of-view and operates in binned by 2 mode producing a
pixel scale of 0.672″. Images were obtained in the $i$-band with an exposure
time of 300 seconds. A total of 29 images were collected over 144 minutes. The
data were reduced using standard IDL routines and photometry was performed
using the AstroImageJ software package (Collins et al., 2017).

###  2.3 Transit photometry - LCO/SINISTRO

We observed a full transit on 2020 November 13, using Sinistro, an optical
camera mounted on a 1m telescope located at McDonald Observatory in Texas,
operated by Las Cumbres Observatory (Brown et al., 2013). Sinistro has a
$26^{\prime}.5\times 26^{\prime}.5$ field of view with a pixel scale of
0.389″. We observed 62 images in total during 339 minutes, using a $V$-band
filter, with an exposure time of 5 min. The data were reduced by the standard
LCOGT BANZAI pipeline (McCully et al., 2018), and photometry was performed
using AstroImageJ software.

###  2.4 Transit photometry - LCO/MuSCAT3

MuSCAT3 is a multi-band simultaneous camera installed on the 2m Faulkes
Telescope North at Las Cumbres Observatory (LCO) on Haleakala, Maui (Narita et
al., 2020). It has four channels, enabling simultaneous photometry in the $g$
(400–550 nm), $r$ (550–700 nm), $i$ (700–820 nm) and $z_{s}$ (820–920 nm)
bands. Each channel has a 2048$\times$2048 pixel CCD camera with a pixel scale
of 0.27″, providing a $9^{\prime}.1\times 9^{\prime}.1$ field of view. We
observed a full transit of TOI-1696.01 on 2020 December 23, from BJD
2459206.703523 to 2459206.827246. We took 36, 41, 89, and 131 exposures with
exposure times of 300, 265, 120, and 80 s in the $g$, $r$, $i$, and $z_{s}$
bands, respectively.

The data reduction was conducted by the standard LCOGT BANZAI pipeline. Then
the differential photometry was conducted by a customized aperture-photometry
pipeline for MuSCAT series (Fukui et al., 2011). The optimized aperture radii
are 8, 6, 10, and 8 pixels (2.16″, 1.62″, 2.7″, and 2.16″) for the $g$, $r$,
$i$, and $z_{s}$ bands, respectively. We optimized a set of comparison stars
for each band to minimize the dispersion of the light curves. For
computational efficiency, and to achieve a more uniform signal-to-noise ratio
(SNR), we subsequently binned the $g$, $r$, $i$, and $z_{s}$ data to 300, 240,
180, and 120 s, respectively.

###  2.5 Transit photometry - NAOJ 188cm/MuSCAT

We also observed a full transit with MuSCAT (Narita et al., 2015), which is
installed on the 188cm telescope of National Astronomical Observatory of Japan
(NAOJ) in Okayama, Japan. MuSCAT has a similar optical design as MuSCAT3 but
has three CCD cameras for the $g$, $r$ and $z_{s}$ bands. On the night of 2021
July 28 we observed TOI-1696 from BJD 2459424.228358 to 2459424.30679. At that
point, the $r$-band camera was not available due to an instrumental issue, so
we observed with only the $g$ and $z_{s}$ bands, using an exposure time of 60
s for both bands.

The data reduction and differential photometry was performed using the
pipeline described in Fukui et al. (2011). The optimized aperture radii were 4
and 6 pixels (1.44″and 2.16″) for the $g$ and $z_{s}$ bands, respectively.
Similarly to the MuSCAT3 data, we binned the $g$ and $z_{s}$ data to 300 and
120 s, respectively.

###  2.6 Speckle imaging - Gemini/’Alopeke

On the nights of 2020 December 03 and 2021 October 14, TOI-1696 was observed
with the ’Alopeke speckle imager (Scott, 2019), mounted on the 8.1 m Gemini
North telescope on Mauna Kea. ’Alopeke simultaneously acquires data in two
bands centered at 562 nm and 832 nm using high speed electron-multiplying CCDs
(EMCCDs). We collected and reduced the data following the procedures described
in Howell et al. (2011). The resulting reconstructed image achieved a contrast
of $\Delta\mathrm{mag}=5.8$ at a separation of 1″ in the 832 nm band. No
secondary sources were detected. The data taken on 2021 October 14 is shown in
Figure 3.

Figure 3: Gemini/’Alopeke reconstructed images and contrast curves produced as
described in Section 2.6.

Figure 4: Palomar/PHARO images and contrast curves (top: Br$\gamma$; bottom:
Hcont) produced as described in Section 2.7.

###  2.7 Adaptive optics imaging - Palomar/PHARO

On 2021 September 19 we conducted near-infrared high-resolution imaging using
the adaptive optics instrument PHARO mounted on the 5 m Hale telescope at
Palomar Observatory (Hayward et al., 2001). We observed TOI-1696 seperately in
the $Br\gamma$ ($2.18\,\rm{\mu m}$) and $H_{cont}$ ($2.29\,\rm{\mu m}$) bands,
reaching a contrast of $\Delta\mathrm{mag}=8$ at a separation of 1″ in both
bands. The AO images and corresponding contrast curves are shown in Figure 4.

###  2.8 High-resolution spectroscopy - Subaru/IRD

We obtained high-resolution spectra of TOI-1696 in the NIR with IRD (Tamura et
al., 2012; Kotani et al., 2018), mounted on the 8.2 m Subaru telescope. IRD
can achieve a spectral resolution of $\sim$70,000 in the wavelength range 930
nm to 1740 nm. The derived spectra were used for the three purposes: to search
for spectral companions (e.g. SB2 scenarios), to measure fundamental stellar
parameters (e.g. effective temperature and metallicity), and to rule out large
radial velocity (RV) variations that would indicate an eclipsing binary (EB),
as well as placing a limit on the mass of the planet. From UT 2021 January 30
to 2022 January 08, we obtained 13 spectra of TOI-1696 using 1800 s exposure
times, as part of a Subaru Intensive Program (Proposal IDs S20B-088I and
S21B-118I). The raw data were reduced using IRAF (Tody, 1993) as well as a
pipeline for the detector’s bias processing and wavelength calibrations
developed by the IRD instrument team (Kuzuhara et al., 2018; Hirano et al.,
2020). For the RV analyses and stellar parameter derivation, we computed a
high-SNR coadded spectrum of the target following the procedures described in
Hirano et al. (2020).

For use as a spectral template in the analysis described in Section 3.2, we
also downloaded archival IRD data of GJ 699 (Barnard’s Star)777Using the
Subaru-Mitaka-Okayama-Kiso-Archive (SMOKA), which was obtained on 2019 March
23 (HST). We reduced and calibrated the GJ 699 data following the same
procedures as the TOI-1696 data.

###  2.9 Medium-resolution spectroscopy - IRTF/SpeX

We collected observations of TOI-1696 on UT 2020 December 09 using SpeX, a
medium‐resolution spectrograph on the NASA Infrared Telescope Facility (IRTF)
on Maunakea (Rayner et al., 2003). We obtained our observations in SXD mode
with a $0\farcs 3\times 15$″slit, providing a spectral resolution of $R\approx
2000$ over a wavelength range 700 nm to 2550 nm. In order to remove sky
background and reduce systematics, the spectra were collected using an ABBA
nod pattern (with a separation of $7\farcs 5$ between the A and B positions)
and with the slit synced to the parallactic angle. We reduced our spectra
using the Spextool reduction pipeline (Cushing et al., 2004) and removed
telluric contamination using xtellcor (Vacca et al., 2003). The derived
spectra were used to calculate the stellar metallicity.

##  3 Analyses & Results

###  3.1 Stellar parameters estimation

In the next subsections we estimate the fundamental stellar parameters of
TOI-1696. First, the stellar effective temperature $T_{\mathrm{eff}}$ and
metallicity $[\mbox{Fe}/\mbox{H}]$ are derived from two independent methods;
one is from the IRD spectra and the other is from the SpeX spectra and
photometric relations. Second, the stellar radius $R_{\star}$, mass
$M_{\star}$, and other related parameters are derived using empirical
relations and the above $T_{\mathrm{eff}}$ and $[\mbox{Fe}/\mbox{H}]$ values.

####  3.1.1 Estimation of $T_{\mathrm{eff}}$ and $[\mbox{Fe}/\mbox{H}]$: from
IRD spectra

We derived the effective temperature $T_{\mathrm{eff}}$ and abundances of
individual elements [X/H] from the coadded IRD spectrum. To avoid amplifying
noise in the spectrum, we decided not to deconvolve the instrumental profile
prior to these analyses.

We determined the parameters by the equivalent width comparison of individual
absorption lines between the synthetic spectra and the observed ones. For
$T_{\mathrm{eff}}$ estimation, 47 FeH molecular lines in the Wing-Ford band at
$990-1020$ nm was used as same as in Ishikawa et al. (2022). We also derived
the abundance of eight metal elements as described in Section A.1.

We iterated the $T_{\mathrm{eff}}$ estimation and the abundance analysis
alternately until $T_{\mathrm{eff}}$ and metallicity were consistent with each
other. First, we derived a provisional $T_{\mathrm{eff}}$ assuming solar
metallicity ($\mathrm{[Fe/H]}=0$), and then we determined the individual
abundances of the eight elements [X/H] using this provisional
$T_{\mathrm{eff}}$. Second, we redetermined $T_{\mathrm{eff}}$ adopting the
iron abundance [Fe/H] as the input metallicity, and then we redetermined the
abundances using the new $T_{\mathrm{eff}}$. We iterated the estimation of
$T_{\mathrm{eff}}$ and [Fe/H] until the final results and the results of the
previous step agreed within the error margin. As a result, we derived
$T_{\mathrm{eff}}$ $=3156\pm 119~{}\rm{K}$ and $[\mbox{Fe}/\mbox{H}]$
$=0.333\pm 0.088~{}\rm{dex}$.

####  3.1.2 Estimation of $T_{\mathrm{eff}}$ and $[\mbox{Fe}/\mbox{H}]$: from
SpeX spectra and photometric relations

Before analyzing our SpeX spectra, we corrected the data to the lab reference
frame using tellrv888https://github.com/ernewton/tellrv (Newton et al., 2014,
2022). We then determined metallicity with
metal999https://github.com/awmann/metal (Mann et al., 2013), using only the
$K$-band part of the spectrum, which is historically the most reliable,
although the metallicities from $H$\- and $J$-band are broadly consistent.

We calculated the stellar parameters using a series of photometric relations,
following the Section 4.3 of (Dressing et al., 2019). First, we calculated the
luminosity of the star using the Gaia EDR3 distance (Stassun & Torres, 2021),
2MASS $J$ magnitude, $r$ magnitude (from the Carlsberg Meridian Catalogue;
Muiños & Evans, 2014), and the metallicity-dependent $r$-$J$ bolometric
correction in Table 3 of Mann et al. (2015). Next, we calculated the radius of
the star using the relation between $R_{\star}$, absolute $K$ magnitude, and
$[\mbox{Fe}/\mbox{H}]$ defined in Table 1 of Mann et al. (2015). Lastly, we
calculated $T_{\mathrm{eff}}$ using the Stefan-Boltzmann law. As a result, we
derived $T_{\mathrm{eff}}$ $=3207\pm 99~{}\rm{K}$ and $[\mbox{Fe}/\mbox{H}]$
$=0.338\pm 0.083~{}\rm{dex}$.

The strong agreement in $T_{\mathrm{eff}}$ and $[\mbox{Fe}/\mbox{H}]$ between
the two methods suggests a high degree of reliability of the measurements. For
the following analyses, we used the weighted mean of the two respective
measurements for $T_{\mathrm{eff}}$ and $[\mbox{Fe}/\mbox{H}]$, specifically,
$T_{\mathrm{eff}}$ $=$ $3185\pm 76$ K and $[\mbox{Fe}/\mbox{H}]$ $=$$0.336\pm
0.060$ dex.

####  3.1.3 Estimation of stellar radius and mass

We estimated other stellar parameters such as stellar mass $M_{\star}$, radius
$R_{\star}$, surface gravity $\log g$, mean density $\rho_{\star}$, and
luminosity $L_{\star}$ following the procedure described in Hirano et al.
(2021). In short, the distributions of the stellar parameters are derived from
a Monte Carlo approach using a combination of several empirical relations as
well as the observed and literature values.

The $R_{\star}$ value was calculated through the empirical relation from Mann
et al. (2015), and $M_{\star}$ from Mann et al. (2019). In deriving the
stellar parameters by Monte Carlo simulations, we adopted Gaussian
distributions for $T_{\mathrm{eff}}$ and $[\mbox{Fe}/\mbox{H}]$ based on our
spectroscopic analyses (see Sections 3.1.1 and 3.1.2), the apparent
$K_{s}$-band magnitude from 2MASS, and the parallax from Gaia EDR3 (Stassun &
Torres, 2021). We assumed zero extinction ($A_{V}=0$), considering the
proximity of the star to Earth.

As a result, we derived $R_{\star}$ $=$ $0.2775\pm 0.0080$ $R_{\odot}$ and
$M_{\star}$ $=$ $0.255\pm 0.0066$ $M_{\odot}$ along with the other parameters
listed in A.1. By interpolating Table 5 of Pecaut & Mamajek (2013) we
determined the spectral type of TOI-1696 to be M4V (M3.9V $\pm$ 0.2).

To check the robustness of this analysis, we confirmed them to be in good
agreement with stellar parameters derived through independent analyses based
on SED fitting and isochrones (see Section A.2 and A.3).

Table 1: Main identifiers, equatorial coordinates, proper motion, parallax, optical and infrared magnitudes, and fundamental parameters of TOI-1696. Parameter | Value | Source
---|---|---
Main identifiers
TIC 470381900 |  TIC v8a
2MASS J04210733+4849116 |  ExoFOPa
WISE J042107.34+484911.5 |  ExoFOPa
UCAC4 695-028795 |  ExoFOPa
Gaia EDR3 270260649602149760 |  Gaia EDR3b
Equatorial coordinates, parallax, and proper motion
R.A. (J2015.5) |  04h21m07.36s |  Gaia EDR3b
Dec. (J2015.5) |  $+$48$\arcdeg$49$\arcmin$11.38$\arcsec$ |  Gaia EDR3b
$\pi$ (mas) | $15.4752\pm 0.0345$ |  Gaia EDR3b
$\mu_{\alpha}$ (mas yr-1) | $12.8726\pm 0.0345$ |  Gaia EDR3b
$\mu_{\delta}$ (mas yr-1) | $-19.0463\pm 0.0269$ |  Gaia EDR3b
Optical and near-infrared photometry
$TESS$ | $13.9664\pm 0.00730068$ |  TIC v8a
$G$ | $15.3056\pm 0.0028$ |  Gaia EDR3b
$B_{\mathrm{p}}$ | $17.0511\pm 0.0051$ |  Gaia EDR3b
$R_{\mathrm{p}}$ | $14.0457\pm 0.0039$ |  Gaia EDR3b
$B$ | $18.467\pm 0.162$ |  ExoFOPa
$V$ | $16.82\pm 1.133$ |  ExoFOPa
$J$ | $12.233\pm 0.023$ |  2MASSc
$H$ | $11.604\pm 0.031$ |  2MASSc
$Ks$ | $11.331\pm 0.023$ |  2MASSc
$W1$ | $11.134\pm 0.023$ |  AllWISEd
$W2$ | $10.984\pm 0.021$ |  AllWISEd
$W3$ | $10.71\pm 0.11$ |  AllWISEd
$W4$ | $8.748\pm$ |  AllWISEd
Fundamental parameters
$T_{\mathrm{eff}}$ (K) | $3185\pm 76$ | This work
$\log g$ (cgs) | $4.959\pm 0.026$ | This work
$[\mbox{Fe}/\mbox{H}]$ (dex) | $0.336\pm 0.060$ | This work
$M_{\star}$ ($M_{\odot}$) | $0.255\pm 0.0066$ | This work
$R_{\star}$ ($R_{\odot}$) | $0.2775\pm 0.0080$ | This work
$\rho_{\star}$ (g cm-3) | $16.8^{+1.5}_{-1.4}$ | This work
distance (pc) | $65.03\pm 0.36$ | This work
Luminosity ($\mathrm{L_{\odot}}$) | $0.00711^{+0.00083}_{-0.00075}$ | This work
ahttps://exofop.ipac.caltech.edu/tess/
bStassun & Torres (2021)
cSkrutskie et al. (2006)
dCutri et al. (2021)

###  3.2 Search for spectroscopic binary stars

If a stellar companion orbits the target star, the observed spectra will
generally be the combination of two stellar spectra with different radial
velocities. To see if TOI-1696 is a spectroscopic binary (i.e. an SB2), we
calculated the cross-correlation function (CCF) of the TOI-1696’s IRD spectra
with that of the well-known single-star GJ 699 (Barnard’s Star). The spectrum
of TOI-1696 used for the analysis was obtained on UT 2021 January 30 08:53,
which corresponds to the an orbital phase of 0.247 based on the TESS
ephemeris.

For the analysis, we divided the spectra into six wavelength bins that are
less affected by telluric absorption: [988, 993 nm], [995, 1000 nm], [1009,
1014 nm], [1016, 1021 nm], [1023, 1028 nm], and [1030, 1033 nm]. We corrected
the telluric absorption signal using the spectra of the rapid-rotator HIP
74625, which was observed at the same night. The CCF to the template spectrum
was calculated for each segment, after barycentric velocity correction.
Finally, we computed the median of the CCFs from each segment. As shown in
Figure 5, the resulting CCF is clearly single-peaked. If the observed transit
signals were actually caused by an eclipsing stellar companion, the RV
difference at quadrature would be $>100\,\rm{km\,s^{-1}}$, which would result
in a second peak in the CCF given that the flux of such a companion would be
detectable. We thus conclude TOI-1696 is not an eclipsing binary.

Figure 5: Calculated CCF of the IRD spectrum of TOI-1696 taken on 2021 January
30 at the orbital phase 0.247, to the template spectrum of GJ699, exhibiting a
single peak with width 9.2 k$\mathrm{m\,s^{-1}}$. The dashed line shows the
auto-correlation function of the GJ699 spectrum as a reference.

###  3.3 Stellar age

Because young stars are active and rapidly rotating, stellar activity and
rotation period can be used as proxy for determining its youth. We did not
find any stellar rotational signal in the TESS SPOC light curve, suggesting
that the star is not very active. Similarly, no strong rotational signal was
found in archival photometric data from ZTF Data Release 9 (Bellm et al.,
2019; Masci et al., 2019) and ASAS-SN (Kochanek et al., 2017).

GJ 699 has a rotation period of 145 days and $v\sin i$ of less than 3
$\,\rm{km\,s^{-1}}$ (Toledo-Padrón et al., 2019), which is below the limit of
IRD’s resolving power ($\sim$70000, corresponding to $\sim
4.5\,\rm{km\,s^{-1}}$). While the CCF of TOI-1696 has a FWHM value consistent
with that of GJ 699 (see Figure 5), even if we assume the rotation axis of
TOI-1696 is in the plane of the sky, relatively short rotation periods cannot
be ruled out, as their rotational broadening would not be resolvable with IRD.
However, fast rotation would most likely be accompanied with surface magnetic
activity levels that would produce detectable photometric signals. We also
used banyan $\Sigma$ (Gagné et al., 2018) to check if TOI-1696 is a member of
any known stellar associations, using its proper motion and the parallax from
Gaia EDR3. banyan $\Sigma$
tool101010http://www.exoplanetes.umontreal.ca/banyan/ returned a value of
99.9% field star, suggesting it is not a member of any nearby young moving
group. The non-detection by GALEX also means that the star is not young enough
to be bright in the UV. We thus conclude that TOI-1696 is most likely a
relatively old, slow rotator.

###  3.4 Transit analysis

We jointly fit the TESS, KeplerCam, Sinistro, MuSCAT3, and MuSCAT datasets
using the PyMC3 (Salvatier et al., 2016),
exoplanet111111https://docs.exoplanet.codes/en/stable/ (Foreman-Mackey et al.,
2019), starry (Luger et al., 2019), and celerite2 (Foreman-Mackey et al.,
2017; Foreman-Mackey, 2018) software packages. The model assumes a chromatic
transit depth, a linear ephemeris, a circular orbit, and quadratic limb
darkening. For efficient and uninformative sampling, the quadratic limb
darkening coefficients were transformed following Kipping (2013). To account
for systematics in the ground-based datasets we included a linear model of
airmass and other covariates, such as the pixel response function peak, width,
and centroids, when available. To account for stellar variability and residual
systematics in the TESS SPOC light curve, we included a Gaussian Process (GP
Rasmussen & Williams, 2005) model with a Matérn-3/2 covariance function. To
account for the possibility of under- or over-estimated uncertainties, we
included a white noise scale parameter for each dataset/band, enabling the
errors to be estimated simultaneously with other free parameters; we placed
Gaussian priors on these white noise scale parameters, with center and width
equal to unity. We placed Gaussian priors on the stellar mass and radius based
on the results in Table 1. We also placed Gaussian priors on the limb
darkening coefficients based on interpolation of the parameters tabulated in
Claret et al. (2012) and Claret (2017), propagating the uncertainties in the
stellar parameters in Table 1 via Monte Carlo simulation.

To optimize the model we used the gradient-based BFGS algorithm (Nocedal &
Wright, 2006) implemented in scipy.optimize to find initial maximum a
posteriori (MAP) parameter estimates. We then used these estimates to
initialize an exploration of parameter space via “no U-turn sampling” (NUTS,
Hoffman & Gelman, 2014), an efficient gradient-based Hamiltonian Monte Carlo
(HMC) sampler implemented in PyMC3.

Detailed plots showing the model fits to the ground-based datasets are shown
in Figure 7, Figure 8, and Figure 9. We did not detect any significant
wavelength dependence of the transit depth (see Figure 10), which rules out
many plausible false positive scenarios involving eclipsing binaries (see
Section 3.6 for more details). The results of this fit are listed in Table 2.
Having established the achromaticity of the transit depth, we conducted a
second fit with an achromatic model to robustly estimate the planet radius.
This fit resulted in a final value of $R_{P}/R_{\star}=0.1025\pm 0.0014$,
corresponding to an absolute radius of $3.09\pm 0.11$ $R_{\earth}$, and all
other parameters were unchanged.

Table 2: Results of joint fit to the TESS and ground-based transit datasets.  Parameter | Value
---|---
Primary transit parameters
$M_{\star}$ [$M_{\odot}$] | $0.255\pm 0.007$
$R_{\star}$ [$R_{\odot}$] | $0.277\pm 0.008$
$T_{0}$ [BJD] | $2458834.20115\pm 0.00058$
$P$ [days] | $2.500311\pm 0.000004$
$R_{P}/R_{\star,T}$ | $0.0952\pm 0.0062$
$R_{P}/R_{\star,V}$ | $0.1021\pm 0.0057$
$R_{P}/R_{\star,g}$ | $0.1036^{+0.0060}_{-0.0068}$
$R_{P}/R_{\star,r}$ | $0.1053\pm 0.0034$
$R_{P}/R_{\star,i}$ | $0.1023\pm 0.0020$
$R_{P}/R_{\star,z}$ | $0.1026\pm 0.0020$
$R_{P}/R_{\star}$ | $0.1025\pm 0.0014^{a}$
$b$ | $0.59^{+0.03}_{-0.04}$
Limb darkening parameters
$u_{1}$ ($T$) | $0.16\pm 0.01$
$u_{2}$ ($T$) | $0.48\pm 0.01$
$u_{1}$ ($V$) | $0.48\pm 0.02$
$u_{2}$ ($V$) | $0.30\pm 0.01$
$u_{1}$ ($g$) | $0.49\pm 0.01$
$u_{2}$ ($g$) | $0.31\pm 0.01$
$u_{1}$ ($r$) | $0.50\pm 0.01$
$u_{2}$ ($r$) | $0.25\pm 0.01$
$u_{1}$ ($i$) | $0.37\pm 0.01$
$u_{2}$ ($i$) | $0.28\pm 0.01$
$u_{1}$ ($z$) | $0.24\pm 0.01$
$u_{2}$ ($z$) | $0.36\pm 0.01$
Derived parameters
$R_{\mathrm{p}}$ [$R_{\oplus}$] | $3.09\pm 0.11^{a}$
$a$ [AU] | $0.0229\pm 0.0002$
$T_{\mathrm{eq}}$ [K] | $489\pm 13^{b}$
$T_{14}$ [hours] | $1.00\pm 0.01$
aDerived from achromatic transit model fit.
bAssuming a Bond albedo of 0.3.
Figure 6: The phase-folded TESS light curve after removing the best-fit GP
noise model, with the best-fit transit model (blue) from our joint analysis of
the TESS and ground-based light curves. Figure 7: Transit model fit to the
MuSCAT3 (M3) data from 2020 December 23, ordered column-wise per bandpass. The
top row shows the raw data with the transit and systematics model, the middle
row shows the systematics-corrected data with only the transit model, and the
bottom row shows the residuals from the fit. The colors of the model
correspond to the photometric bandpass of each dataset; see also Figure 10.
Figure 8: Same as Figure 7, but for the MuSCAT (M1) data from 2021 July 28.
Figure 9: Same as Figure 7, but for the KeplerCam and LCO data from 2020
February 17 and 2021 November 13, respectively. Figure 10: Posteriors of the
planet-to-star radius ratio ($R_{P}/R_{\star}$) in each bandpass (left) and
impact parameter (right) from the joint fit to the TESS data and the ground-
based data shown in Figure 7, Figure 8, and Figure 9; the gray shaded region
in the right panel represents the uniform prior used in the fit, while the
blue histogram is the posterior.

###  3.5 Companion mass constraints

To put a limit on the mass of TOI-1696.01, we fit an RV model with a circular
orbit to the RV data from Subaru/IRD. Between the $H$-band and the $YJ$-band
spectra obtained with IRD, we opted to use the $H$-band spectra for RV
analysis because of its higher SNR.121212There have been reports of
unpredictable systematic errors caused by persistence light on the detector in
$H$-band, especially when bright stars are observed before fainter stars. We
checked the objects observed before TOI-1696 and found that none were more
than 1.2 mag brighter in the $H$-band, i.e. persistence light isn’t likely to
be a problem with these data. The data observed on 2021 January 29 was
excluded because of the possibility of an RV offset, as there was a gap of 8
months relative to the succeeding observations. We also removed any data with
the clouds passing, which can cause systematic errors. The final dataset
consisted of 9 RV measurements from 2021 September 29 to 2022 January 8.

We used the RV model included in PyTransit which we simplified to have five
free parameters: phase-zero epoch $\rm{T_{0}}$, period, RV semi-amplitude, RV
zero point, and RV jitter term. For the $\rm{T_{0}}$ and the period, we put
Gaussian priors using the $\rm{T_{0}}$ and period derived from the transit
analysis. For the other parameters we put wide uniform priors. We ran the
built-in Differential Evolution optimizer and then sample the parameters with
Markov Chain Monte Carlo (MCMC) using 30 walkers and 104 steps. We use the
following equation to derive the planet mass,

$\centering
M_{p}=\Big{(}\frac{PM_{s}^{2}}{2\pi}\Big{)}^{1/3}\frac{K(1-e^{2})^{1/2}}{\sin(i)}\@add@centering$
(1)

where $M_{\mathrm{p}}$ is planet mass, $M_{\star}$ is star mass, $P$ is
orbital period, $K$ is RV semi-amplitude, $e$ is eccentricity (fixed to zero),
and $i$ is inclination (fixed to 90∘). To propagate uncertainties, we use the
posteriors for $M_{\star}$ and $P$ from previous analyses.

In Figure 11 we plot Keplerian orbital models corresponding to different
masses encompassing the 68th, 95th, and 99.7th percentiles of the semi-
amplitude posterior distribution. The 2-$\sigma$ upper limit is $48.8$
$M_{\earth}$ which places the companion 2 orders of magnitude below the
deuterium burning mass limit. The best-fit semi-amplitude is
$\rm{K}=14.4\,\rm{ms^{-1}}$, which corresponds to a mass of
$\rm{M_{p}}=12.3$$M_{\earth}$, and the best-fit jitter value is
$\sigma_{K}$=62 $\mathrm{m\,s^{-1}}$.

We calculated an expected planetary mass of $\sim$$8$ $M_{\earth}$ with MRExo
131313https://github.com/shbhuk/mrexo, which uses a mass-radius relationship
calibrated for planets around M dwarfs (Kanodia et al., 2019). This mass
corresponds to a semi-amplitude of 9.4$\mathrm{m\,s^{-1}}$, but the observed
RV data exhibits significantly larger variability ($\sigma\approx$
52$\mathrm{m\,s^{-1}}$). We interpret this variability as being responsible
for the large jitter value found by the fit, which suggests it is out-of-phase
with TOI-1696.01. Since the star appears to be quiet, one explanation for this
signal is the existence of an additional (possibly non-transiting) planet, but
more RV measurements would be required to determine if this is the case.
Furthermore, if such a planet were dynamically interacting with TOI-1696.01,
then this could help explain TOI-1696.01’s location in a sparsely populated
part of the period-radius plane (see Section 4).

Figure 11: Phase-folded RVs with Keplerian models corresponding to the 1-, 2-,
and 3-$\sigma$ mass upper limits. Gray points with the error bars show the
errors estimated from the data processing method described in Section 2.8. The
error bars in orange show the original errors + jitter term value of 62
$\mathrm{m\,s^{-1}}$ (added in quadrature) from the best-fit RV model (orange
line, best $\rm{M_{p}}=12.3$$M_{\earth}$.)

###  3.6 Eliminating false positive scenarios

A number of astrophysical scenarios can mimic the transit signal detected from
TESS photometry, including an eclipsing binary (EB) with a grazing transit
geometry, a hierarchical EB (HEB), and a diluted eclipse of a background (or
foreground) EB (BEB) along the line of sight of the target. In the following,
we will examine the plausibility of each scenario.

First, the Renormalised Unit Weight Error (RUWE) from Gaia EDR3 is 1.12, which
suggests that TOI-1696 is single (Belokurov et al., 2020). We can also rule
out the EB scenario based on the analysis of the IRD CCF in Section 3.2, and
the mass constraint derived in Section 3.1.1. Finally, the absence of any
wavelength dependence of the transit depth from our chromatic transit analysis
(Section 3.4) is incompatible with contamination from a star of different
spectral type (colour) than the host star, the details of which are discussed
in the Appendix B. In the absence of dilution, the measured radius of $3.09\pm
0.11$ $R_{\earth}$ (0.27 $R_{\mathrm{Jup}}$) equals the true radius, which
makes it significantly smaller than the lower limit of 0.8 $R_{\mathrm{Jup}}$
expected for brown dwarfs (Burrows et al., 2011).

Grazing transit geometries can also be eliminated, as the impact parameter is
constrained to $b<0.7$ at the 99% level based on our transit and contamination
analyses. The apparent boxy shape of our follow-up lightcurves is in stark
contrast with the V-shaped transit expected for grazing orbits. Hence, grazing
EB scenario is ruled out.

Moreover, we can constrain the classes of HEBs that can reproduce the observed
transit depth and shape using our multi-band observations. We aim to compute
the eclipse depths for a range of plausible HEBs in the bluest and reddest
bandpasses where they are expected to vary significantly. We adopt the method
presented in Bouma et al. (2020) to perform the calculation taking into
account non-zero impact parameter, the details of which are discussed in the
Appendix C. Comparing the simulated eclipse depths with the observed depth in
each band, we found that there is no plausible HEB configuration explored in
our simulation that can reproduce the observed depths in multiple bands
simultaneously. Hence, the HEB scenario is ruled out.

Although, TOI-1696’s probability of being a BEB is very high a priori given
its location at the galactic plane, we argue in the following that the BEB
scenario is extremely unlikely.

Our MuSCAT3 observation can resolve the signal down to 3″, which represents
the maximum radius within which the signal must originate. Furthermore, our
high-resolution speckle imaging ruled any nearby star and blended sources down
to 0.1″at a delta mag of 4.5. We checked archival images taken more than 60
years apart, but the proper motion of TOI-1696 is not enough to obtain a clear
view along the line of sight of the star. However, we can use statistical
arguments to estimate the probability of a chance-aligned star. To do this, we
use the population synthesis code Trilegal141414http://stev.oapd.inaf.it/cgi-
bin/trilegal (Girardi et al., 2005), which can simulate the Galactic stellar
population along any line of sight. Given the position of TOI-1696, we found a
probability of $5\times 10^{-8}$ to find a star brighter than $T$=16151515$T$
denotes the TESS bandpass. The maximum delta magnitude was computed using
dT=-2.5$\log_{10}$(depth), which translates to the magnitude that can produce
a 100% eclipse, within an area equal to the smallest MuSCAT3 photometric
aperture (aperture radius $=$ 3″). Assuming all such stars are binary and
preferentially oriented edge-on to produce eclipses with period and depth
consistent with the TESS detection, then this can represent a very
conservative upper limit of a BEB scenario. Despite the small probability of a
BEB based on the trivial star counting argument, we discuss relevant tools in
the following section for a more thorough statistical modeling.

###  3.7 Statistical validation

Here we quantify the false positive probability (FPP) of TOI-1696.01 using the
Python package Vespa and Triceratops (Morton, 2015; Giacalone & Dressing,
2020), the details of which are discussed in Section D. Although we were able
to rule out the classes of EB, BEB, and HEB in Section 3.6, we ran Vespa
considering all these scenarios for completeness and computed a formal
FPP$<1\times 10^{-6}$ which robustly quantifies TOI-1696.01 as a statistically
validated planet. Additionally, we validated TOI-1696.01 using Triceratops and
found FPP=0.0020. Giacalone et al. (2021) noted that TOIs with FPP $<0.015$
have a high enough probability of being bona fide planets to be considered
validated. The low FPPs calculated using Vespa and Triceratops added further
evidence to the planetary nature of TOI-1696.01. We now refer to the planet as
TOI-1696 b in the remaining sections.

##  4 Discussion

Figure 12: TOI-1696 b (blue) in the context of known transiting planets
(contours). TOI-1696 b appears to be within or close to the boundaries of the
Neptunian desert (solid black lines) in the period-radius plane defined by
Mazeh et al. (2016). The dashed lines refer to the boundaries’ uncertainty
regions. The orange points indicate planets orbiting M dwarfs
($T_{\mathrm{eff}}$ $<3800$K) and the red points indicate the five planets
most similar in this parameter space to TOI-1696 b: K2-25 b, K2-320 b, GJ 1214
b, TOI-269 b, and TOI-2406 b.

###  4.1 The nature of the planet

Here, we consider the nature of TOI-1696 b by placing it in context with the
population of known exoplanets161616Based on a query of the NASA Exoplanet
Archive “Confirmed Planets” table on 2022 January 31,
https://exoplanetarchive.ipac.caltech.edu/. Figure 12 shows a radius vs period
diagram, indicating that there are only a handful of planets with similar
characteristics to TOI-1696 b. The measured planetary radius $R_{\mathrm{p}}$
of $3.09\pm 0.11$ $R_{\earth}$ and the orbital period $P$ of $2.50031\pm
0.00001$ days, places it securely within the bounds of the Neptunian desert as
defined by Mazeh et al. (2016). The region occupied by TOI-1696 remains
sparsely populated despite recent discoveries of TESS planets within the
Neptunian desert (e.g. Murgas et al., 2021; Brande et al., 2022).

It should be noted that the Neptunian desert was originally determined based
on a population of planets orbiting mainly solar-type stars from the Kepler
mission. Because TOI-1696 is an M dwarf, the incident flux at a given orbital
separation will be less than solar-type stars. Nevertheless, we emphasize that
the target exists in a sparsely populated region of parameter space, despite
the large number of planets discovered around M dwarfs since the Kepler
mission (i.e. from K2 and TESS). For example, if we limit the comparison to
the 279 confirmed planets around M dwarfs with $T_{\mathrm{eff}}$ below 3800
K, only 14 planets have been found so far with orbital periods shorter than 10
days and planetary radii in the range 2.5$R_{\earth}$ $<$$R_{\mathrm{p}}$ $<5$
$R_{\earth}$. As shown in Figure 12, TOI-1696 b is similar to K2-25 b(Mann et
al., 2016), K2-320 b(Castro González et al., 2020), GJ 1214 b(Charbonneau et
al., 2009), TOI-269 b(Cointepas et al., 2021), and TOI-2406 b(Wells et al.,
2021) in terms of orbital period and radius. In particular, TOI-2406 b appears
most similar to TOI-1696 b as it orbits around a mid-M dwarf with an effective
temperature of $3100\pm 75$, and has a radius of $2.94\pm 0.17$ $R_{\earth}$
and orbital period of 3.077 days. TOI-2406 is also thought to be relatively
old without any activity signal. As both TOI-1696 b and TOI-2406 b are
excellent targets for detailed characterization studies, together they may
provide unique insights into this class of planet. There is also some
similarity between TOI-1696 b and the Neptunian Desert planets orbiting young
host stars, such as AU Mic b and c, K2-25 b, K2-95 b and K2-264 b. It has been
suggested that these planets may have inflated radii and could possibly still
be undergoing atmospheric mass-loss (e.g. Mann et al., 2016). Further study of
TOI-1696 b could reveal whether its similarity to these planets (despite being
older) is only superficial, or if it is indicative of an inflated radius.

###  4.2 Prospects for transmission spectroscopy

Given the rarity of this planet, it would be useful to assess its prospects
for future atmospheric observations to understand its formation and evolution.
In particular, the relatively large size of the planet compared to its host
star makes it a good candidate for transmission spectroscopy. Using Equation 1
in Kempton et al. (2018), we calculated the transmission spectroscopy metric
(TSM) of TOI-1696 b from its mass, radius, equilibrium temperature, stellar
radius, and $J$-band magnitude. We used the values in Figure 1 and 2, and
assumed a mass of $8$ $M_{\earth}$ estimated by MRExo. The derived TSM value
of TOI-1696 b is $105.6$. For reference, Kempton et al. (2018) suggested that
planets with TSM$>$90 are ideal targets for atmospheric follow-up.

For comparison, we calculated the TSM for the known population of transiting M
dwarf planets. We selected planets with $T_{\mathrm{eff}}$ $<3800\rm{K}$,
$R_{\mathrm{p}}$ $<10R_{\oplus}$, and $\rm{H}<11\rm{mag}$171717Based on a
query of the NASA Exoplanet Archive Confirmed Planets table as of 2022 January
31. For planets without mass measurements, we assumed the masses predicted by
MRExo. For planets without an equilibrium temperature, we estimated it from
the semi-major axis and the host star’s effective temperature (assuming zero
albedo). Figure 13 shows the computed TSM values for the selected samples of
planets. The TSM of TOI-1696 b places it in the top 10, making it one of the
best targets for future atmospheric investigations.

Figure 13: Planetary equilibrium temperature vs radius for TOI-1696 b and
other planets with $Rp<10R_{\oplus}$, with the host stars having
$T_{\mathrm{eff}}$ $<3800\rm{K}$ and $H<11\rm{mag}$. The point size represents
the calculated TSM values. Data points with a planet name beside them are
those with a higher TSM values than the target. Figure 14: Initial H2/He
atmospheric mass fraction of a TOI-1696 b-like planet that satisfies the
radius of $3.09\pm 0.11$ $R_{\oplus}$ and $T_{\mathrm{eq}}=489\pm 13$ K after
photo-evaporative mass loss for $8$ Gyr under the standard XUV radiation field
($L_{\mathrm{XUV}}$) and $10L_{\mathrm{XUV}}$. The grey region shows the H2/He
atmospheric mass fraction that reproduces the observed radius of TOI-1696 b
with a rocky core.

###  4.3 Existence of a primordial atmosphere

Up to this point in the section, the discussion has been based on the
assumption that the target has an atmosphere. Usually it is thought that
planets above the so-called radius gap can retain their atmospheres (Weiss &
Marcy, 2014; Rogers, 2015). However, does TOI-1696 b actually have an H2/He
atmosphere? Here we study the atmospheric mass that TOI-1696 b can retain
after $\sim 8$ Gyr under a stellar XUV irradiation. The mass of TOI-1696 b
remains poorly constrained as discussed in Section 3.5. We modeled TOI-1696 b
as a rocky planet with Earth-like core compositions (MgSiO3:Fe = 7:3) in the
mass range from $0.5M_{\oplus}$ to $20M_{\oplus}$. The silicate mantle and
iron core were described by the 3rd-order Birch-Murnagham EoS for MgSiO3
perovskite (Karki et al., 2000; Seager et al., 2007) and the Vinet EoS for
$\epsilon$-Fe (Anderson et al., 2001), respectively. The Thomas-Fermi Dirac
EoS (Salpeter & Zapolsky, 1967) was applied to high-pressure EoS for MgSiO3 at
$P\geq 4.90$ TPa and Fe at $P\geq 2.09\times 10^{4}$ GPa (Seager et al., 2007;
Zeng & Sasselov, 2013). The pressure and temperature in a H2/He envelope were
calculated using the SCvH EoS (Saumon et al., 1995).

We computed the thermal evolution of TOI-1696 b with a H2/He atmosphere by
calculating its interior structure in hydrostatic equilibrium for $\sim 8$
Gyr, and calculated its mass loss process. The initial mass fraction of a
H2/He atmosphere for a rocky planet ranges from 0.001% to 30% of its core
mass. The energy-limited hydrodynamic escape (Watson et al., 1981) controls
the mass loss rate given by

$\frac{dM_{\mathrm{p}}}{dt}=-\eta\frac{R^{3}_{\mathrm{p}}L_{\mathrm{XUV}}(t)}{4GM_{\mathrm{p}}a^{2}K_{\mathrm{tide}}},$
(2)

$\eta$ is the heating efficiency due to stellar XUV irradiation,
$L_{\mathrm{XUV}}$ is the stellar XUV luminosity, $G$ is the gravitational
constant, and $R_{\mathrm{p}}$ is the planetary radius (Erkaev et al., 2007).
Since the heating efficiency for a hydrogen-rich upper atmosphere was lower
than 20 % (Shematovich et al., 2014; Ionov & Shematovich, 2015), we adopted
$\eta=0.1$. $K_{\mathrm{tide}}$ is the reduction factor of a gravitational
potential owing to the effect of a stellar tide:

$K_{\mathrm{tide}}(\xi)=1-\frac{3}{2\xi}+\frac{1}{2\xi^{3}}<1,\,\,\,\,\,\xi=\frac{R_{\mathrm{H}}}{R_{\mathrm{p}}},$
(3)

where $R_{\mathrm{H}}$ is the Hill radius. The XUV luminosity
($L_{\mathrm{XUV}}$) of TOI-1696 followed from the X-ray-to-bolometric
luminosity relations of M-type stars (Jackson et al., 2012), where we adopted
the current luminosity of TOI-1696 as its bolometric luminosity. We also
considered a $10L_{\mathrm{XUV}}$ model because of the large uncertainty in
$L_{\mathrm{XUV}}$ of young M dwarfs.

Figure 14 shows the initial H2/He atmosphere of a TOI-1696 b-like planet that
reproduces the radius of $3.09\pm 0.11$ $R_{\oplus}$ at the current location
(i.e., $T_{\mathrm{eq}}=489\pm 13$ K) after the mass loss driven by the
standard XUV radiation ($L_{\mathrm{XUV}}$: blue) and 10 times higher one
($10L_{\mathrm{XUV}}$: red). The grey region shows the H2/He atmospheric mass
fraction of TOI-1696 b with a rocky core that satisfies its observed radius.
The observed radius of TOI-1696 b favors the existence of a H2/He atmosphere
atmosphere with $\gtrsim 3$ wt% unless its core contains icy material. We find
that TOI-1696 b can possess the H2/He atmosphere for 8 Gyr if its core mass is
larger than $\sim 1.5M_{\oplus}$ ($\sim 4M_{\oplus}$ for 10$L_{\mathrm{XUV}}$
models). If TOI-1696 b initially had the H2/He atmosphere of $\lesssim 3\%$,
it should be completely lost. Also, TOI-1696 b with mass of $\gtrsim
10M_{\oplus}$ can retain almost all the H2/He atmosphere accreted from a disk.
These suggest that TOI-1696 b with a rocky core of $\gtrsim 1.5-4M_{\oplus}$
is likely to be a sub-Neptune with a H2/He atmosphere.

##  5 Conclusions

TESS found transit signals of a sub-Neptune planet orbiting a mid-M dwarf
TOI-1696. To validate and characterize the planetary system, we conducted
follow-up observations of this system including ground-based transit
photometry, high-resolution imaging, and high- and medium-resolution
spectroscopy.

We have used several methods to determine the stellar parameters based on the
results of the spectroscopic observations, and have confirmed that the results
are consistent. The host star, TOI-1696, is a M-type star with a $M_{\star}$
at $0.255\pm 0.0066$ $M_{\odot}$ and $T_{\mathrm{eff}}$ at $3185\pm 76$ K.

The fact that this target is located near the Galactic plane makes validation
difficult. We used the results obtained to rule out various scenarios that
could reproduce the TESS signal (grazing EB, HEB, and BEB).

The validated planet, TOI-1696 b is a Sub-Neptune size planet with the radius
at $3.09$ $R_{\earth}$ and rotation period at $2.5$ days, which locates in the
Neptunian desert. To see its atmospheric properties, we calculated how much of
the atmosphere it currently retains, and found the planet likely to retain the
H2/He atmosphere if it has a core of $>$ 1.5–4$\rm{M_{\oplus}}$. In order to
statistically evaluate the feasibility of transmission spectroscopy on this
planet, we have also calculated and compared the TSM and concluded that this
target is one of the planets with the best prospects for atmospheric detection
among the currently known Sub-Neptune-sized planets. In addition, future RV
observations with high-resolution infrared spectrographs such as IRD will
allow us to place more substantial limits on the planetary mass.

##  6 Acknowledgements

Funding for the TESS mission is provided by NASA’s Science Mission
Directorate. We acknowledge the use of public TESS 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).

This work makes use of observations from the Las Cumbres Observatory global
telescope network. Some of the observations in the paper is based on
observations made with the MuSCAT3 instrument, developed by 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 research is in part on data collected at the Subaru Telescope, which is
operated by the National Astronomical Observatory of Japan, and at the Gemini
North telescope, located within the Maunakea Science Reserve and adjacent to
the summit of Maunakea. We are honored and grateful for the opportunity of
observing the Universe from Maunakea, which has cultural, historical, and
natural significance in Hawaii. Our data reductions benefited from PyRAF and
PyFITS that are the products of the Space Telescope Science Institute, which
is operated by AURA for NASA. This research made use of
Astropy,181818http://www.astropy.org a community-developed core Python package
for Astronomy (Astropy Collaboration et al., 2013, 2018). Some of the
observations in the paper made use of the High-Resolution Imaging
instrument(s) ‘Alopeke. ‘Alopeke was funded by the NASA Exoplanet Exploration
Program and built at the NASA Ames Research Center by Steve B. Howell, Nic
Scott, Elliott P. Horch, and Emmett Quigley. ‘Alopeke (and/or Zorro) was
mounted on the Gemini North (and/or South) telescope of the international
Gemini Observatory, a program of NSF’s NOIRLab, which is managed by the
Association of Universities for Research in Astronomy (AURA) under a
cooperative agreement with the National Science Foundation. on behalf of the
Gemini partnership: the National Science Foundation (United States), National
Research Council (Canada), Agencia Nacional de Investigación y Desarrollo
(Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina),
Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and
Korea Astronomy and Space Science Institute (Republic of Korea). Some of the
observations in this paper made use of the Infrared Telescope Facility, which
is operated by the University of Hawaii under contract 80HQTR19D0030 with the
National Aeronautics and Space Administration. The IRTF observations were
collected under the program 2020B115 (PI: S. Giacalone). This work has made
use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This work is supported by
Grant-in-Aid for JSPS Fellows, Grant Number JP20J21872, JSPS KAKENHI Grant
Numbers JP20K14518, JP19K14783, JP21H00035, JP18H05439, JP18H05439,
JP20K14521, JP17H04574, JP21K20376, JP21K13975, JP18H05442, JP15H02063, and
JP22000005, SATELLITE Research from Astrobiology Center (Grant Number
AB031010, AB022006, and AB031014), and JST CREST Grant Number JPMJCR1761.

E. E-B. acknowledges financial support from the European Union and the State
Agency of Investigation of the Spanish Ministry of Science and Innovation
(MICINN) under the grant PRE2020-093107 of the Pre-Doc Program for the
Training of Doctors (FPI-SO) through FSE funds.

##  Appendix A Detailed methods of stellar parameter estimation

###  A.1 Abundances of eight metal elements from IRD spectra

We calculated the abundances of seven other elements other than iron from IRD
spectra. We used 28 lines in total caused by neutral atoms of Na, Mg, Ca, Ti,
Cr, Mn, and Fe and singly ionized Sr. The detailed procedures of abundance
analysis and error estimation are described in Ishikawa et al. (2020). Figure
A.15 shows the final values of abundance after the iteration. From the final
values of the abundances of the eight elements, [M/H] was determined by
calculating the average weighted by the inverse of the square of their
estimated errors.

Figure A.15: Metallicity values derived from IRD spectrum. The horizontal
dashed line corresponds to the weighted average [M/H].

###  A.2 Estimation of Stellar Radius and Mass: SED Fitting

As an independent determination of the basic stellar parameters, we performed
an analysis of the broadband spectral energy distribution (SED) of the star
together with theGaia EDR3 parallax (Stassun & Torres, 2021), in order to
determine an empirical measurement of the stellar radius, following the
procedures described in Stassun & Torres (2016); Stassun et al. (2017, 2018).
We pulled the $JHK_{S}$ magnitudes from 2MASS, the W1–W3 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
A.16).

We performed a fit using NExtGen stellar atmosphere models, with the effective
temperature ($T_{\rm eff}$) and metallicity ([Fe/H]) constrained from the
spectroscopic analysis. The remaining free parameter is the extinction
$A_{V}$, which we fixed at zero due to the star’s proximity. The resulting fit
(Figure A.16) has a reduced $\chi^{2}$ of 1.7. Integrating the (unreddened)
model SED gives the bolometric flux at Earth, $F_{\rm bol}=5.20\pm 0.25\times
10^{-11}$ erg s-1 cm-2. Taking the $F_{\rm bol}$ and $T_{\rm eff}$ together
with the Gaia parallax, gives the stellar radius, $R_{\star}=0.276\pm 0.015$
R⊙. We used the $T_{\mathrm{eff}}$ and $[\mbox{Fe}/\mbox{H}]$ values from
spectroscopic results as priors for the parameter estimation.

In addition, we estimated the stellar mass from the empirical relations of
Mann et al. (2019), giving $M_{\star}=0.279\pm 0.014$ M⊙. Finally, the radius
and mass together imply a mean stellar density of $\rho_{\star}=18.79\pm 3.26$
g cm-3.

Figure A.16: Spectral energy distribution of TOI-1696. Red symbols represent
the observed photometric measurements, where the horizontal bars represent the
effective width of the passband. Blue symbols are the model fluxes from the
best-fit NextGen atmosphere model (black).

###  A.3 Stellar parameter comparison

In addition to the methods described above, we used the Python package
isochrones, which calculates stellar parameters from the stellar evolution
models. The three methods are not fully independent, as some of them use the
same relations such as mass derivation from Mann et al. (2019), but comparing
three results are useful to confirm the results are robust. The derived
stellar parameters agreed within $1\sim 2\sigma$, as shown in A.1. We pick up
the results from the empirical relations as our final stellar parameters in
Table 1.

Table A.1: Stellar parameters which were derived from empirical relations (Method 1; Section 3.1.3), SED fitting (Method 2; Section A.2) and isochrones (Method 3;Section A.3). †The resulting posterior is approximately zero and non-Gaussian as a result of using a tight uniform prior close to 0 for numerical reasons. Parameter | Method 1 | Method 2 | Method 3
---|---|---|---
$T_{\mathrm{eff}}$ (K) | - | $3130\pm 75$ | $3159\pm 40$
$[\mbox{Fe}/\mbox{H}]$ (dex) | - | $0.2\pm 0.3$ | $0.232^{+0.035}_{-0.038}$
$M_{\star}$ ($M_{\odot}$) | $0.255\pm 0.0066$ | $0.279\pm 0.014$ | $0.276^{+0.006}_{-0.005}$
$R_{\star}$ ($R_{\odot}$) | $0.2775\pm 0.0080$ | $0.280\pm 0.014$ | $0.291\pm 0.005$
$\log g$ (cgs) | $4.959\pm 0.026$ | $4.990\pm 0.049$ | $4.955^{+0.008}_{-0.007}$
$\rho_{\star}$ (g cm-3) | $16.8^{+1.5}_{-1.4}$ | $18.0\pm 2.9$ | $16.282^{+0.598}_{-0.617}$
distance (pc) | $65.03\pm 0.36$ | - | $65.390^{+0.540}_{-0.464}$
Luminosity ($\mathrm{L_{\odot}}$) | $0.00711^{+0.00083}_{-0.00075}$ | - | -
$\mathrm{A_{V}}$ (mag) | 0 (fixed) | 0 (fixed) |  $\sim$0†
$F_{bol}$ (cgs) | - | $5.19(18)\times 10^{-11}$ | -
$M_{K}s$ (mag) | $7.265\pm 0.026$ | - | -

##  Appendix B Contamination Analysis

Contamination leads to a decrease in the observed transit depth (the planet
appears to be smaller than it truly is), and this effect is achromatic even if
the host and the contaminant(s) are of different spectral types. Having
simultaneous multicolor photometry allows us to measure possible contamination
and consequently provides strong constraints on the false positive scenarios
discussed in Section 3.6.

Following the methods presented in Parviainen et al. (2020, 2021), we used the
physics-based contamination model included in PyTransit v21 to model the light
curves using a transit model that includes a light contamination component
based on model stellar spectra leveraging multicolor photometry. Fitting the
transit+contamination model to MuSCAT3 lightcurves allows us to measure the
contamination in $i$-band191919We adopt $i$ as reference passband for
simplicity, the effective temperature of the host ($T_{\mathrm{eff,H}}$), and
the effective temperature of the contaminant ($T_{\mathrm{eff,C}}$).

We used normal priors for the period and $\rm{T_{0}}$ based on the results of
our transit analysis. We also used normal priors on limb darkening, host
effective temperature, and host star density, based on our spectroscopic
analysis. Among them, the spectroscopic priors are the most important. Without
a limb darkening prior, the transit fit in $g$-band is boxy perhaps due to the
sparse data sampling. Without the $T_{\mathrm{eff,H}}$ prior, the posteriors
are not well behaved. Without the host $\rho_{\star}$ prior, the model
converges to very high values ($\sim$33g cm-3) which is inconsistent with the
results from our previous analyses.

The joint and marginal posteriors of the relevant parameters are shown in
Figure B.1. Significant levels of blending from sources with effective
temperature different from that of the host star are excluded, and also the
blending from sources with $T_{\mathrm{eff,C}}$ $\sim$ $T_{\mathrm{eff,H}}$
are strongly constrained.

Figure B.1: Joint and marginal posteriors for the key parameters from the
transit+contamination modelling of the MuSCAT3 multicolor light curves.
Contamination due to sources with significantly different effective
temperature than the host is ruled out.

##  Appendix C HEB simulation

We assumed that each system was composed of the primary star (TOI-1696, Star
1), plus a tertiary companion (Star 3) eclipsing a secondary companion (Star
2) every $2.5$ d. For a grid of secondary and tertiary star masses ranging
from 0.1 to 0.4$M_{\odot}$, we then calculated the observed maximum eclipse
depth caused by Star 3 eclipsing Star 2 in MuSCAT3 $g$\- and $z$-bands using
the following procedure. First, we interpolated $L_{\star}$ and
$T_{\mathrm{eff}}$ of Star 2 and Star 3 from MIST isochrones given their
masses, and the age, metallicity, and mass of Star 1 in Table 1. We then
computed the blackbody function of each star given their $T_{\mathrm{eff}}$
then convolved it with the transmission functions for each band downloaded
from the SVO filter profile service202020http://svo2.cab.inta-
csic.es/theory/fps/. We then integrated the result using the trapezoidal
method and computed the bolometric flux $F_{\rm{bol}}$, using the integrated
functions above. Using Stefan-Boltzmann law and given $T_{\mathrm{eff}}$ and
$L_{\star}$, we computed the component radii and luminosities to derive the
eclipse depth.

Figure C.2 shows the HEB configurations that produce eclipse depths in $g$\-
(blue) and $z$-bands (red) that are consistent with the observed depth for two
given impact parameters. The lower impact parameter corresponds to the
3-$\sigma$ lower limit derived from our contamination analysis while the other
impact parameter corresponds to the median value derived in our transit
analysis. We confirm that indeed eclipses of an HEB are always deeper in the
red than in the blue bands (i.e higher $m_{2}$/$m_{1}$ in $z$\- than $g$-band)
since the eclipsing companions are usually redder than the central star. The
important point here is that the HEB configurations that produce eclipses
consistent with our observation do not overlap within 1-$\sigma$ in $g$\- and
$z$-bands for any reasonable impact parameters. Note also that our
contamination analysis constrained possible contaminants to have the same
colour as the host star, so only masses very close to TOI-1696 (vertical
dashed line in Figure C.2) are allowed. Thus, we can rule out the HEB false
positive scenario.

Figure C.2: HEB mass configurations which produce eclipse depths in $g$-band
(blue) and $z$-band (red) consistent with the observed depths (indicated in
the upper left corner of the first panel). The left panel corresponds to the
lower limit of the impact parameter and the right for the median value. The
colored solid line and dashed lines correspond to confidence regions that are
consistent with the observed depths within 1- and 2-$\sigma$, respectively.
The vertical black line corresponds to the mass of the central star (i.e.
TOI-1696). The fact that the red and blue regions do not overlap within
1-$\sigma$ taking into account impact parameter rules out the HEB false
positive scenario.

##  Appendix D Validation with Vespa and Triceratops

Vespa 212121https://github.com/timothydmorton/VESPA was originally developed
as a tool for statistical validation of planet candidates identified by the
Kepler mission (e.g. Morton et al., 2016), but has also been used extensively
to validate planets from subsequent missions, such as K2 (e.g. Livingston et
al., 2018; de Leon et al., 2021). Vespa compares the likelihood of a planetary
scenario to the likelihoods of several astrophysical false positive scenarios
involving eclipsing binaries (EBs), hierarchical triple systems (HEBs),
background eclipsing binaries (BEBs), and the double-period cases of all these
scenarios. The likelihoods and priors for each scenario are based on the shape
of the transit signal, the star’s location in the Galaxy, and single-,
binary-, and triple-star model fits to the observed photometric and
spectroscopic properties of the star generated using isochrones. We used the
MuSCAT3 lightcurve because of its high SNR and low levels of limb darkening,
which provides the best constraint on the transit shape. We also used the
Gemini and Palomar contrast curves described in Section 2.6, a maximum
aperture radius of maxrad =3″(interior to which the transit signal must be
produced), and ran the simulation using a population size of n=$10^{6}$,
resulting to a formal FPP$<1\times 10^{-6}$.

We also used Triceratops 222222https://github.com/stevengiacalone/triceratops
which is a tool developed to validate TOIs (Giacalone & Dressing, 2020;
Giacalone et al., 2021) by calculating the Bayesian probabilities of the
observed transit originating from several scenarios involving the target star,
nearby resolved stars, and hypothetical unresolved stars in the immediate
vicinity of the target. These probabilities were then compared to calculate a
false positive probability (FPP; the total probability of the transit
originating from something other than a planet around the target star) and a
nearby false positive probability (NFPP; the total probability of the transit
originating from a nearby resolved star). Given our follow-up photometry rules
out nearby stars as a potential source of the transit signal, we eliminate all
stars except the target in the Triceratops analysis. As an additional
constraint, we use the contrast curve from our follow-up speckle imaging as a
direct input in Triceratops. For the sake of reliability, we performed the
calculation 20 times for the planet candidate and found FPP=0.0020. The low
FPPs calculated using Vespa and Triceratops are small enough to statistically
validate TOI-1696.01 as a planet.

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