11institutetext:  Observatoire de Genève, Université de Genève, 51 Ch. des
Maillettes, 1290 Sauverny, Switzerland 22institutetext: Harvard University,
Cambridge, MA 02138 33institutetext: Center for Astrophysics, Harvard &
Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA 44institutetext:
Department of Physics and Astronomy, University of New Mexico, 210 Yale Blvd
NE, Albuquerque, NM 87106, USA 55institutetext: Department of Physics and
Kavli Institute for Astrophysics and Space Research, Massachusetts Institute
of Technology, Cambridge, MA 02139, USA 66institutetext: Department of
Astronomy, Wellesley College, Wellesley, MA 02481, USA 77institutetext:
Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal las
Torres 2640, Peñalolén, Santiago, Chile 88institutetext: Millennium Institute
for Astrophysics, Chile 99institutetext: Vanderbilt University, Department of
Physics & Astronomy, 6301 Stevenson Center Lane, Nashville, TN 37235, USA
1010institutetext: Department of Physics, University of Warwick, Gibbet Hill
Road, Coventry, CV4 7AL, UK 1111institutetext: Centre for Exoplanets and
Habitability, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK
1212institutetext: Department of Astrophysical Sciences, Princeton University,
4 Ivy Lane, Princeton, NJ 08540, USA 1313institutetext: Université Côte
d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de
l’Observatoire, CS 34229, 06304 Nice cedex 4, France 1414institutetext:
University of Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France
1515institutetext: School of Physics and Astronomy, University of Leicester,
LE1 7RH, UK 1616institutetext: NASA Ames Research Center, Moffett Field, CA
94035, USA 1717institutetext: Max-Planck-Institut für Astronomie, Königstuhl
17, 69117 Heidelberg, Germany 1818institutetext: Institute for Advanced Study,
Princeton, NJ 08540 George Mason University, 4400 University Drive, Fairfax,
VA, 22030 USA 1919institutetext: NASA Goddard Space Flight Center, Exoplanets
and Stellar Astrophysics Laboratory (Code 667), Greenbelt, MD 20771, USA
2020institutetext: European Space Agency (ESA), European Space Research and
Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
2121institutetext: School of Physics & Astronomy, University of Birmingham,
Edgbaston, Birmingham B15 2TT, United Kingdom 2222institutetext: El Sauce
Observatory, Coquimbo Province, Chile 2323institutetext: Centre for
Astrophysics, University of Southern Queensland, Toowoomba, QLD, 4350,
Australia 2424institutetext: Dept. of Physics & Astronomy, Swarthmore College,
Swarthmore PA 19081, USA 2525institutetext: Department of Physics and
Astronomy, University of Louisville, Louisville, KY 40292, USA
2626institutetext: Concordia Station, IPEV/PNRA, Antarctica 2727institutetext:
Ellinbank Observatory, Australia 2828institutetext: Brierfield Observatory,
New South Wales, Australia 2929institutetext: Space Telescope Science
Institute, 3700 San Martin Drive, Baltimore, MD, 21218, USA 3030institutetext:
Royal Astronomical Society, Burlington House, Piccadilly, London W1J 0BQ, UK
3131institutetext: Patashnick Voorheesville Observatory, Voorheesville, NY
12186, USA 3232institutetext: SETI Institute, Mountain View, CA 94043, USA
3333institutetext: Hazelwood Observatory, Australia 3434institutetext: Perth
Exoplanet Survey Telescope, Perth, Western Australia 3535institutetext:
Department of Astrophysical and Planetary Sciences, University of Colorado,
Boulder, CO 80309, USA 3636institutetext: Mt. Stuart Observatory, New Zealand

# Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limit

Nolan Grieves , Populating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limitPopulating the
brown dwarf and stellar boundary: Five stars with transiting companions near
the hydrogen-burning mass limit<EMAIL_ADDRESS>François Bouchy
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Monika Lendl Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Theron Carmichael
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limitPopulating the
brown dwarf and stellar boundary: Five stars with transiting companions near
the hydrogen-burning mass limit Ismael Mireles Populating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limit Avi Shporer
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Kim K. McLeod Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Karen A. Collins
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Rafael Brahm Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limitPopulating the brown
dwarf and stellar boundary: Five stars with transiting companions near the
hydrogen-burning mass limitPopulating the brown dwarf and stellar boundary:
Five stars with transiting companions near the hydrogen-burning mass limit
Keivan G. Stassun Populating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limitPopulating the
brown dwarf and stellar boundary: Five stars with transiting companions near
the hydrogen-burning mass limit Sam Gill Populating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limitPopulating the
brown dwarf and stellar boundary: Five stars with transiting companions near
the hydrogen-burning mass limitPopulating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limit Luke G. Bouma Populating the brown dwarf and stellar boundary: Five
stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Tristan Guillot
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Marion Cointepas Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limitPopulating the brown
dwarf and stellar boundary: Five stars with transiting companions near the
hydrogen-burning mass limitPopulating the brown dwarf and stellar boundary:
Five stars with transiting companions near the hydrogen-burning mass limit
Leonardo A. Dos Santos Populating the brown dwarf and stellar boundary: Five
stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Sarah L. Casewell
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Jon M. Jenkins Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Thomas Henning
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Louise D. Nielsen Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Angelica Psaridi
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Stéphane Udry Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Damien Ségransan
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Jason D. Eastman Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit George Zhou
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Lyu Abe Populating the brown dwarf and stellar boundary:
Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Abelkrim Agabi
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Gaspar Bakos Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limitPopulating the brown
dwarf and stellar boundary: Five stars with transiting companions near the
hydrogen-burning mass limitPopulating the brown dwarf and stellar boundary:
Five stars with transiting companions near the hydrogen-burning mass limit
David Charbonneau Populating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limitPopulating the
brown dwarf and stellar boundary: Five stars with transiting companions near
the hydrogen-burning mass limit Kevin I. Collins Populating the brown dwarf
and stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limit Knicole D.
Colon Populating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limitPopulating the brown
dwarf and stellar boundary: Five stars with transiting companions near the
hydrogen-burning mass limit Nicolas Crouzet Populating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limit Georgina
Dransfield Populating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limitPopulating the brown
dwarf and stellar boundary: Five stars with transiting companions near the
hydrogen-burning mass limit Phil Evans Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Robert F. Goeke
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Rhodes Hart Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Jonathan M. Irwin
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Eric L.N. Jensen Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Andrés Jordán
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limitPopulating the
brown dwarf and stellar boundary: Five stars with transiting companions near
the hydrogen-burning mass limit John F. Kielkopf Populating the brown dwarf
and stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limit David W.
Latham Populating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limitPopulating the brown
dwarf and stellar boundary: Five stars with transiting companions near the
hydrogen-burning mass limit Wenceslas Marie-Sainte Populating the brown dwarf
and stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limit Djamel
Mékarnia Populating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limitPopulating the brown
dwarf and stellar boundary: Five stars with transiting companions near the
hydrogen-burning mass limit Peter Nelson Populating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limit Samuel N.
Quinn Populating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limitPopulating the brown
dwarf and stellar boundary: Five stars with transiting companions near the
hydrogen-burning mass limit Don J. Radford Populating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limit David R.
Rodriguez Populating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limitPopulating the brown
dwarf and stellar boundary: Five stars with transiting companions near the
hydrogen-burning mass limit Pamela Rowden Populating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limit
François–Xavier Schmider Populating the brown dwarf and stellar boundary: Five
stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit Richard P. Schwarz
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Jeffrey C. Smith Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limitPopulating the brown
dwarf and stellar boundary: Five stars with transiting companions near the
hydrogen-burning mass limitPopulating the brown dwarf and stellar boundary:
Five stars with transiting companions near the hydrogen-burning mass limit
Chris Stockdale Populating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limitPopulating the
brown dwarf and stellar boundary: Five stars with transiting companions near
the hydrogen-burning mass limit Olga Suarez Populating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limitPopulating the brown dwarf and stellar boundary: Five stars
with transiting companions near the hydrogen-burning mass limit Thiam-Guan Tan
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Amaury H.M.J. Triaud Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit William Waalkes
Populating the brown dwarf and stellar boundary: Five stars with transiting
companions near the hydrogen-burning mass limitPopulating the brown dwarf and
stellar boundary: Five stars with transiting companions near the hydrogen-
burning mass limit Geof Wingham Populating the brown dwarf and stellar
boundary: Five stars with transiting companions near the hydrogen-burning mass
limitPopulating the brown dwarf and stellar boundary: Five stars with
transiting companions near the hydrogen-burning mass limit

(Received XX; accepted XX)

We report the discovery of five transiting companions near the hydrogen-
burning mass limit in close orbits around main sequence stars originally
identified by the Transiting Exoplanet Survey Satellite (TESS) as TESS Objects
of Interest (TOIs): TOI-148, TOI-587, TOI-681, TOI-746, and TOI-1213. Using
TESS and ground-based photometry as well as radial velocities from the
CORALIE, CHIRON, TRES, and FEROS spectrographs, we found the companions have
orbital periods between 4.8 and 27.2 days, masses between 77 and 98
$\mathrm{M_{\rm Jup}}$, and radii between 0.81 and 1.66 $\mathrm{R_{\rm
Jup}}$. These targets have masses near the uncertain lower limit of hydrogen
core fusion ($\sim$73-96 $\mathrm{M_{\rm Jup}}$), which separates brown dwarfs
and low-mass stars. We constrained young ages for TOI-587 (0.2 $\pm$ 0.1 Gyr)
and TOI-681 (0.17 $\pm$ 0.03 Gyr) and found them to have relatively larger
radii compared to other transiting companions of a similar mass. Conversely we
estimated older ages for TOI-148 and TOI-746 and found them to have relatively
smaller companion radii. With an effective temperature of 9800 $\pm$ 200 K,
TOI-587 is the hottest known main-sequence star to host a transiting brown
dwarf or very low-mass star. We found evidence of spin-orbit synchronization
for TOI-148 and TOI-746 as well as tidal circularization for TOI-148. These
companions add to the population of brown dwarfs and very low-mass stars with
well measured parameters ideal to test formation models of these rare objects,
the origin of the brown dwarf desert, and the distinction between brown dwarfs
and hydrogen-burning main sequence stars.

###### Key Words.:

Stars: low-mass, brown dwarfs; binaries: eclipsing

##  1 Introduction

Brown dwarfs are objects with masses in between giant planets and low-mass
stars. They are often defined with a lower limit of $\sim$13 $\mathrm{M_{\rm
Jup}}$, the approximate mass at which an object can begin to ignite deuterium
fusion in its core, and with an upper limit of $\sim$80 $\mathrm{M_{\rm
Jup}}$, the approximate mass at which an object becomes sufficiently massive
to fuse hydrogen nuclei into helium nuclei within its core: the principal
characteristic of a main-sequence star. However, these boundaries are not
clear-cut as the exact masses where deuterium and hydrogen fusion occur depend
on the chemical composition of the object (e.g., Baraffe et al., 2002; Spiegel
et al., 2011; Dieterich et al., 2014). A defining characteristic of brown
dwarfs is their relative low occurrence rate ($\lessapprox$1%) in close orbits
($\lessapprox$5 AU) around main-sequence stars compared to giant planets and
other stars, or the ’brown dwarf desert’ (e.g., Marcy & Butler, 2000; Grether
& Lineweaver, 2006; Sahlmann et al., 2011; Santerne et al., 2016; Grieves et
al., 2017), with recent studies finding a dry desert for periods $<$ 100 days
(e.g., Kiefer et al., 2019, 2021).

The relative lack of brown dwarf companions may be related to a transition of
the formation mechanisms required to form giant planets and low-mass stars. In
this case, lower mass brown dwarfs may form similar to giant planets via core
accretion (Pollack et al., 1996) or disk instability (Cameron, 1978; Boss,
1997) and higher mass brown dwarfs may form similar to stars from
gravitational collapse and turbulent fragmentation of molecular clouds (Padoan
& Nordlund, 2004; Hennebelle & Chabrier, 2008). The boundary of these
formation mechanisms is unclear and certainly depends on an object’s initial
environment.

Using a statistical study of 62 brown dwarfs Ma & Ge (2014) found the “driest”
part of the desert in the mass range 35 $\mathrm{M_{\rm Jup}}$ $<$ $M_{b}$ sin
$i$ $<$ 55 $\mathrm{M_{\rm Jup}}$ with periods less than 100 days. Ma & Ge
(2014) also suggest 42.5 $\mathrm{M_{\rm Jup}}$ may represent a transition
between brown dwarfs that formed more similar to giant planets and those that
formed more similar to main-sequence stars, as they found that brown dwarfs
with masses above 42.5 $\mathrm{M_{\rm Jup}}$ have an eccentricity
distribution more consistent with binaries. However, Ma & Ge (2014) were
limited by a small sample size and more brown dwarfs have been found even in
the driest part of the desert (e.g., Persson et al., 2019; Carmichael et al.,
2019). Other studies have also suggested two separate populations for lower
and higher mass brown dwarfs based on metallicity and eccentricity
distributions (e.g., Maldonado & Villaver, 2017; Kiefer et al., 2021).
Conversely, some studies have suggested a more continuous formation between
giant planets and low-mass stars where giant planets range from 0.3 - 60 or 73
$\mathrm{M_{\rm Jup}}$ based on a continuum of their mass-density relation
(Hatzes & Rauer, 2015; Persson et al., 2019). While Whitworth (2018) argues
brown dwarfs should not be distinguished from hydrogen-burning stars as they
have more similarities to stars than planets.

Figure 1: TOI-148 light curves (top) and RVs (bottom) phased to the
companion’s orbital period. The red lines in the upper plot show the best-fit
transit model to each photometry data set from our EXOFASTv2 analysis
described in Section 3.4.1. In the lower plot the red line shows the best-fit
Keplerian model to the RVs from our EXOFASTv2 analysis.

Figure 2: TOI-587 light curves (top) and RVs (bottom) phased to the
companion’s orbital period. The red lines display our best-fit models from
EXOFASTv2 as described in Figure 1.

Individual well-characterized brown dwarfs and very low-mass stars provide
crucial insight into these possible formation scenarios. Particularly
transiting brown dwarfs whose radii can be precisely determined allowing for a
better interpretation of models, unlike brown dwarfs detected via radial
velocities only, whose upper mass limits are not clearly defined and may
actually be low-mass stars (e.g., Kiefer et al., 2021). Space-based
photometric missions are ideal to find these rare objects given their robust
photometric precision and long uninterrupted observations, and recent missions
such as $Kepler$ (Borucki et al., 2010) and $K2$ (Howell et al., 2014) have
led to successful follow-up mass measurements of transiting brown dwarfs
(e.g., Bayliss et al., 2017; Cañas et al., 2018; Carmichael et al., 2019;
Persson et al., 2019). The currently operating space-based all-sky Transiting
Exoplanet Survey Satellite (TESS; Ricker et al., 2015) has continued to
populate the sparse desert with well-characterized brown dwarfs and very low-
mass stars (e.g., Šubjak et al., 2020; Carmichael et al., 2020, 2021; Mireles
et al., 2020).

We report the discovery of five transiting companions with masses close to the
upper boundary of the brown dwarf regime that were each first identified as
TESS Objects of Interests (TOIs): TOI-148, TOI-587, TOI-681, TOI-746, and
TOI-1213. Each object has robust photometric and spectroscopic measurements
allowing precisely determined characteristics, and given their close proximity
to the hydrogen-burning limit they are ideal to test current formation models
and comparisons between brown dwarfs and low-mass stars. In Section 2 we
describe our photometry, spectroscopy, and imaging observations. In Section 3
we detail our analysis of the systems including the host stars and their
companions. In Section 4 we discuss our results and in Section 5 we give our
conclusions.

##  2 Observations

Figure 3: TOI-681 light curves (top) and RVs (bottom) phased to the
companion’s orbital period. The red lines display our best-fit models from
EXOFASTv2 as described in Figure 1.

Figure 4: TOI-746 light curves (top) and RVs (bottom) phased to the
companion’s orbital period. The red lines display our best-fit models from
EXOFASTv2 as described in Figure 1.

Figure 5: TOI-1213 light curves (top) and RVs (bottom) phased to the
companion’s orbital period. The red lines display our best-fit models from
EXOFASTv2 as described in Figure 1.

Figure 6: SOAR/HRCam speckle interferometry imaging with I-band
autocorrelation functions (Ziegler et al., 2020) for TOI-148 (TIC 393940766;
top left), TOI-587 (TIC 294090620; top right), TOI-681 (TIC 410450228; middle
left), TOI 746 (TIC 167418903; middle right), and TOI 1213 (TIC 399144800;
bottom). The 5$\sigma$ contrast curves with a linear fit are shown with black
solid lines. The auto-correlation functions obtained in I-band are shown
within the contrast curve plots.

###  2.1 TESS photometry

In this section we describe the TESS observations for each star. We refer the
reader to tables 6 \- 10 for the stellar parameters and properties of each
star. We display phased TESS photometry for all five of our stars with
transiting companions as well as transit observations from all available
ground-based photometry, described in Section 2.2, in Figures 1 \- 5. We
obtained TESS photometry from exomast111https://exo.mast.stsci.edu, which is
part of the Barbara A. Mikulski Archive for Space Telescopes (MAST)
astronomical data archive hosted by the Space Telescope Science Institute.

TOI-148 (TIC 393940766) was observed by TESS in Sector 1 (UT 2018 July 25 to
UT 2018 August 22) and the light curve was derived from Full Frame Image (FFI)
observations with a cadence of 30 minutes and processed by the Quick Look
Pipeline (QLP; Huang et al., 2020a, b). QLP transits were identified with a
high signal to noise ratio every 4.87 days for a total of six transits
detected in the QLP data. TOI-148 was observed again by TESS in Sector 28 (UT
2020 July 31 to UT 2020 August 25) with 2-minute cadence exposures. The
2-minute data were processed by the Science Processing Operations Center
(SPOC; Jenkins et al., 2016) pipeline which produces two light curves per
sector called Simple Aperture Photometry (SAP) and Presearch Data Conditioning
Simple Aperture Photometry (PDCSAP; Smith et al., 2012; Stumpe et al., 2012,
2014). We use the PDCSAP light curves for our analysis. The SPOC pipeline
detected the transit signatures in the transit search pipeline (Jenkins, 2002;
Jenkins et al., 2010) and these transit signatures were fit to a limb-darkened
transit model (Li et al., 2019). The transit fits passed all of the data
validation module’s diagnostic tests (Twicken et al., 2018), including the
difference image centroiding test, which localized the source of the transit
signal to within 1.23 $\pm$ 2.6 arcsec. This difference image centroiding test
complements the speckle interferometry results in Section 2.4. A total of four
transits were detected in the 2-minute cadence data; we note a $\sim$5 day gap
in the middle of the TESS Sector 28 data. No secondary transit or eclipse was
detected above 3.3$\sigma$ (426 ppm), and no additional transit signals were
detected in the multiplanet transit search.

TOI-587 (TIC 294090620) was observed in TESS Sector 8 (UT 2019 February 2 to
UT 2019 February 28) with FFI observations. Two transits with a depth of
$\sim$0.5% were identified in the QLP processed light curve with a separation
8.0 days.

TOI-681 (TIC 410450228) was observed in TESS Sectors 8 (UT 2019 February 2 -
27), 9 (UT 2019 February 28 to UT 2019 March 26), 27 (UT 2020 July 5 - 30),
and 31 (UT 2020 October 22 to UT 2020 November 18) with 2-minute cadence
exposures. The 2-minute data were processed by SPOC which identified two 1%
deep transits 15.8 days apart. TOI-681 was also observed with FFI observations
in Sectors 1 (UT 2018 July 25 to UT 2018 August 22), 4 (UT 2018 October 19 to
UT 2018 November 15), 5 (UT 2018 November 15 to UT 2018 December 11), 7 (UT
2019 January 7 to UT 2019 February 1), 10 (UT 2019 March 26 to UT 2019 April
21), and 11 (UT 2019 April 22 to UT 2019 May 20). The transit signature passed
all the data validation diagnostic tests and was localized to within 0.726
$\pm$ 2.5 arcsec in the multisector 8 and 9 search. No statistically weak
secondary was detected above the 3.3 sigma (426 ppm) level, and no further
transiting planet signatures were detected in the multiplanet search. This
star was also observed in sector 27 but only one transit was observed. It was
re-observed in sector 31, passed all the data validation diagnostic tests,
including the difference image centroiding that localized the source to within
0.958 $\pm$ 2.5 arcsec, and no statistically significant weak secondaries were
detected above the 2.8$\sigma$ (629 ppm) level.

TOI-746 (TIC 167418903) was observed by TESS in Sectors 1-13 (UT 2018 July 25
to UT 2019 July 17) with FFI observations as well as 2-minute cadence
exposures in Sectors 11 - 13 (UT 2019 May 21 to UT 2019 July 17) and 28 - 33
(UT 2020 July 31 to UT 2021 January 13). The FFI observations of all sectors
were processed by the QLP and the 2-minute data were processed with the SPOC
pipeline, both showing a transit-like event occurring every 10.98 days. We
detected 17 transits in the FFI data and 11 transits in the 2-minute data.

Telescope | Location | Date | Filter | Aperture radius | Coverage
---|---|---|---|---|---
|  | [UTC] |  | [arcsec] |
TOI 148.01 (TIC 393940766) |  |  |  |  |
LCO-SAAO 1m | South Africa | 2020-06-07 | $i^{\prime}$ | 4.7 | ingress
LCO-SSO 1m | Australia | 2020-06-27 | $i^{\prime}$ | 5.1 | ingress
LCO-SSO 1m | Australia | 2020-07-02 | $i^{\prime}$ | 4.7 | egress
El-Sauce 0.36m | Chile | 2020-07-12 | $R_{c}$ | 5.9 | full
LCO-SAAO 1m | South Africa | 2020-07-21 | $i^{\prime}$ | 4.3 | full
TOI 681.01 (TIC 410450228) |  |  |  |  |
Brierfield 0.36m | Australia | 2019-10-26 | I | 10.3 | full
CHAT 0.7m | Chile | 2019-11-26 | $i^{\prime}$ | 8.4 | egress
El Sauce 0.36m | Chile | 2019-11-27 | B | 7.4 | full
Mt. Stuart 0.32m | New Zealand | 2020-04-01 | $g^{\prime}$ | 4.4 | full
ASTEP 0.4m | Antarctica | 2020-06-19 | $R_{c}$ | 10.2 | full
TOI 746.01 (TIC 167418903) |  |  |  |  |
LCO-SAAO 1m | South Africa | 2019-02-18 | $z^{\prime}$ | 6.2 | ingress
LCO-SAAO 1m | South Africa | 2019-03-01 | $u^{\prime}$ | 5.9 | full
LCO-SAAO 1m | South Africa | 2019-04-25 | $z^{\prime}$ | 5.9 | ingress
PEST 0.31m | Australia | 2020-10-25 | V | 7.4 | full
TOI 1213.01 (TIC 399144800) |  |  |  |  |
MEarth-S 0.4m | Chile | 2020-02-23 | RG715 | 5.0 | full
ASTEP 0.4m | Antarctica | 2020-08-04 | $R_{c}$ | 10.2 | full

  * •

Observatory acronyms: ASTEP–Antarctic Search for Transiting ExoPlanets;
CHAT–Chilean-Hungarian Automated Telescope; LCO–Las Cumbres Observatory;
PEST–Perth Exoplanet Survey Telescope

Table 1: Summary of Ground-based Photometric Follow-up Observations.

TOI-1213 (TIC 399144800) was observed by TESS in Sectors 10 and 11 (UT 2019
March 26 to UT 2019 May 21) with 2-minute cadence exposures. The 2-minute data
was processed by the SPOC pipeline, which showed one transit-like event in
each sector, spaced 27.214 days apart. The multisector data validation report
for sectors 10 and 11 indicated that the transit signature passed all the DV
diagnostic tests, localized the source to within 3.8 $\pm$ 2.1 arcsec, and
detected no weak secondaries above 3.1$\sigma$ (435 ppm), and no additional
transiting planet signatures were found.

###  2.2 Ground-based photometric follow-up

We acquired ground-based time-series photometry of TOI-148, TOI-681, TOI-746,
and TOI-1213 as part of the TESS Follow-up Observing Program
(TFOP)222https://tess.mit.edu/followup. The TFOP’s Sub Group 1 (SG1; seeing-
limited photometry) group includes observers at more than a hundred telescopes
distributed around the world. TFOP SG1 partners choose targets to follow up
using the TESS Transit Finder, which is a customized version of the Tapir
software package (Jensen, 2013). Photometric data are extracted by each
observer most often using the AstroImageJ (AIJ) software package (Collins et
al., 2017). Data and analysis notes are uploaded to the ExoFOP-
TESS333https://exofop.ipac.caltech.edu/tess/ repository and submitted to the
SG1 team for validation.

In the case of the objects described here, we used the observations to rule
out nearby eclipsing binaries as sources of the TESS signal, confirm the
events on target, determine the TESS photometric deblending factors for each
field, place constraints on transit depth differences across optical filter
bands, and refine the TESS ephemerides by extending the time baselines. We
summarize the observations that resulted in data useful for fitting in Table 1
and we plot the resulting light curves in Figures 1, 3, 4, and 5.

The optimal photometric aperture radii used to extract light curves for these
targets depends on the combination of pixel size, seeing disk size, focus
(some observations are intentionally defocused to avoid saturation in the case
of very bright targets), and the presence of on-sky neighbors visible in the
images. We checked the apertures listed in Table 1 against the Gaia DR2
catalog to determine the extent to which they might be contaminated by other
stars. In the case of TOI-681, there is a Gaia neighbor 7” away, and so inside
most of the apertures used; however, at 6.4 magnitudes fainter than the
target, the contribution is negligible within the photometric precision.
Similarly, in the case of TOI-746, there is a possible Gaia blend at a
separation of 6 arcsec, just at the edge of the apertures used, but at 8.8
magnitudes fainter it is insignificant. We describe checks for smaller-
separation neighbors in Section 2.4.

###  2.3 Spectroscopic follow-up and radial velocities

Star | $T_{\rm eff}$ | $\left[{\rm Fe}/{\rm H}\right]$ | $\log g_{*}$ | $v\sin i_{*}$ | Source
---|---|---|---|---|---
| [K] | dex | [cgs] | [km-1] |
TOI-148 | 5836 $\pm$ 286 | -0.28 $\pm$ 0.28 | 4.11 $\pm$ 0.37 | 10.1 $\pm$ 0.8 | CORALIE
TOI-587 | 10400 $\pm$ 300 | 0.07 $\pm$ 0.12 | 4.20 $\pm$ 0.30 | 34.0 $\pm$ 2.0 | TRES
TOI-681 | 7297 $\pm$ 45 | -0.12 $\pm$ 0.05 | 4.32 $\pm$ 0.14 | 30.8 $\pm$ 0.8 | GALAH DR2
TOI-746 | 5593 $\pm$ 215 | 0.01 $\pm$ 0.29 | 4.30 $\pm$ 0.29 | 6.1 $\pm$ 1.2 | CORALIE
TOI-1213 | 5430 $\pm$ 215 | 0.28 $\pm$ 0.16 | 4.47 $\pm$ 0.26 | 4.0 $\pm$ 1.2 | CORALIE

  * •

TOI-148, TOI-746, and TOI-1213 parameters were obtained from CORALIE spectra
by combining the analysis results of both SpecMatch-Emp (Yee et al., 2017) and
with an iSpec (Blanco-Cuaresma et al., 2014) analysis. The high temperature of
TOI-587 precluded using SpecMatch-Emp and iSpec analysis and we use a separate
analysis described in Section 3.1 on the TRES spectra. For TOI-681 we use
GALAH DR2 results (Buder et al., 2018).

Table 2: Table of stellar parameters derived from spectra. We refer the reader
to the final adopted parameters for each star presented in tables 6 \- 10.

We obtained spectra and radial velocities of the five stars using observations
from the 1.5 m SMARTS/CHIRON, Euler 1.2 m/CORALIE, MPG/ESO 2.2 m/FEROS, and
1.5 m SAO Tillinghast/TRES facilities. We summarize the radial velocity (RV)
measurements of each star in Table 5 and each star’s phased radial velocities
with their best Keplerian fits (see Section 3) are displayed in Figures 1 \-
5.

For TOI-148, TOI-681, TOI-746, and TOI-1213, we obtained RVs with the high
resolution CORALIE spectrograph on the Swiss 1.2 m Euler telescope at La Silla
Observatory, Chile (Queloz et al., 2001). CORALIE has a resolution of $R$
$\sim$ 60,000 and is fed by two fibers: a 2 arcsec on-sky science fiber
encompassing the star and another fiber that can either connect to a Fabry-
Pérot etalon for simultaneous wavelength calibration or on-sky for background
subtraction of sky flux. We observed all four stars in the simultaneous Fabry-
Pérot wavelength calibration mode. The spectra were reduced with the CORALIE
standard reduction pipeline and RVs were computed for each epoch by cross-
correlating with a binary G2 mask (Pepe et al., 2002).

We obtained 11 CORALIE observations for TOI-148 from UT 2018 September 23 to
UT 2019 July 15. Nine CORALIE observations of TOI-681 were obtained from UT
2019 May 19 to UT 2020 March 15. We obtained eight CORALIE observations for
TOI-746 from UT 2019 October 21 to UT 2020 March 12. TOI-1213 was observed
four times with CORALIE from UT 2020 February 4 to UT 2020 March 17.

We used the TRES instrument on Mt. Hopkins, Arizona to obtain reconnaissance
spectra for TOI-587. TRES has a resolving power of $R\sim 44\,000$ and covers
a wavelength range of 390 to 910 nm. We use multiple echelle orders for each
spectrum to measure a relative RV at each phase in the orbit of the transiting
companion. We visually review each individual order to omit those with low
signal-to-noise per resolution element (S/N) and we remove obvious cosmic
rays. Each order is cross-correlated with the highest S/N spectrum of the star
and then the average RV of all the orders per spectrum is taken as the RV of
the star at a given orbital phase. The spectra of TOI-587 were taken between
UT 2019 April 16 and UT 2019 April 30 with exposure times of 150 s and 360 s,
giving a signal-to-noise per resolution element between 66 and 117.

Figure 7: Spectral energy distributions for TOI-148 (top left), TOI-587 (top
right), TOI-681 (middle left), TOI-746 (middle right), TOI-1213 (bottom). Red
symbols represent the observed photometric measurements, where the horizontal
bars represent the effective width of the bandpass. Blue symbols are the model
fluxes from the best-fit Kurucz atmosphere model (black).

TOI-618, TOI-746, and TOI-1213 were monitored with the FEROS spectrograph
(Kaufer et al., 1999) mounted on the MPG 2.2m telescope in the ESO La Silla
Observatory. These observations were performed between June of 2019 and March
of 2020 in the context of the Warm gIaNts with tEss (WINE) collaboration which
focuses in the discovery and orbital characterization of transiting planets
with period longer than $\approx$ 10 days (e.g., Jordán et al., 2020; Brahm et
al., 2020; Schlecker et al., 2020).

We obtained between two and four spectra per target on different epochs in
order to determine if they presented radial velocity variations consistent to
those produced by an orbiting planetary companion. All observations were
executed with the simultaneous calibration technique, where a second fiber is
illuminated with a Thorium-Argon lamp to trace instrumental velocity drifts
during the exposure. The exposure times adopted were 400 s, 1200 s, and 900s ,
for TOI-618, TOI-746, and TOI-1213, respectively. The FEROS data were
processed from raw images to precision radial velocities with the ceres
pipeline (Brahm et al., 2017). We used a G2-type binary mask as a template to
compute the radial velocities through the cross-correlation technique. We also
obtained line bisector span measurements from the cross-correlation function.
These observations showed that these three systems were presenting radial
velocity variations with amplitudes larger than those produced by planet mass
companions, and therefore were dropped from the queue of the WINE project.

TOI-1213 was observed with the CTIO High Resolution spectrometer (CHIRON;
Tokovinin et al., 2013; Paredes, 2021), mounted on the CTIO 1.5-meter Small
and Moderate Aperture Research Telescope System (SMARTS) telescope. CHIRON is
a fiber-fed high resolution echelle spectrograph, with a resolving power of R
= 80,000 and a wavelength range of 410 nm to 870 nm. The target was observed
by CHIRON 7 times, three times between UT 2020 February 7 and UT 2020 March 9,
and four times between UT 2020 December 8 and UT 2020 December 25. Each
observation was composed of 3 x 20 minute exposures. The spectral extraction
was performed by the default CHIRON pipeline (Piskunov & Valenti, 2002), and
the RVs were derived from the CHIRON spectra by a least-squares deconvolution
technique (Zhou et al., 2020), and are listed in Table 5.

###  2.4 High-resolution imaging

We used speckle imaging from the high resolution camera (HRCam; Tokovinin,
2018) mounted on the southern astrophysical research (SOAR) 4.1 m telescope in
Cerro Pachón, Chile to verify there are no stars close to our targets that
would significantly contaminate the transit or RV signals we observe. The
relatively large $21^{\prime\prime}$ pixels of TESS can result in photometric
contamination causing astrophysical false positives such as a background or
nearby eclipsing binary stars if they fall within the same TESS image profile
as the target. Close contaminants can also lead to inaccurate estimates of the
transit depth from a diluted transit in a blended light curve.

All five targets were observed with HRCam, which uses the speckle
interferometry techniques in a visible bandpass similar to that of TESS.
Ziegler et al. (2020) provides a description of HRCam observations of TESS
targets with data reduction described in Tokovinin (2018). SOAR speckle
imaging was obtained on UT 2018 September 24 for TOI-148, UT 2019 May 18 for
both TOI-587 and TOI-681, UT 2020 January 7 for TOI-746, and UT 2019 December
12 for TOI-1213. We detect no nearby starts within $3^{\prime\prime}$ for all
five stars. We show the 5-$\sigma$ detection sensitivity and the speckle auto-
correlation function from the SOAR observations in Figure 6.

##  3 Analysis

###  3.1 Spectral analysis

We derived stellar parameters including effective temperature $T_{\rm eff}$,
surface gravity $\log g_{*}$, and metalicity $\left[{\rm Fe}/{\rm H}\right]$
using SpecMatch-Emp (Yee et al., 2017) on CORALIE spectra for TOI-148,
TOI-746, and TOI-1213. Spectra were coadded onto a common wavelength axis to
increase signal-to-noise prior to spectral analysis. SpecMatch-Emp uses a
large library of stars with well-determined parameters to match the input
spectra and derive spectral parameters. We use a spectral region that includes
the Mg I b triplet (5100 - 5400 $\AA$) to match our spectra. SpecMatch-Emp
uses $\chi^{2}$ minimisation and a weighted linear combination of the five
best matching spectra in the SpecMatch-Emp library to determine $T_{\rm eff}$,
$\log g_{*}$, and $\left[{\rm Fe}/{\rm H}\right]$.

We also determine $T_{\rm eff}$, $\log g_{*}$, and $\left[{\rm Fe}/{\rm
H}\right]$ using coadded CORALIE spectra for TOI-148, TOI-746, and TOI-1213
with the analysis package iSpec (Blanco-Cuaresma et al., 2014). We used the
synthesis method to fit individual spectral lines of the coadded spectra. For
TOI-148, TOI-746, and TOI-1213 we used the radiative transfer code SPECTRUM
(Gray & Corbally, 1994) to generate model spectra with MARCS model atmospheres
(Gustafsson et al., 2008), version 5 of the GES (GAIA ESO survey) atomic line
list provided within iSpec and solar abundances from Asplund et al. (2009).
Using the same method as Grieves et al. (2021), we combine the iSpec analysis
results and SpecMatch-Emp results for TOI-148, TOI-746, and TOI-1213. In order
to create wide uncertainties we include the entire uncertainty range of both
results that includes the lowest and highest uncertainty values of both
methods. We present these spectroscopically derived parameters in Table 2.

TOI-587 is a very hot star which is outside the range of temperatures in the
spectral library of SpecMatch-Emp. TOI-587 also falls outside the valid
temperature range for the MARCS model atmospheres and we instead use the
ATLAS9 model atmospheres Castelli & Kurucz (2004). Macroturbulence was
estimated using equation (5.10) from Doyle et al. (2014) and microturbulence
was accounted for at the synthesis stage using equation (3.1) from the same
source. The H$\alpha$, NaID and Mg I b lines were used to infer the effective
temperature $T_{\rm eff}$ and gravity $\log g_{*}$ while FeI and FeII lines
were used to determine the metallicity $\left[{\rm Fe}/{\rm H}\right]$ and the
projected rotational velocity $v\sin i_{*}$. Trial synthetic model spectra
were fit until an acceptable match to the data was found. Uncertainties were
estimated by varying individual parameters until the model spectrum was no
longer well-matched to the data.

For TOI-681 we use stellar parameters from GALAH DR2 (Buder et al., 2018)
spectroscopy as we find these parameters more robust given their higher
signal-to-noise ratio (S/N) compared to our CORALIE spectra. We do not find
GALAH DR2 data for the other stars. Our wavelet analysis (Gill et al., 2018,
2019) is also able to determine surface rotational velocity $v\sin i_{*}$ from
spectra which we apply to TOI-148, TOI-587, TOI-746, and TOI-1213 and present
in Table 2. For TOI-681 we present the $v\sin i_{*}$ from GALAH DR2. We also
examined the spectra and their cross-correlation functions (CCFs) with a
binary template (e.g., Pepe et al., 2002) when available and do not find any
evidence that the targets are double-lined spectroscopic binaries.

###  3.2 Spectral Energy Distribution analysis

Star | $\chi_{\nu}^{2}$ | $T_{\rm eff}$ | $\left[{\rm Fe}/{\rm H}\right]$ | $\log g_{*}$ | $A_{V}$ | $F_{\rm bol}$ | $R_{\star}$
---|---|---|---|---|---|---|---
|  | [K] | dex | [cgs] | mag |  $10^{-10}$ [erg s-1 cm-2] | R⊙
TOI-148 | 1.4 | 5975 $\pm$ 150 | -0.50 $\pm$ 0.25 | 4.25 $\pm$ 0.1 | 0.03 $\pm$ 0.03 | 3.405 $\pm$ 0.079 | 1.192 $\pm$ 0.068
TOI-587 | 0.9 | 9800 $\pm$ 200 | -0.10 $\pm$ 0.15 | 4.15 $\pm$ 0.15 | 0.02 $\pm$ 0.02 | 252.9 $\pm$ 5.9 | 2.031 $\pm$ 0.092
TOI-681 | 1.0 | 7390 $\pm$ 150 | -0.25 $\pm$ 0.25 | 4.20 $\pm$ 0.15 | 0.22 $\pm$ 0.02 | 12.41 $\pm$ 0.14 | 1.586 $\pm$ 0.067
TOI-746 | 1.6 | 5700 $\pm$ 150 | -0.25 $\pm$ 0.25 | 4.40 $\pm$ 0.10 | 0.18 $\pm$ 0.02 | 5.126 $\pm$ 0.059 | 0.957 $\pm$ 0.051
TOI-1213 | 1.2 | 5675 $\pm$ 175 | 0.00 $\pm$ 0.25 | 4.45 $\pm$ 0.10 | 0.34 $\pm$ 0.03 | 10.47 $\pm$ 0.12 | 0.951 $\pm$ 0.059

Star | $M_{\star}^{a}$ | $M_{\star}^{b}$ | $P_{\rm rot}/\sin i$ | $\tau_{\star}^{c}$ | $R^{\prime}_{\rm HK}$ | $\tau_{\star}^{d}$
---|---|---|---|---|---|---
| M⊙ | M⊙ | [d] | [Gyr] | dex | [Gyr]
TOI-148 | 0.94 $\pm$ 0.26 | 1.03 $\pm$ 0.06 | 5.97 $\pm$ 0.47 | 0.55 $\pm$ 0.07 | – | –
TOI-587 | 2.12 $\pm$ 0.29 | 2.32 $\pm$ 0.14 | 3.02 $\pm$ 0.18 | – | – | –
TOI-681 | 1.45 $\pm$ 0.25 | 1.51 $\pm$ 0.09 | 2.61 $\pm$ 0.13 | – | – | –
TOI-746 | 0.84 $\pm$ 0.12 | 0.98 $\pm$ 0.06 | 7.9 $\pm$ 1.6 | 0.52 $\pm$ 0.06 | $-4.50\pm 0.05$ | 0.60 $\pm$ 0.23
TOI-1213 | 0.93 $\pm$ 0.15 | 1.01 $\pm$ 0.06 | 12.0 $\pm$ 3.6 | 1.1 $\pm$ 0.2 | – | –

  * •

aStellar mass inferred from $R_{\star}$ and spectroscopic $\log g_{*}$.
bStellar mass estimated via empirical relations of Torres et al. (2010).
cSystem age estimated from inferred rotation period via empirical relations of
Mamajek & Hillenbrand (2008). dSystem age estimated from inferred
$R^{\prime}_{\rm HK}$ via empirical relations of Mamajek & Hillenbrand (2008).
The ages derived from stellar rotation and activity are likely underestimated
due to the stellar rotations likely being affected by the companions as
discussed in Section 4.1.

Table 3: Table of stellar parameters derived from SED fitting and empirical
relations. We refer the reader to the final adopted parameters for each star
presented in tables 6 \- 10.

As an independent check on the derived stellar parameters, we performed an
analysis of the broadband spectral energy distributions (SEDs) of each star,
together with the Gaia DR2 parallax in order to constrain the basic stellar
parameters and 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 GALEX NUV and FUV fluxes, the $B_{T}V_{T}$
magnitudes from Tycho-2, the $BVgri$ magnitudes from APASS, the $JHK_{S}$
magnitudes from 2MASS, the W1–W4 magnitudes from WISE, and the $GG_{\rm
BP}G_{\rm RP}$ magnitudes from Gaia. For the hottest source we also pulled the
TD1/wide UV fluxes from the TD1 satellite (Thompson et al., 1978). Together,
the available photometry spans the full stellar SED over the wavelength range
0.15–22 $\mu$m (see Figure 7). We performed a fit using Kurucz stellar
atmosphere models, with the priors on effective temperature ($T_{\rm eff}$),
surface gravity ($\log g$), and metallicity ([Fe/H]) from the spectroscopic
analysis. The remaining parameter is the extinction ($A_{V}$), which we
limited to the maximum line-of-sight extinction from the Galactic dust maps of
Schlegel et al. (1998).

The resulting fits (Figure 7) have small reduced $\chi^{2}$ values reported in
Table 3, which also summarizes the other resulting stellar parameters:
Integrating the (unreddened) model SED gives the bolometric flux at Earth,
$F_{\rm bol}$; taking the $F_{\rm bol}$ and $T_{\rm eff}$ together with the
Gaia DR2 parallax, adjusted by $+0.08$ mas to account for the systematic
offset reported by Stassun & Torres (2018), gives the stellar radius,
$R_{\star}$. We can then infer the stellar mass, $M_{\star}$, empirically from
$R_{\star}$ and $\log g$, as well as estimate it via the empirical relations
of Torres et al. (2010).

We can also estimate the stellar rotation periods from the spectroscopic
$v\sin i$ together with the above $R_{\star}$, giving an upper limit of
$P_{\rm rot}/\sin i$. From the excess GALEX UV emission, when present, we can
also estimate the chromospheric activity indicator, $R^{\prime}_{\rm HK}$ via
the empirical relations of Findeisen et al. (2011). In turn, these provide
another estimate of the stellar rotation period via the empirical rotation-
activity relations of Mamajek & Hillenbrand (2008). Finally, these activity
measures provide an estimate of the stellar age, $\tau_{\star}$ again via the
empirical activity-age relations of Mamajek & Hillenbrand (2008). However, we
note the ages derived from stellar rotation and activity are likely
underestimated due to the stellar rotations likely being affected by the
companions (e.g., tidal locking) as discussed in Section 4.1.

###  3.3 TOI-681 kinematic analysis and cluster membership

TOI-681 has been previously reported to be a member of the open star cluster
NGC 2516 (Gaia Collaboration et al., 2018; Cantat-Gaudin et al., 2018; Kounkel
& Covey, 2019; Meingast et al., 2021). We reassessed its position and
kinematics relative to NGC 2516 as follows. First, we collected the NGC 2516
members reported by Cantat-Gaudin et al. (2018). To define a set of reference
“neighborhood” stars, we then queried Gaia DR2 for stars within 4 standard
deviations of the mean values of NGC 2516’s right ascension, declination, and
parallax. The corresponding positions, proper motions, and Gaia DR2 radial
velocities are shown in Figure 14.

TOI-681 is well within the cloud of cluster members (dark black points in
Figure 14) in each dimension, rather than being within the outlying
neighborhood (gray points). While TOI 681 did not have a Gaia DR2 RV, we
measured a barycenter-corrected velocity with CORALIE of
22.120${}^{+0.096}_{-0.087}$ km s-1 and with FEROS of 23.75$\pm$0.14 km s-1.
This is an independent line of support for the cluster membership, as the mean
(Gaia-derived) cluster RV is 24.1 km s-1. Independent age indicators for
TOI-681 such as the photospheric lithium abundance or the rotation period are
not applicable due to the stellar type ($T_{\rm eff}\,\approx\,7400\,{\rm
K}$). Nonetheless, given the six-dimensional position and kinematic overlap
with the other cluster members, we proceed under the assumption that TOI-681
is a member of NGC 2516.

Reported ages of NGC 2516 vary between 100 Myr and 300 Myr (Jeffries et al.,
1997, 1998; Randich et al., 2018; Gaia Collaboration et al., 2018; Kounkel &
Covey, 2019). While determining absolute ages for clusters is a challenging
problem (Soderblom et al., 2014), NGC 2516 appears to be slightly older than
the Pleiades based on the main sequence turn-off and gyrochronology (Cummings
& Kalirai 2018; Fritzewski et al. 2020; L. Bouma et al., in preparation). The
current consensus Pleiades age based on the main sequence turn-off and the
lithium depletion boundary is $125\pm 20$ Myr (see Soderblom et al. 2014). We
therefore expect the age of NGC 2516 to be within the interval of 140 to 200
Myr. We adopt $170\pm 25$ Myr and use this value as the age of TOI-681. This
is older than the absolute model-averaged age of $\approx 90$ Myr determined
by Randich et al. (2018) using isochrones, which we suspect might be explained
by the presence of blue-stragglers on the main sequence turn-off (Cummings &
Kalirai, 2018).

###  3.4 Global modeling

####  3.4.1 Modeling with EXOFASTv2

Figure 8: EXOFASTv2 posterior distributions of the companion radii without
(red) and with (blue) upper limits on the companion radius for TOI-681 and
TOI-1213 as described in Section 3.4.2.

We derive companion parameters and final stellar parameters using EXOFASTv2
(Eastman et al., 2013; Eastman, 2017; Eastman et al., 2019). A full
description of EXOFASTv2 is given in Eastman et al. (2019), which can fit any
number of transit and RV sources while exploring the vast parameter space
through a differential evolution Markov Chain coupled with a Metropolis-
Hastings Monte Carlo sampler. A built-in Gelman-Rubin statistic (Gelman &
Rubin, 1992; Gelman et al., 2003; Ford, 2006) is used to check the convergence
of the chains. For each fit we use 2 $\times$ $n_{\text{\rm{parameters}}}$
walkers, or chains, and run until the fit passes the default convergence
criteria for EXOFASTv2 that is described in Eastman et al. (2019). For each
star we simultaneously fit the RVs and photometry and determine stellar
parameters using the Modules for Experiments in Stellar Astrophysics (MESA)
Isochrones & Stellar Tracks (MIST; Paxton et al., 2015; Choi et al., 2016;
Dotter, 2016) isochrones.

We place Gaussian priors on $R_{*}$ and $T_{\rm eff}$ from the SED analysis
described in Section 3.2 and do not fit the SED again within the EXOFASTv2
global model. We place Gaussian priors on $\left[{\rm Fe}/{\rm H}\right]$ from
the spectroscopic analysis described in Section 3.1. For TOI-681 we use the
NGC 2516 cluster age discussed in Section 3.3 as a prior. We place upper
boundaries on the companion radius for TOI-681 and TOI-1213 due to the grazing
nature of their transits, which we discuss further in Section 3.4.2.

EXOFASTv2 inherently applies priors on the quadratic limb darkening by
interpolating the Claret & Bloemen (2011) limb darkening models at each step
in $\log g_{*}$, $T_{\rm eff}$, and $\left[{\rm Fe}/{\rm H}\right]$. We use
the inherent EXOFASTv2 limb darkening fitting without applying priors on any
filters for TOI-148, TOI-681, TOI-746, and TOI-1213. However, given TOI-587’s
high $T_{\rm eff}$ we disable the limb darkening table interpolation using the
noclaret option in EXOFASTv2 and apply Gaussian priors of $u_{1}$ = 0.15 $\pm$
0.1 for the linear limb-darkening coefficient and $u_{2}$ = 0.25 $\pm$ 0.1 for
the quadratic limb-darkening coefficient for the TOI-587 TESS FFI lightcurve.
To account for smearing in the 30-minute TESS full frame exposures, we specify
an exposure time of 30 minutes and average over 10 data points to integrate a
model over the exposure time equivalent to a midpoint Riemann sum (Eastman et
al., 2019).

Specific priors used for each EXOFASTv2 fit are displayed in Tables 6 \- 10 as
well as the final results for both the host star and companion parameters. All
other fitted and derived parameters from our EXOFASTv2 model have conservative
physical boundaries that are detailed in Table 3 of Eastman et al. (2019),
which also gives a thorough explanation of each parameter. The final EXOFASTv2
transit and RV Keplerian fits are displayed as the red lines in Figures 1 \-
5.

####  3.4.2 TOI-681 and TOI-1213 grazing transits

TOI-681 and TOI-1213 both have v-shaped light curves which suggests that their
companions have grazing transits. In such cases where transiting companions
have a grazing geometry there is a degeneracy between the companion radius and
impact parameter of the transit and the upper limit of the companion radius is
unconstrained by the light curve. For TOI-681 we find that the posterior
distribution of both the companion radius and impact parameter are bimodal
with the lower companion radius and impact parameter being favored. We show
the unconstrained posterior distribution of the companion radius in Figure 8.
Given this clear bimodality and a more probable lower-radius solution both
physically and statistically, we remodeled TOI-681 with very conservative
boundaries of 0 and 5 $\mathrm{R_{\rm Jup}}$ for the companion radius. We show
the new companion radius posterior distribution in Figure 8 that finds a clear
peak at $\sim$1.5 $\mathrm{R_{\rm Jup}}$.

Figure 9: Top: Full light curve of TOI-1213 for TESS sectors 12 and 13. The
blue dashed vertical lines display the times of transit and the red dashed
vertical lines show the expected occultation times which we determined to be
at a phase of 0.6581. Bottom: Zoom in of the time where the first occultation
of TOI-1213 should occur with a box model with a depth equal to the standard
deviation of the TESS photometry during the total eclipse duration (0.149
days) calculated from our EXOFASTv2 model.

The posterior distribution for the companion radius of TOI-1213 does not
clearly favor the lower-radius solution, and the most probable solution is at
a much larger radius than physically expected. We therefore put a tighter
upper boundary of 3.0 $\mathrm{R_{\rm Jup}}$ for TOI-1213 when remodeling the
system based on the physical limit of nondetections of the occultations in the
TESS light curve. From our EXOFASTv2 model we find an eclipse impact parameter
of 0.403${}^{+0.041}_{-0.027}$ showing the system should be aligned to see an
occultation in the lightcurve if it is within the TESS detection limits. As
displayed in Figure 9 we do not find any occultations of TOI-1213b within the
precision of the TESS light curve, which allows us to put an upper limit on
the occultation depth and thus an upper limit on the companion radius. The
lower panel of Figure 9 shows the first occultation and displays a box model
of an occultation with a depth equal to the standard deviation (1725 ppm) of
the TESS data during the total eclipse duration (0.149${}^{+0.015}_{-0.014}$
days) calculated from our EXOFASTv2 model. We set this standard deviation of
1725 ppm as our detection limit and the lower limit of the occultation depth.
To turn this occultation depth limit into an upper limit on the companion
radius, we obtained simulated PHOENIX spectra (Husser et al., 2013) of a G6V
star for TOI-1213 and M7.5V for TOI-1213b (from our calculated mass of 97.5
$\mathrm{M_{\rm Jup}}$) and integrated the total flux of each spectrum over
the TESS bandpass of 600 - 1000 nm. We then multiply this total flux of the
modeled G6V star by the area of TOI-1213 $\pi\mbox{$R_{*}$}^{2}$. The
companion radius can then be computed by setting the occultation depth to the
TESS precision:

$\mathrm{Depth}_{\mathrm{occ}}=\frac{\mathrm{Flux}_{b}\pi
R_{b}^{2}}{\mathrm{Flux}_{A}\pi R_{A}^{2}}.$ (1)

With a lower limit on occultation of 1725 ppm, we find an upper limit on the
companion radius of 3.00 $\mathrm{R_{\rm Jup}}$. We set 3.0 $\mathrm{R_{\rm
Jup}}$ as the upper limit on TOI-1213b and display the companion radius with
and without boundaries in Figure 8.

##  4 Discussion

The five transiting companions analyzed here have masses around the hydrogen-
burning mass limit, the upper boundary of brown dwarfs and lower boundary of
main sequence stars, which is generally adopted as 80 $\mathrm{M_{\rm Jup}}$
(e.g., Marcy & Butler, 2000; Grether & Lineweaver, 2006). However, this border
depends on initial formation conditions including the initial radius of the
object, the efficiency of convection in the outermost layers, opacity,
metallicity, and the initial abundance of deuterium (e.g., Chabrier & Baraffe,
1997; Baraffe et al., 2002). Dieterich et al. (2018) summarizes previous model
predictions for the stellar-substellar boundary which range from 73.3 - 96.4
$\mathrm{M_{\rm Jup}}$ (e.g., Burrows et al., 2001), whose predictions differ
from observed populations (e.g., Dieterich et al., 2014) and differ from the
$\sim$70 $\mathrm{M_{\rm Jup}}$ boundary estimate by Dupuy & Liu (2017) using
astrometric masses of ultracool binaries.

This brown dwarf and stellar boundary is important as small changes in mass
can cause vastly different lives for these objects, where low-mass M-dwarfs
may burn hydrogen for up to trillions of years (e.g., Adams & Laughlin, 1997)
compared to brown dwarfs that will only have a short-lived deuterium burning
stage of less than a billion years (e.g., Spiegel et al., 2011) before cooling
and shrinking. The exact population these five objects belong to is uncertain,
but we can put them into context with other transiting brown dwarfs and very
low-mass stars as discussed in Section 4.2. We first explore the possible
tidal effects on these individual systems in Section 4.1.

###  4.1 Tidal circularization and spin-orbit synchronization

The gravitational and tidal interactions between a star and a close-in
orbiting companion (another star, brown dwarf, or planet) have varying effects
on the rotation, orbit, and momentum axes of the system. In terms of
timescales, the first effect that may be induced is spin-orbit
synchronization, or tidal locking, where the stellar rotation period and
orbital period become equal from tidal torques (e.g., Zahn, 1977; Zahn &
Bouchet, 1989; Witte & Savonije, 2002; Mazeh, 2008). A system with an
eccentric orbit can reach a tidally locked state when the stellar rotation
period becomes equal to the equilibrium rotation period, which can be
predicted by tidal models (Fleming et al., 2019). A star’s rotation period is
generally expected to reduce over time from magnetic braking (Skumanich,
1972); however, this affect may be slowed down due to tidal torques (e.g.,
Verbunt & Zwaan, 1981; Fleming et al., 2018, 2019). On longer timescales and
particularly for short orbital periods (e.g., Porb $\lesssim$ 10 days) the
orbital eccentricity may be damped and the orbit may become circular (e.g.,
tidal circularization, Goldreich & Soter, 1966; Hut, 1981; Adams & Laughlin,
2006). Evolution of the system’s obliquity, or the angle between the stellar
spin axis and the orbital axis occurs even more slowly than eccentricity
dampening (e.g., Hut, 1981; Winn et al., 2005; Barker & Ogilvie, 2009). Here
we examine possible tidal effects including eccentricity dampening or
circularization, stellar rotation spin up, and spin-orbit synchronization of
the brown dwarf and low-mass star systems presented in this work.

From our spectroscopic analysis we find a $v\sin i_{*}$ = 10.1 $\pm$ 0.1 km
s-1 for TOI-148, which is on the upper end of $v\sin i_{*}$ distributions for
stars of similar mass (e.g., Robles et al., 2008), indicating TOI-148’s
stellar rotation period may be affected by tidal torques with its companion.
With this $v\sin i_{*}$ we put an upper limit on the stellar rotation period
($P_{rot}$ $\leq$ $2\pi\mbox{$R_{*}$}/\mbox{$v\sin i_{*}$}$) of 5.97 $\pm$
0.47 days for TOI-148, which is smaller than expected given its older age of
7.7 $\pm$ 3.7 Gyr in comparison to other rotational periods of older stars
with similar masses (e.g., Lorenzo-Oliveira et al., 2019). Additionally the
upper limit of the stellar rotation period is less than one day larger than
the orbital period of 4.87 days for TOI-148b, suggesting that TOI-148 may be
close to a tidally locked state. We find the eccentricity of TOI-148 $e$ =
0.005${}^{+0.006}_{-0.004}$ to be insignificant (using the significance test
from Lucy & Sweeney (1971) we find P($e$ $>$ 0) = 0.63, which fails the 5%
significance level) also suggesting TOI-148 has undergone tidal
circularization.

TOI-681 is relatively hot ($T_{\rm eff}$ = 7440${}^{+150}_{-140}$ K) and fast
rotating ($P_{\rm rot}/\sin i$ = 2.61 $\pm$ 0.13 days) star, which can create
enhanced magnetic fields from spin-orbit tidal synchronization for short
period systems and has been thought to cause inflated radii of similar low-
mass companions (e.g., Chabrier et al., 2007; Mazeh, 2008). However, given its
relatively long period of 15.78 days and young 0.170 $\pm$ 0.025 Gyr age
TOI-681b is unlikely to have reached spin-orbit synchronization. TOI-587 is
also a young 0.2 $\pm$ 0.1 Gyr star that is unlikely to have undergone spin-
orbit synchronization with $P_{\rm rot}/\sin i$ = 3.02 $\pm$ 0.18 days and
$P_{orb}$ = 8.04 days.

TOI-746 is an older 6.5${}^{+4.3}_{-3.9}$ Gyr star with a companion on a
moderately eccentric $e$ = 0.199 $\pm$ 0.003 orbit. As discussed, tidal
torques can drive a star’s rotation rate toward a tidally locked state where
the tidal torques fix the rotation period $P_{rot}$ to the equilibrium
rotation period $P_{eq}$. Tidal models can predict $P_{eq}$ including the
“constant phase lag” (CPL; Ferraz-Mello et al., 2008; Heller et al., 2011)
equilibrium tidal model. Following Barnes (2017) and Fleming et al. (2019) the
CPL model permits a 1:1 and 3:2 spin-orbit state by:

$\centering P_{eq}^{\text{CPL}}=\cases{P}_{eq}\text{ if }e<\sqrt{1/19}\\\
\frac{2}{3}P_{eq}\text{ if }e\geq\sqrt{1/19}.\\\ {}\@add@centering$ (2)

Using the second case we find $P_{eq}$ = 7.32 days for TOI-746 and with an
upper limit on the rotation period of $P_{\rm rot}/\sin i$ = 7.9 $\pm$ 1.6
days TOI-746 may be in a supersychronous 3:2 spin–orbit state. We also
consider the system may be in a pseudo-synchronous rotation state (Hut, 1981)
that approximates spin-orbit synchronization around the time of periastron.
Zimmerman et al. (2017) explored possible pseudosynchronization for heartbeat
binary stars with $Kepler$ lightcurves but found generally that their sample
clustered around $\frac{3}{2}$ times the pseudosynchronization period
indicating that they have plateaued prematurely in their synchronization. We
roughly estimate this using Kepler’s third law to determine what the period
would be if the companion was in a circular orbit at the periastron distance:

$P_{\mathrm{peri}}=P_{\mathrm{orb}}(1-e)^{3/2}.$ (3)

Assuming this circular orbit at periastron we find $P_{\mathrm{peri}}$ = 7.88
$\pm$ 0.05 days which is very similar to the upper limit of the rotation
period suggesting TOI-746 may be in a pseudo-synchronous rotation at
periastron.

TOI-1213 is also relatively older 5.3${}^{+4.2}_{-3.4}$ Gyr star with a
companion on an eccentric $e$ = 0.498${}^{+0.003}_{-0.002}$ orbit. We find
$P_{eq}$ = 18.14 days for TOI-1213, and with $P_{\rm rot}/\sin i$ = 12.0 $\pm$
3.6 days TOI-1213 does not appear to have spin-orbit synchronization. However,
assuming a circular orbit at periastron we find $P_{\mathrm{peri}}$ = 9.64
$\pm$ 0.09 days, which is within uncertainties of the upper limit of the
stellar rotation period suggesting TOI-1213 may be in a pseudo-synchronous
rotation at periastron.

###  4.2 Discoveries in context with transiting brown dwarfs and very low-mass
stars

Figure 10: Radius-mass diagram for the 54 brown dwarfs and low-mass stars
presented in Table 4. The five companions presented in this work are
highlighted in red. The gray vertical dashed lines display the 13 and 80
$\mathrm{M_{\rm Jup}}$ approximate boundaries of the brown dwarf regime. The
colored lines display isochrone models from Baraffe et al. (2003, 2015) for
low mass stars and substellar objects at solar metallicity with ages of 0.1,
0.5, 1, 5, and 10 Gyr. The histogram at the top displays relative occurrence
of these transiting objects. We note the brown dwarf RIK 72b is not shown
because its radius is 3.1 $\mathrm{R_{\rm Jup}}$.

List of Published 13-150 $\mathrm{M_{\rm Jup}}$ Transiting Companions as of
June 2021  Name M2 [$\mathrm{M_{\rm Jup}}$ ] R2 [$\mathrm{R_{\rm Jup}}$ ] $P$
[days] $ecc$ M1 [$\mathrm{M_{\odot}}$ ] R1 [$\mathrm{R_{\odot}}$ ] $T_{\rm
eff}$[K] $\left[{\rm Fe}/{\rm H}\right]$ Reference HATS-70b
12.9${}_{-1.6}^{+1.8}$ 1.38${}_{-0.07}^{+0.08}$ 1.89 ¡0.18 1.78 $\pm$ 0.12
1.88${}_{-0.07}^{+0.06}$ 7930${}_{-820}^{+630}$ 0.04${}_{-0.11}^{+0.10}$ (1)
TOI-1278b 18.5 $\pm$ 0.5 1.09${}_{-0.20}^{+0.24}$ 14.48 0.013 $\pm$ 0.004 0.54
$\pm$ 0.02 0.57 $\pm$ 0.01 3799 $\pm$ 42 -0.01 $\pm$ 0.28 (2) GPX-1b 19.7
$\pm$ 1.6 1.47 $\pm$ 0.10 1.74 0.000 $\pm$ 0.000 1.68 $\pm$ 0.10 1.56 $\pm$
0.10 7000 $\pm$ 200 0.35 $\pm$ 0.10 (3) Kepler-39b 20.1${}_{-1.2}^{+1.3}$
1.24${}_{-0.10}^{+0.09}$ 21.09 0.112 $\pm$ 0.057 1.29${}_{-0.07}^{+0.06}$ 1.40
$\pm$ 0.10 6350 $\pm$ 100 0.10 $\pm$ 0.14 (4) CoRoT-3b 21.7 $\pm$ 1.0 1.01
$\pm$ 0.07 4.26 0 (fixed) 1.37 $\pm$ 0.09 1.56 $\pm$ 0.09 6740 $\pm$ 140 -0.02
$\pm$ 0.06 (5) KELT-1b 27.4 $\pm$ 0.9 1.12${}_{-0.03}^{+0.04}$ 1.22
0.010${}_{-0.007}^{+0.010}$ 1.33 $\pm$ 0.06 1.47 $\pm$ 0.04 6516 $\pm$ 49 0.05
$\pm$ 0.08 (6) NLTT 41135b 33.7${}_{-2.6}^{+2.8}$ 1.13${}_{-0.17}^{+0.27}$
2.89 ¡0.02 0.19${}_{-0.02}^{+0.03}$ 0.21${}_{-0.01}^{+0.02}$ 3230 $\pm$ 130
-0.25 $\pm$ 0.25 (7) WASP-128b 37.2 $\pm$ 0.8 0.94 $\pm$ 0.02 2.21 ¡0.007 1.16
$\pm$ 0.04 1.15 $\pm$ 0.02 5950 $\pm$ 50 0.01 $\pm$ 0.12 (8) CWW 89Ab
39.2${}_{-1.1}^{+0.9}$ 0.94 $\pm$ 0.02 5.29 0.189 $\pm$ 0.002 1.10 $\pm$ 0.04
1.03 $\pm$ 0.02 5755 $\pm$ 49 0.20 $\pm$ 0.09 (9) (10) KOI-205b 39.9 $\pm$ 1.0
0.81 $\pm$ 0.02 11.72 ¡0.031 0.93 $\pm$ 0.03 0.84 $\pm$ 0.02 5237 $\pm$ 60
0.14 $\pm$ 0.12 (11) TOI-1406b 46.0${}_{-2.7}^{+2.6}$ 0.86 $\pm$ 0.03 10.57
0.026${}_{-0.010}^{+0.013}$ 1.18${}_{-0.09}^{+0.08}$ 1.35 $\pm$ 0.03 6290
$\pm$ 100 -0.08 $\pm$ 0.09 (12) EPIC 212036875b 52.3 $\pm$ 1.9 0.87 $\pm$ 0.02
5.17 0.132 $\pm$ 0.004 1.29${}_{-0.06}^{+0.07}$ 1.50 $\pm$ 0.03
6238${}_{-60}^{+59}$ 0.01 $\pm$ 0.10 (10) (13) TOI-503b 53.7 $\pm$ 1.2
1.34${}_{-0.15}^{+0.26}$ 3.68 0 (fixed) 1.80 $\pm$ 0.06
1.70${}_{-0.04}^{+0.05}$ 7650${}_{-160}^{+140}$ 0.30${}_{-0.09}^{+0.08}$ (14)
TOI-852b 53.7${}_{-1.3}^{+1.4}$ 0.83 $\pm$ 0.04 4.95
0.004${}_{-0.003}^{+0.004}$ 1.32${}_{-0.04}^{+0.05}$ 1.71 $\pm$ 0.04
5768${}_{-81}^{+84}$ 0.33 $\pm$ 0.09 (15) AD 3116b 54.2 $\pm$ 4.3 1.02 $\pm$
0.28 1.98 0.146 $\pm$ 0.024 0.28 $\pm$ 0.02 0.29 $\pm$ 0.08 3184 $\pm$ 29 0.16
$\pm$ 0.10 (16) CoRoT-33b 59.0${}_{-1.7}^{+1.8}$ 1.10 $\pm$ 0.53 5.82 0.070
$\pm$ 0.002 0.86 $\pm$ 0.04 0.94${}_{-0.08}^{+0.14}$ 5225 $\pm$ 80 0.44 $\pm$
0.10 (17) RIK 72b 59.2${}_{-6.7}^{+6.8}$ 3.10 $\pm$ 0.31 97.76
0.108${}_{-0.006}^{+0.012}$ 0.44 $\pm$ 0.04 0.96 $\pm$ 0.10 3349 $\pm$ 142
0.00 $\pm$ 0.10 (18) TOI-811b 59.9${}_{-8.6}^{+13.0}$ 1.26 $\pm$ 0.06 25.17
0.509 $\pm$ 0.075 1.32${}_{-0.07}^{+0.05}$ 1.27${}_{-0.09}^{+0.06}$ 6107 $\pm$
77 0.40${}_{-0.09}^{+0.07}$ (15) TOI-263b 61.6 $\pm$ 4.0 0.91 $\pm$ 0.07 0.56
0.017${}_{-0.010}^{+0.009}$ 0.44 $\pm$ 0.04 0.44 $\pm$ 0.03 3471 $\pm$ 33 0.00
$\pm$ 0.10 (19) KOI-415b 62.1 $\pm$ 2.7 0.79${}_{-0.07}^{+0.12}$ 166.79 0.689
$\pm$ 0.000 0.94 $\pm$ 0.06 1.25${}_{-0.10}^{+0.15}$ 5810 $\pm$ 80 -0.24 $\pm$
0.11 (20) WASP-30b 62.5 $\pm$ 1.2 0.95${}_{-0.02}^{+0.03}$ 4.16 0 (fixed)
1.25${}_{-0.04}^{+0.03}$ 1.39 $\pm$ 0.03 6202${}_{-51}^{+42}$
0.08${}_{-0.05}^{+0.07}$ (21) LHS 6343c 62.7 $\pm$ 2.4 0.83 $\pm$ 0.02 12.71
0.056 $\pm$ 0.032 0.37 $\pm$ 0.01 0.38 $\pm$ 0.01 3130 $\pm$ 20 0.04 $\pm$
0.08 (22) CoRoT-15b 63.3 $\pm$ 4.1 1.12${}_{-0.15}^{+0.30}$ 3.06 0 (fixed)
1.32 $\pm$ 0.12 1.46${}_{-0.14}^{+0.31}$ 6350 $\pm$ 200 0.10 $\pm$ 0.20 (23)
TOI-569b 64.1${}_{-1.4}^{+1.9}$ 0.75 $\pm$ 0.02 6.56
0.002${}_{-0.001}^{+0.002}$ 1.21 $\pm$ 0.05 1.48 $\pm$ 0.03
5768${}_{-92}^{+110}$ 0.29${}_{-0.08}^{+0.09}$ (12) EPIC 201702477b 66.9 $\pm$
1.7 0.76 $\pm$ 0.07 40.74 0.228 $\pm$ 0.003 0.87 $\pm$ 0.03 0.90 $\pm$ 0.06
5517 $\pm$ 70 -0.16 $\pm$ 0.05 (24) LP261-75b 68.1 $\pm$ 2.1 0.90 $\pm$ 0.01
1.88 ¡0.007 0.30 $\pm$ 0.01 0.31 $\pm$ 0.00 3100 $\pm$ 50 … (25) NGTS-7Ab
75.5${}_{-13.7}^{+3.0}$ 1.38${}_{-0.14}^{+0.13}$ 0.68 0 (fixed) 0.24 $\pm$
0.03 0.61 $\pm$ 0.06 3359${}_{-89}^{+106}$ 0.00 $\pm$ 0.10 (26) KOI-189b 78.6
$\pm$ 3.5 1.00 $\pm$ 0.02 30.36 0.275 $\pm$ 0.004 0.76 $\pm$ 0.05 0.73 $\pm$
0.02 4952 $\pm$ 40 -0.12 $\pm$ 0.10 (27) TOI-148b 77.1${}_{-4.6}^{+5.8}$
0.81${}_{-0.06}^{+0.05}$ 4.87 0.005${}_{-0.004}^{+0.006}$
0.97${}_{-0.09}^{+0.12}$ 1.20 $\pm$ 0.07 5990 $\pm$ 140 -0.24 $\pm$ 0.25 this
work TOI-587b 81.1${}_{-7.0}^{+7.1}$ 1.32${}_{-0.06}^{+0.07}$ 8.04
0.051${}_{-0.036}^{+0.049}$ 2.33 $\pm$ 0.12 2.01 $\pm$ 0.09 9800 $\pm$ 200
0.08${}_{-0.12}^{+0.11}$ this work TOI-746b 82.2${}_{-4.4}^{+4.9}$
0.95${}_{-0.06}^{+0.09}$ 10.98 0.199 $\pm$ 0.003 0.94${}_{-0.08}^{+0.09}$
0.97${}_{-0.03}^{+0.04}$ 5690 $\pm$ 140 -0.02 $\pm$ 0.23 this work EBLM
J0555-57Ab 87.9 $\pm$ 4.0 0.82${}_{-0.06}^{+0.13}$ 7.76 0.089 $\pm$ 0.004 1.18
$\pm$ 0.08 1.00${}_{-0.07}^{+0.14}$ 6386 $\pm$ 124 -0.04 $\pm$ 0.14 (28)
TOI-681b 88.7${}_{-2.3}^{+2.5}$ 1.52${}_{-0.15}^{+0.25}$ 15.78
0.093${}_{-0.019}^{+0.022}$ 1.54${}_{-0.05}^{+0.06}$ 1.47 $\pm$ 0.04
7440${}_{-140}^{+150}$ -0.08 $\pm$ 0.05 this work OGLE-TR-123b 89.0 $\pm$ 11.5
1.29 $\pm$ 0.09 1.80 0 (fixed) 1.29 $\pm$ 0.26 1.55 $\pm$ 0.10 6700 $\pm$ 300
… (29) TOI-694b 89.0 $\pm$ 5.3 1.11 $\pm$ 0.02 48.05 0.521 $\pm$ 0.002
0.97${}_{-0.04}^{+0.05}$ 1.00 $\pm$ 0.01 5496${}_{-81}^{+87}$ 0.21 $\pm$ 0.08
(30) KOI-607b 95.1${}_{-3.4}^{+3.3}$ 1.09${}_{-0.06}^{+0.09}$ 5.89 0.395 $\pm$
0.009 0.99 $\pm$ 0.05 0.92 $\pm$ 0.03 5418${}_{-85}^{+87}$
0.38${}_{-0.09}^{+0.07}$ (10) J1219-39b 95.4${}_{-2.5}^{+1.9}$
1.14${}_{-0.05}^{+0.07}$ 6.76 0.055 $\pm$ 0.000 0.83 $\pm$ 0.03
0.81${}_{-0.02}^{+0.04}$ 5412${}_{-65}^{+81}$ -0.21 $\pm$ 0.07 (21) OGLE-
TR-122b 96.3 $\pm$ 9.4 1.17${}_{-0.13}^{+0.20}$ 7.27 0.205 $\pm$ 0.008 0.98
$\pm$ 0.14 1.05${}_{-0.09}^{+0.20}$ 5700 $\pm$ 300 0.15 $\pm$ 0.36 (31)
TOI-1213b 97.5${}_{-4.2}^{+4.4}$ 1.66${}_{-0.55}^{+0.78}$ 27.22
0.498${}_{-0.002}^{+0.003}$ 0.99${}_{-0.06}^{+0.07}$ 0.99 $\pm$ 0.04 5590
$\pm$ 150 0.25${}_{-0.14}^{+0.13}$ this work K2-76b 98.7 $\pm$ 2.0
0.89${}_{-0.05}^{+0.03}$ 11.99 0.255${}_{-0.006}^{+0.007}$ 0.96 $\pm$ 0.03
1.17${}_{-0.06}^{+0.03}$ 5747${}_{-70}^{+64}$ 0.01 $\pm$ 0.04 (32) CoRoT
101186644 100.5 $\pm$ 11.5 1.01${}_{-0.25}^{+0.06}$ 20.68 0.402 $\pm$ 0.006
1.20 $\pm$ 0.20 1.07 $\pm$ 0.07 6090 $\pm$ 200 0.20 $\pm$ 0.20 (33) J2343+29Ab
102.7 $\pm$ 7.3 1.24 $\pm$ 0.07 16.95 0.161${}_{-0.003}^{+0.002}$ 0.86 $\pm$
0.10 0.85${}_{-0.06}^{+0.05}$ 5150${}_{-60}^{+90}$ 0.10 $\pm$ 0.14 (34) EBLM
J0954-23Ab 102.8${}_{-5.9}^{+6.0}$ 0.98 $\pm$ 0.17 7.58 0.042 $\pm$ 0.001 1.17
$\pm$ 0.08 1.23 $\pm$ 0.17 6406 $\pm$ 124 -0.01 $\pm$ 0.14 (28) KOI-686b 103.4
$\pm$ 5.1 1.22 $\pm$ 0.04 52.51 0.556 $\pm$ 0.004 0.98 $\pm$ 0.07 1.04 $\pm$
0.03 5834 $\pm$ 100 -0.06 $\pm$ 0.13 (27) TIC 220568520b 107.2 $\pm$ 5.2 1.25
$\pm$ 0.02 18.56 0.096 $\pm$ 0.003 1.03 $\pm$ 0.04 1.01 $\pm$ 0.01 5589 $\pm$
81 0.26 $\pm$ 0.07 (30) HATS551-016B 114.7${}_{-6.3}^{+5.2}$
1.46${}_{-0.04}^{+0.03}$ 2.05 0.080 $\pm$ 0.020 0.97${}_{-0.06}^{+0.05}$
1.22${}_{-0.03}^{+0.02}$ 6420 $\pm$ 90 -0.60 $\pm$ 0.06 (35) OGLE-TR-106b
121.5 $\pm$ 22.0 1.76 $\pm$ 0.17 2.54 0.000 $\pm$ 0.020 … 1.31 $\pm$ 0.09 … …
(36) EBLM J1431-11Ab 126.9${}_{-3.9}^{+3.8}$ 1.45${}_{-0.05}^{+0.07}$ 4.45 0
(fixed) 1.20 $\pm$ 0.06 1.11${}_{-0.03}^{+0.04}$ 6161 $\pm$ 124 0.15 $\pm$
0.14 (28) HAT-TR-205-013B 129.9 $\pm$ 10.5 1.62 $\pm$ 0.06 2.23 0.012 $\pm$
0.021 1.04 $\pm$ 0.13 1.28 $\pm$ 0.04 6295${}_{-335}^{+245}$ … (37) TIC
231005575b 134.1 $\pm$ 3.1 1.50 $\pm$ 0.03 61.78 0.298${}_{-0.001}^{+0.004}$
1.04 $\pm$ 0.04 0.99 $\pm$ 0.05 5500 $\pm$ 85 -0.44 $\pm$ 0.06 (38)
HATS551-021B 138.2${}_{-5.2}^{+14.7}$ 1.53${}_{-0.08}^{+0.06}$ 3.64 0.060
$\pm$ 0.020 1.10 $\pm$ 0.10 1.20${}_{-0.01}^{+0.08}$ 6670 $\pm$ 220 -0.40
$\pm$ 0.10 (35) EBLM J2017+02Ab 142.2${}_{-6.7}^{+6.6}$
1.49${}_{-0.10}^{+0.13}$ 0.82 0 (fixed) 1.10 $\pm$ 0.07
1.20${}_{-0.05}^{+0.08}$ 6161 $\pm$ 124 -0.07 $\pm$ 0.14 (28) KIC 1571511B
148.1 $\pm$ 0.5 1.74${}_{-0.01}^{+0.00}$ 14.02 0.327 $\pm$ 0.003
1.26${}_{-0.03}^{+0.04}$ 1.34 $\pm$ 0.01 6195 $\pm$ 50 0.37 $\pm$ 0.08 (39)
WTS 19g-4-02069B 149.8 $\pm$ 6.3 1.69 $\pm$ 0.06 2.44 0 (fixed) 0.53 $\pm$
0.02 0.51 $\pm$ 0.01 3300 $\pm$ 140 … (40)

Table 4: References. (1) Zhou et al. 2019; (2) Artigau et al. 2021; (3) Benni
et al. 2020; (4) Bonomo et al. 2015; (5) Deleuil et al. 2008; (6) Siverd et
al. 2012; (7) Irwin et al. 2010; (8) Hodžić et al. 2018; (9) Nowak et al.
2017; (10) Carmichael et al. 2019; (11) Díaz et al. 2013; (12) Carmichael et
al. 2020; (13) Persson et al. 2019; (14) Šubjak et al. 2020; (15) Carmichael
et al. 2021; (16) Gillen et al. 2017; (17) Csizmadia et al. 2015; (18) David
et al. 2019; (19) Palle et al. 2021; (20) Moutou et al. 2013; (21) Triaud et
al. 2013; (22) Johnson et al. 2011; (23) Bouchy et al. 2011; (24) Bayliss et
al. 2017; (25) Irwin et al. 2018; (26) Jackman et al. 2019; (27) Díaz et al.
2014; (28) von Boetticher et al. 2019; (29) Pont et al. 2006; (30) Mireles et
al. 2020; (31) Pont et al. 2005b; (32) Shporer et al. 2017; (33) Tal-Or et al.
2013; (34) Chaturvedi et al. 2016; (35) Zhou et al. 2014; (36) Pont et al.
2005a; (37) Beatty et al. 2007; (38) Gill et al. 2020; (39) Ofir et al. 2012;
(40) Nefs et al. 2013. Note. The brown dwarf binary system from Stassun et al.
(2006), triple system from Triaud et al. (2020), and white dwarf companions
are not included.

Here we place these five transiting companions into context by comparing them
with other very low-mass stars and brown dwarfs using transiting brown dwarfs
from the list compiled by Carmichael et al. (2021). We also include 21 low-
mass stars with masses between 80 and 150 $\mathrm{M_{\rm Jup}}$ from the list
compiled by Mireles et al. (2020). We exclude the brown dwarf binary system
from Stassun et al. (2006) and triple system from Triaud et al. (2020) so as
only to focus on transiting companions. We also exclude brown dwarfs and low-
mass stars known to transit white dwarfs (e.g., Parsons et al., 2012a, b, c).
We add the three recent transiting brown dwarf discoveries of GPX-1b (Benni et
al., 2020), TOI-263b (Palle et al., 2021), and TOI-1278b (Artigau et al.,
2021). This includes a total of 54 transiting companions in the mass range of
13 - 150 $\mathrm{M_{\rm Jup}}$ presented in Table 4.

####  4.2.1 13-150 $\mathrm{M_{\rm Jup}}$ transiting companion radius-mass
relationship

Figure 10 places the five objects studied here in the radius-mass diagram with
transiting brown dwarfs and low-mass stars with masses up to 150
$\mathrm{M_{\rm Jup}}$. We also plot the theoretical isochrones for solar
metallicity at ages 0.1, 0.5, 1, 5, and 10 Gyr from Baraffe et al. (2003,
2015). Theoretical isochrones for low-mass stars and brown dwarfs (e.g.,
Baraffe et al., 2003, 2015) show the age of the object should affect its
radius for a particular mass, with older objects having smaller radii. This is
particularly true for brown dwarfs that do not have the long-term outward
pressure of hydrogen fusion to balance out the crush of gravity. Using well-
defined ages Carmichael et al. (2021) displayed a clear contrast between the
radii of an old and a young brown dwarf; further systems with well-
characterized ages are crucial to test this age-radius effect.

We derive young ages for TOI-681 (0.170 $\pm$ 0.025 Gyr from cluster
membership) and TOI-587 (0.2 $\pm$ 0.1 Gyr from MIST isochrone stellar
modeling of the hot A star) and see relatively enlarged radii for both of
these objects. However, TOI-681b displays a slightly grazing transit and
therefore the radius may be overestimated. TOI-681’s age is notably close to
the Pleiades cluster whose brown dwarf and very low-mass star candidates were
spectroscopically classified as late M dwarfs (e.g., Dahm, 2015).

As discussed in Section 3.4.2 TOI-1213b’s radius is not well constrained from
the grazing transit geometry and possibly overestimated given its age of
5.3${}^{+4.2}_{-3.4}$ Gyr. We find an older 7.7 $\pm$ 3.7 Gyr age for TOI-148
and with $R_{b}$=0.81${}^{+0.05}_{-0.06}$ $\mathrm{R_{\rm Jup}}$ TOI-148b has
one of the smallest radii among 13-150 $\mathrm{M_{\rm Jup}}$ transiting
companions. We also find an older 6.5${}^{+4.3}_{-3.9}$ Gyr age for TOI-746
and a relatively small 0.95${}^{+0.09}_{-0.06}$ $\mathrm{R_{\rm Jup}}$
companion radius.

The histogram on top of Figure 10 displays relative occurrence of these
transiting objects. Currently more massive brown dwarfs seem to have a
slightly higher occurrence than less massive brown dwarfs. However, we note
this is an incomplete sample and more systems are needed to understand the
occurrence of these objects. Additionally we note that there may be a bias of
not publishing low-mass stars as many current transit and RV research teams
emphasize lower mass companion discoveries.

####  4.2.2 13-150 $\mathrm{M_{\rm Jup}}$ transiting companion eccentricity
distribution.

By interpreting the eccentricity distribution of known brown dwarf candidate
companions around FGK-type stars, many of which only had lower-mass estimates
($M_{\rm{BD}}$ sin $i$), Ma & Ge (2014) suggested that brown dwarfs could be
split at $\sim$42.5 $\mathrm{M_{\rm Jup}}$. Brown dwarfs below 42.5
$\mathrm{M_{\rm Jup}}$ may primarily form in the protoplanetary disk through
core-accretion or disk gravitational instability and brown dwarfs above this
mass may dominantly form like a stellar binary through molecular cloud
fragmentation. This was suggested because lower-mass brown dwarfs showed a
trend in their eccentricity distribution with lower maximum eccentricity with
increasing mass, consistent with eccentricity scattering with other objects
formed in the disk (e.g., ‘planet–planet scattering’, Rasio & Ford, 1996;
Chatterjee et al., 2008; Ford & Rasio, 2008). Where higher-mass brown dwarfs
showed more diverse eccentricities similar to that of stellar binaries (Ma &
Ge, 2014). This trend was again analyzed for known brown dwarf companions by
Grieves et al. (2017) who found an overall similar distribution. Additionally,
Kiefer et al. (2021) found the eccentricity distribution for brown dwarfs and
low-mass M-dwarf companions around FGK stars at less than 60 pc of the Sun
with a true mass measured to match that of Ma & Ge (2014).

We analyze the eccentricity distribution for transiting brown dwarfs and low-
mass stars up to 150 $\mathrm{M_{\rm Jup}}$ in Figure 11. Although the higher-
mass brown dwarfs and low-mass stars display a larger range in eccentricities,
the sample size is still too small to make a claim that these represent two
separate populations. The symbols in Figure 11 are colored by period, and as
expected the companions with the highest eccentricities have relatively longer
orbital periods.

Figure 11: Eccentricity and mass for transiting brown dwarfs and low-mass
stellar companions. The color of each circle denotes the period. Transiting
companions presented in this work have green edges and error bars. The
vertical dashed lines are on the masses of 13, 42.5, and 80 $\mathrm{M_{\rm
Jup}}$. Figure 12: Companion mass and host star effective temperature $T_{\rm
eff}$ for transiting brown dwarfs and low-mass stellar companions (gray
circles) with the five new companions of this work shown with red error bars.
We also display giant planets that have both RV and transit data from the NASA
exoplanet archive555https://exoplanetarchive.ipac.caltech.edu (1089 giant
planets) with blue circles. The circles are inversely sized by the companion
period to highlight a higher proportion of brown dwarfs and low-mass stars in
close orbit around F dwarfs. The histograms at the top display the number of
relative companions in 500 K $T_{\rm eff}$ bins. The vertical dashed green
lines display approximate $T_{\rm eff}$ borders of stellar types. Figure 13:
Companion mass and host star metallicity $\left[{\rm Fe}/{\rm H}\right]$ for
transiting brown dwarfs and low-mass stellar companions. We split the
companions between 13 - 42.5, 42.5 - 80, and 80 - 150 $\mathrm{M_{\rm Jup}}$
to visualize possible metallicity differences between low-mass and high-mass
brown dwarfs and low-mass stars. The histograms at the top display the number
of companions in 0.1 dex $\left[{\rm Fe}/{\rm H}\right]$ bins for these mass
ranges.

####  4.2.3 13-150 $\mathrm{M_{\rm Jup}}$ transiting companion host stars

We review the host star effective temperature and stellar type of transiting
brown dwarfs and low-mass stars in Figure 5. G and F-type host stars are the
most common while there are only four hotter K-type stars hosting a transiting
companion in the mass range 13 - 150 $\mathrm{M_{\rm Jup}}$. As noted by
Carmichael et al. (2020) we see a relatively large percentage of transiting
BDs with M dwarf host stars, which is in contrast to hot Jupiters that have a
relatively smaller percentage of M dwarf host stars. TOI-587 is the hottest
main-sequence host star of a transiting brown dwarf or low-mass star below 150
$\mathrm{M_{\rm Jup}}$ with a $T_{\rm eff}$ = $9800^{+200}_{-200}$ K. From the
most recent
table666http://www.pas.rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt
of mean dwarf star effective temperatures by Pecaut & Mamajek (2013) we find
stellar types of F9.5V for TOI-148, A0V for TOI-587, A9V for TOI-681, G4V for
TOI-746, and G6V for TOI-1213.

In Figure 5, following Bouchy et al. (2011), the symbol size is inversely
proportional to the companion orbital period in order to highlight the higher
proportion of brown dwarfs and low-mass stars found in close orbit around F
dwarfs compared to those around G dwarfs. A plausible conjecture is that G
dwarfs may have engulfed their close-in brown-dwarf companions while F dwarfs,
which undergo less magnetic braking (e.g., Sadeghi Ardestani et al., 2017),
would have preserved them (Guillot et al., 2014). The two companions orbiting
G dwarfs from this study, TOI-746 and TOI-1213, are both relatively long-
period (10.98 days and 27.22 days, respectively) and eccentric (see Figure
11), indicating that tides have played a limited role in their dynamical
evolution. On the other hand, TOI-148, the companion with the shortest orbital
period in this study, 4.87 days, orbits around an F dwarf, and is circular,
thus somewhat strengthening this tendency for close-in massive companions to
be found preferentially around F dwarfs (Guillot et al., 2014). A deeper,
quantitative study is warranted. The relative lack of these companions around
K dwarfs and their presence around M dwarfs as shown in Figure 5 is
unexplained.

We display host star metallicity $\left[{\rm Fe}/{\rm H}\right]$ in Figure 13
of transiting brown dwarfs and low-mass stars. Figure 13 shows the most common
metallicity for brown dwarf host stars is at $\left[{\rm Fe}/{\rm H}\right]$
$\sim$ 0, which is consistent with previous findings that brown dwarfs are not
preferentially found around metal rich stars like hot Jupiters and are more
consistent with metallicity distributions of stars without substellar
companions or stars with low-mass planets (e.g., Ma & Ge, 2014; Mata Sánchez
et al., 2014; Maldonado et al., 2019; Adibekyan, 2019). Maldonado & Villaver
(2017) found that stars with less massive brown dwarfs tend to have higher
metallicities than stars with more massive brown dwarfs, which is consistent
with the interpretations of Ma & Ge (2014) and Maldonado et al. (2019) that
more massive brown dwarfs tend to form more like low-mass stars. Narang et al.
(2018) also found that the metallicity of host stars with brown dwarf
companions is lower compared to 1-4 $\mathrm{M_{\rm Jup}}$ mass objects but
similar to more massive ($>$4 $\mathrm{M_{\rm Jup}}$) planets, suggesting
similar formation mechanisms for both. Figure 13 has relatively few companions
to make significant statistical claims that these populations have inherently
different metallicites, but the distribution is still in agreement with a
possible separate population for more massive ($\gtrsim$42.5 $\mathrm{M_{\rm
Jup}}$) brown dwarfs having a metallicity distribution more similar to low-
mass stars (Maldonado & Villaver, 2017; Kiefer et al., 2021).

##  5 Conclusion

We report the discovery and characterization of five transiting companions
near the hydrogen-burning mass limit detected by TESS as objects of interest:
TOI-148 (UCAC4 260-199322), TOI-587 (HD 74162), TOI-681 (TYC 8911-00495-1),
TOI-746 (TYC 9177-00082-1), and TOI-1213 (TYC 8970-00020-1). We combine TESS
photometry with ground-based photometry and spectra from the CORALIE, CHIRON,
TRES, and FEROS spectrographs to find companion masses between 77 and 98
$\mathrm{M_{\rm Jup}}$ and companion radii between 0.81 and 1.66
$\mathrm{R_{\rm Jup}}$. We found young ages for TOI-587 (from isochrone
stellar modeling) and TOI-681 (from cluster membership) and find their
companion radii to be relatively larger compared to companions of similar
masses, as expected from theoretical isochrone models. However, TOI-681b has a
grazing transit making its companion radius not as well-constrained, and
TOI-1213b also has a grazing transit that creates an even less well-
constrained companion radius. TOI-148 and TOI-746 have relatively older ages
and smaller companion radii. TOI-587 is the hottest main-sequence star
($T_{\rm eff}$ = 9800 $\pm$ 200 K) known to host a transiting brown dwarf or
low-mass star below 150 $\mathrm{M_{\rm Jup}}$. We find evidence of spin-orbit
synchronization for TOI-148 and TOI-746, tidal circularization for TOI-148,
and possible pseudosynchronization at periastron for TOI-1213. The sample of
transiting brown dwarfs and low-mass stars we analyzed is still too small to
make significant statistical claims; however, their eccentricity and
metallicity distributions are still consistent with previous suggestions of
two separate populations for lower and higher mass brown dwarfs. These
companions are all near the hydrogen-burning mass limit and add to the
statistical sample needed to distinguish the population differences between
brown dwarfs and low-mass stars.

###### Acknowledgements.

We thank the Swiss National Science Foundation (SNSF) and the Geneva
University for their continuous support to our planet low-mass companion
search programs. This work was carried out in the frame of the Swiss National
Centre for Competence in Research (NCCR) $PlanetS$ supported by the Swiss
National Science Foundation (SNSF). This publication makes use of The Data &
Analysis Center for Exoplanets (DACE), which is a facility based at the
University of Geneva (CH) dedicated to extrasolar planet data visualization,
exchange, and analysis. DACE is a platform of NCCR $PlanetS$ and is available
at https://dace.unige.ch. This paper includes data collected by the TESS
mission. Funding for the TESS mission is provided by the NASA Explorer
Program. We are grateful to the CHIRON team: Todd Henry, Leonardo Paredes,
Hodari James, Azmain Nisak, Rodrigo Hinojosa, Roberto Aviles, and Wei-Chun
Jao, for carrying out the CHIRON observations and data reduction. This work
has made use of data from the European Space Agency (ESA) mission $Gaia$,
processed by the $Gaia$ Data Processing and Analysis Consortium (DPAC).
Funding for the DPAC has been provided by national institutions, in particular
the institutions participating in the $Gaia$ Multilateral Agreement. This work
makes use of observations from the LCOGT network. LCOGT telescope time was
granted by NOIRLab through the Mid-Scale Innovations Program (MSIP). MSIP is
funded by NSF. We acknowledge support from the French and Italian Polar
Agencies, IPEV and PNRA, and from Université Côte d’Azur under Idex UCAJEDI
(ANR-15-IDEX-01). MEarth is funded by the David and Lucile Packard Fellowship
for Science and Engineering, the National Science Foundation under grants
AST-0807690, AST-1109468, AST-1004488 (Alan T. Waterman Award) and
AST-1616624, and the John Templeton Foundation. This publication was made
possible through the support of a grant from the John Templeton Foundation.
The opinions expressed in this publication are those of the authors and do not
necessarily reflect the views of the John Templeton Foundation. This research
received funding from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (grant agreement n∘
803193/BEBOP), and from the Science and Technology Facilities Council (STFC;
grant n∘ ST/S00193X/1). 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. We acknowledge the use of public TESS Alert data from pipelines at
the TESS Science Office and at the TESS Science Processing Operations Center.
SG has been supported by STFC through consolidated grants ST/L000733/1 and
ST/P000495/1. KKM acknowledges support from the New York Community Trust Fund
for Astrophysical Research. AJ acknowledges support from FONDECYT project
1210718, and from ANID – Millennium Science Initiative – ICN12_009. LAdS is
supported by funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (project Four
Aces grant agreement No 724427).

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##  Appendix A Supplementary material

Time [BJD TDB] | RV [m s-1] | RV error [m s-1] | Instrument
---|---|---|---
TOI-148 |  |  |
2458384.515064 | -30660.46 | 30.42 | CORALIE
2458386.814005 | -37976.20 | 82.56 | CORALIE
2458408.719335 | -20372.36 | 85.21 | CORALIE
2458428.534714 | -20473.55 | 63.01 | CORALIE
2458479.532552 | -38130.30 | 191.13 | CORALIE
2458495.531823 | -25865.29 | 221.07 | CORALIE
2458496.547259 | -20001.33 | 122.21 | CORALIE
2458656.803753 | -20849.44 | 130.90 | CORALIE
2458657.770975 | -23724.86 | 115.92 | CORALIE
2458663.857660 | -35835.81 | 149.59 | CORALIE
2458679.761215 | -33895.58 | 178.17 | CORALIE
TOI-587 |  |  |
2458589.719888 | 376.98 | 1201.42 | TRES
2458594.622423 | -8024.60 | 637.52 | TRES
2458597.701320 | 3.14 | 821.62 | TRES
2458598.631813 | 1292.14 | 745.23 | TRES
2458599.640043 | 0.00 | 821.62 | TRES
2458601.636267 | -6391.02 | 604.17 | TRES
2458603.630556 | -6396.90 | 1140.20 | TRES
TOI-681 |  |  |
2458622.513448 | 26180.44 | 88.22 | CORALIE
2458654.485737 | 26094.93 | 78.95 | CORALIE
2458818.766341 | 16662.76 | 114.76 | CORALIE
2458819.812002 | 17277.56 | 102.12 | CORALIE
2458842.699941 | 27731.61 | 128.99 | CORALIE
2458850.641613 | 17162.30 | 84.73 | CORALIE
2458852.779240 | 18827.26 | 102.06 | CORALIE
2458857.727110 | 27269.20 | 85.20 | CORALIE
2458923.549796 | 24577.10 | 130.60 | CORALIE
2458641.493741 | 23125.7 | 349.9 | FEROS
2458643.486061 | 20111.0 | 213.9 | FEROS
2458645.490361 | 18394.8 | 331.0 | FEROS
2458652.498401 | 29384.2 | 605.8 | FEROS
TOI-746 |  |  |
2458777.827622 | 26662.93 | 63.11 | CORALIE
2458815.804367 | 39986.84 | 44.16 | CORALIE
2458820.773420 | 25318.60 | 40.97 | CORALIE
2458824.651474 | 35494.88 | 63.08 | CORALIE
2458830.772597 | 27610.22 | 45.59 | CORALIE
2458839.622606 | 38959.05 | 71.50 | CORALIE
2458844.682083 | 29562.96 | 70.22 | CORALIE
2458920.561788 | 26623.69 | 100.59 | CORALIE
2458798.773421 | 25294.4 | 10.3 | FEROS
2458804.702041 | 39780.9 | 7.9 | FEROS
TOI-1213 |  |  |
2458886.78385 | 19685.0 | 30.0 | CHIRON
2458909.72687 | 21761.0 | 29.0 | CHIRON
2458917.78559 | 19130.0 | 30.0 | CHIRON
2458883.615306 | 22638.52 | 24.61 | CORALIE
2458895.675990 | 34772.99 | 70.44 | CORALIE
2458920.746399 | 27968.23 | 57.41 | CORALIE
2458925.564278 | 31941.32 | 69.56 | CORALIE
2458882.839021 | 23064.1 | 6.0 | FEROS
2458908.787371 | 23728.5 | 7.6 | FEROS
2458915.735351 | 20533.3 | 7.2 | FEROS
Table 5: Radial Velocities Figure 14: Kinematic analysis of TOI-681 exhibiting
its membership to the open star cluster NGC 2516. Black points are NGC 2516
members reported by Cantat-Gaudin et al. (2018). Gray points are randomly
drawn from a cube in $\\{\alpha,\delta,\pi\\}$ centered on the cluster, with
side widths $\pm 4\sigma$, where $\sigma$ is the standard deviation of the
Cantat-Gaudin et al. (2018) cluster member right ascension, declination, and
parallax.

Star Name & Aliases: TOI 148, TIC 393940766, UCAC4 260-199322, 2MASS
J22331696-3809349
Parameter Unit Source Value Stellar Parameters $\alpha$ Right Ascension
(hh:mm:ss) TICv8 22:33:16.99 $\delta$ Declination (deg:min:sec) TICv8
-38:09:35.38 $V_{mag}$ V-band magnitude TICv8 12.40 $\varpi$ Parallax (mas)
GAIA DR2 $2.441\pm 0.017$ $v\sin i_{*}$ Surface Rotational Velocity (km s-1)
CORALIE $10.1\pm 0.8$ Parameter Unit Exofast Value Priors $M_{*}$ Mass
($\mathrm{M_{\odot}}$) - $0.97^{+0.12}_{-0.09}$ $R_{*}$ Radius
($\mathrm{R_{\odot}}$) $\mathcal{G\text{[1.192,0.068]}}$
$1.20^{+0.07}_{-0.07}$ $L_{*}$ Luminosity ($\mathrm{L_{\odot}}$) -
$1.66^{+0.26}_{-0.23}$ $\rho_{*}$ Density (cgs) - $0.80^{+0.17}_{-0.12}$
$\log{g}$ Surface gravity (cgs) - $4.27^{+0.06}_{-0.06}$ $T_{\rm eff}$
Effective Temperature (K) $\mathcal{G\text{[5975,150]}}$ $5990^{+140}_{-140}$
$[{\rm Fe/H}]$ Metallicity (dex) $\mathcal{G\text{[-0.28,0.28]}}$
$-0.24^{+0.25}_{-0.25}$ $Age$ Age (Gyr) - $7.7^{+3.7}_{-3.7}$ $EEP$ Equal
Evolutionary Point - $416^{+17}_{-41}$ Companion Parameters $M_{b}$ Mass
($\,M_{\rm J}$) - $77.1^{+5.8}_{-4.6}$ $R_{b}$ Radius ($\,R_{\rm J}$) -
$0.81^{+0.05}_{-0.06}$ $P$ Period (days) - $4.867103^{+0.000015}_{-0.000014}$
$T_{C}$ Time of conjunction ($\rm{BJD_{TDB}}$) -
$2458327.32980^{+0.00200}_{-0.00210}$ $a$ Semi-major axis (AU) -
$0.0571^{+0.0021}_{-0.0017}$ $i$ Inclination (Degrees) -
$86.85^{+0.65}_{-0.53}$ $e$ Eccentricity - $0.0052^{+0.0060}_{-0.0037}$
$\omega_{*}$ Argument of Periastron (Degrees) - $-63.0^{+87.0}_{-71.0}$
$T_{eq}$ Equilibrium temperature (K) - $1321^{+46}_{-49}$ $K$ RV semi-
amplitude (m/s) - $8950.0^{+51.0}_{-52.0}$ $\delta$ Transit depth (fraction) -
$0.00476^{+0.00017}_{-0.00017}$ $\tau$ Ingress/egress transit duration (days)
- $0.01280^{+0.00170}_{-0.00170}$ $T_{14}$ Total transit duration (days) -
$0.13790^{+0.00200}_{-0.00200}$ $b$ Transit Impact parameter -
$0.565^{+0.061}_{-0.088}$ $\rho_{P}$ Density (cgs) - $183.0^{+45.0}_{-32.0}$
log gP Surface gravity - $5.471^{+0.066}_{-0.059}$ $\langle F\rangle$ Incident
Flux (109 erg s-1 cm-2) - $0.69^{+0.10}_{-0.10}$
Wavelength Parameters R Sloani TESS $u_{1}$ linear limb-darkening coeff
$0.314^{+0.056}_{-0.055}$ $0.259^{+0.033}_{-0.031}$ $0.262^{+0.041}_{-0.040}$
$u_{2}$ quadratic limb-darkening coeff $0.304^{+0.051}_{-0.051}$
$0.291^{+0.026}_{-0.026}$ $0.294^{+0.035}_{-0.035}$
RV Parameters CORALIE $\gamma_{\rm rel}$ Relative RV Offset (m/s)
$-29137^{+52}_{-53}$ $\sigma_{J}$ RV Jitter (m/s) $69^{+23}_{-54}$
$\sigma_{J}^{2}$ RV Jitter Variance $4800^{+3600}_{-4500}$

  * •

Priors are for the EXOFASTv2 global model only, where
$\mathcal{G\text{[a,b]}}$ are Gaussian priors. The topmost parameters were not
modeled with EXOFASTv2 and the source of their value is displayed.

Table 6: TOI-148 stellar and companion parameters.

Star Name & Aliases: TOI 587, TIC 294090620, HD 74162, HIP 42654, TYC
6024-00943-1, 2MASS J08413504-2211395
Parameter Unit Source Value Stellar Parameters $\alpha$ Right Ascension
(hh:mm:ss) TICv8 08:41:35.02 $\delta$ Declination (deg:min:sec) TICv8
-22:11:39.47 $V_{mag}$ V-band magnitude TICv8 7.8 $\varpi$ Parallax (mas) Gaia
DR2 4.755$\pm$0.028 $v\sin i_{*}$ Surface Rotational Velocity (km s-1) TRES
34.0$\pm$2.0 Parameter Unit Exofast Value Priors $M_{*}$ Mass
($\mathrm{M_{\odot}}$) - $2.33^{+0.12}_{-0.12}$ $R_{*}$ Radius
($\mathrm{R_{\odot}}$) $\mathcal{G\text{[2.031,0.092]}}$
$2.01^{+0.09}_{-0.09}$ $L_{*}$ Luminosity ($\mathrm{L_{\odot}}$) -
$33.50^{+4.20}_{-3.90}$ $\rho_{*}$ Density (cgs) - $0.41^{+0.06}_{-0.05}$
$\log{g}$ Surface gravity (cgs) - $4.20^{+0.04}_{-0.04}$ $T_{\rm eff}$
Effective Temperature (K) $\mathcal{G\text{[9800,200]}}$ $9800^{+200}_{-200}$
$[{\rm Fe/H}]$ Metallicity (dex) $\mathcal{G\text{[0.07,0.12]}}$
$0.08^{+0.11}_{-0.12}$ $Age$ Age (Gyr) - $0.2^{+0.1}_{-0.1}$ $EEP$ Equal
Evolutionary Point - $326^{+11}_{-16}$ Companion Parameters $M_{b}$ Mass
($\,M_{\rm J}$) - $81.1^{+7.1}_{-7.0}$ $R_{b}$ Radius ($\,R_{\rm J}$) -
$1.32^{+0.07}_{-0.06}$ $P$ Period (days) - $8.043450^{+0.000730}_{-0.000720}$
$T_{C}$ Time of conjunction ($\rm{BJD_{TDB}}$) -
$2458520.15829^{+0.00053}_{-0.00053}$ $a$ Semi-major axis (AU) -
$0.1054^{+0.0018}_{-0.0018}$ $i$ Inclination (Degrees) -
$87.93^{+1.00}_{-0.63}$ $e$ Eccentricity - $0.0510^{+0.0490}_{-0.0360}$
$\omega_{*}$ Argument of Periastron (Degrees) - $70.0^{+100.0}_{-100.0}$
$T_{eq}$ Equilibrium temperature (K) - $2062^{+55}_{-56}$ $K$ RV semi-
amplitude (m/s) - $4580.0^{+360.0}_{-360.0}$ $\delta$ Transit depth (fraction)
- $0.00459^{+0.00008}_{-0.00008}$ $\tau$ Ingress/egress transit duration
(days) - $0.01660^{+0.00260}_{-0.00220}$ $T_{14}$ Total transit duration
(days) - $0.22080^{+0.00240}_{-0.00200}$ $b$ Transit Impact parameter -
$0.400^{+0.120}_{-0.200}$ $\rho_{P}$ Density (cgs) - $43.3^{+7.6}_{-6.5}$ log
gP Surface gravity - $5.059^{+0.053}_{-0.054}$ $\langle F\rangle$ Incident
Flux (109 erg s-1 cm-2) - $4.09^{+0.46}_{-0.42}$
Wavelength Parameters TESS $u_{1}$ linear limb-darkening coeff
$0.133^{+0.057}_{-0.058}$ $u_{2}$ quadratic limb-darkening coeff
$0.245^{+0.085}_{-0.086}$
RV Parameters TRES $\gamma_{\rm rel}$ Relative RV Offset (m/s)
$-3280^{+330}_{-320}$ $\sigma_{J}$ RV Jitter (m/s) $0^{+82}_{-0}$
$\sigma_{J}^{2}$ RV Jitter Variance $-100^{+6900}_{-6700}$

  * •

Priors are for the EXOFASTv2 global model only, where
$\mathcal{G\text{[a,b]}}$ are Gaussian priors. The topmost parameters were not
modeled with EXOFASTv2 and the source of their value is displayed.

Table 7: TOI-587 stellar and companion parameters.

Star Name & Aliases: TOI 681, TIC 410450228, TYC 8911-00495-1, UCAC4
148-012283, 2MASS J07513479-6024448
Parameter Unit Source Value Stellar Parameters $\alpha$ Right Ascension
(hh:mm:ss) TICv8 07:51:34.79 $\delta$ Declination (deg:min:sec) TICv8
-60:24:44.6 $V_{mag}$ V-band magnitude TICv8 10.885 $\varpi$ Parallax (mas)
GAIA DR2 2.442$\pm$0.013 $v\sin i_{*}$ Surface Rotational Velocity (km s-1)
GALAH $30.80\pm 0.78$ Parameter Unit Exofast Value Priors $M_{*}$ Mass
($\mathrm{M_{\odot}}$) - $1.54^{+0.06}_{-0.05}$ $R_{*}$ Radius
($\mathrm{R_{\odot}}$) $\mathcal{G\text{[1.586,0.067]}}$
$1.47^{+0.04}_{-0.04}$ $L_{*}$ Luminosity ($\mathrm{L_{\odot}}$) -
$5.98^{+0.65}_{-0.58}$ $\rho_{*}$ Density (cgs) - $0.68^{+0.05}_{-0.05}$
$\log{g}$ Surface gravity (cgs) - $4.29^{+0.02}_{-0.02}$ $T_{\rm eff}$
Effective Temperature (K) $\mathcal{G\text{[7390,150]}}$ $7440^{+150}_{-140}$
$[{\rm Fe/H}]$ Metallicity (dex) $\mathcal{G\text{[-0.12,0.05]}}$
$-0.08^{+0.05}_{-0.05}$ $Age$ Age (Gyr) $\mathcal{G\text{[0.170,0.025]}}$
$0.170^{+0.025}_{-0.025}\dagger$ $EEP$ Equal Evolutionary Point -
$264^{+6}_{-7}$ Companion Parameters $M_{b}$ Mass ($\,M_{\rm J}$) -
$88.7^{+2.5}_{-2.3}$ $R_{b}$ Radius ($\,R_{\rm J}$) [0,5]
$1.52^{+0.25}_{-0.15}$ $P$ Period (days) - $15.778482^{+0.000026}_{-0.000026}$
$T_{C}$ Time of conjunction - 2450000 ($\rm{BJD_{TDB}}$) -
$2458546.47759^{+0.00068}_{-0.00069}$ $a$ Semi-major axis (AU) -
$0.1449^{+0.0018}_{-0.0017}$ $i$ Inclination (Degrees) -
$87.62^{+0.09}_{-0.11}$ $e$ Eccentricity - $0.0930^{+0.0220}_{-0.0190}$
$\omega_{*}$ Argument of Periastron (Degrees) - $-86.5^{+7.2}_{-5.6}$ $T_{eq}$
Equilibrium temperature (K) - $1143^{+26}_{-25}$ $K$ RV semi-amplitude (m/s) -
$5209.0^{+72.0}_{-67.0}$ $\delta$ Transit depth (fraction) -
$0.01120^{+0.00340}_{-0.00170}$ $\tau$ Ingress/egress transit duration (days)
- $0.07207^{+0.00085}_{-0.00084}$ $T_{14}$ Total transit duration (days) -
$0.14410^{+0.00170}_{-0.00170}$ $b$ Transit Impact parameter -
$0.958^{+0.025}_{-0.017}$ $\rho_{P}$ Density (cgs) - $31.0^{+11.0}_{-11.0}$
log gP Surface gravity - $4.979^{+0.086}_{-0.130}$ $\langle F\rangle$ Incident
Flux (109 erg s-1 cm-2) - $0.38^{+0.04}_{-0.03}$
Wavelength Parameters B I R Sloang TESS $u_{1}$ linear limb-darkening coeff
$0.362^{+0.048}_{-0.048}$ $0.180^{+0.034}_{-0.034}$ $0.132^{+0.046}_{-0.046}$
$0.376^{+0.045}_{-0.045}$ $0.153^{+0.033}_{-0.033}$ $u_{2}$ quadratic limb-
darkening coeff $0.336^{+0.049}_{-0.049}$ $0.350^{+0.034}_{-0.035}$
$0.278^{+0.047}_{-0.048}$ $0.370^{+0.046}_{-0.047}$ $0.320^{+0.033}_{-0.034}$
RV Parameters CORALIE FEROS $\gamma_{\rm rel}$ Relative RV Offset (m/s)
$22120^{+96}_{-87}$ $23750^{+140}_{-140}$ $\sigma_{J}$ RV Jitter (m/s)
$95^{+3}_{-7}$ $0^{+0}_{-0}$ $\sigma_{J}^{2}$ RV Jitter Variance
$9040^{+710}_{-1400}$ $-23000^{+21000}_{-16000}$

  * •

Priors are for the EXOFASTv2 global model only, where
$\mathcal{G\text{[a,b]}}$ are Gaussian priors and priors in brackets represent
hard limit priors. The topmost parameters were not modeled with EXOFASTv2 and
the source of their value is displayed.
$\dagger$Age of cluster NGC 2516.

Table 8: TOI-681 stellar and companion parameters.

Star Name & Aliases: TOI 746, TIC 167418903, TYC 9177-00082-1, UCAC4
112-012172, 2MASS J06382899-6738563
Parameter Unit Source Value Stellar Parameters $\alpha$ Right Ascension
(hh:mm:ss) TICv8 06:38:28.99 $\delta$ Declination (deg:min:sec) TICv8
-67:38:56.22 $V_{mag}$ V-band magnitude TICv8 11.807 $\varpi$ Parallax (mas)
GAIA DR2 4.167$\pm$0.014 $v\sin i_{*}$ Surface Rotational Velocity (km s-1)
CORALIE 6.1$\pm$1.2 Parameter Unit Exofast Value Priors $M_{*}$ Mass
($\mathrm{M_{\odot}}$) - $0.94^{+0.09}_{-0.08}$ $R_{*}$ Radius
($\mathrm{R_{\odot}}$) $\mathcal{G\text{[0.957,0.051]}}$
$0.97^{+0.04}_{-0.03}$ $L_{*}$ Luminosity ($\mathrm{L_{\odot}}$) -
$0.89^{+0.12}_{-0.11}$ $\rho_{*}$ Density (cgs) - $1.45^{+0.12}_{-0.13}$
$\log{g}$ Surface gravity (cgs) - $4.44^{+0.03}_{-0.03}$ $T_{\rm eff}$
Effective Temperature (K) $\mathcal{G\text{[5700,150]}}$ $5690^{+140}_{-140}$
$[{\rm Fe/H}]$ Metallicity (dex) $\mathcal{G\text{[0.01,0.29]}}$
$-0.02^{+0.23}_{-0.23}$ $Age$ Age (Gyr) - $6.5^{+4.3}_{-3.9}$ $EEP$ Equal
Evolutionary Point - $368^{+30}_{-32}$ Companion Parameters $M_{b}$ Mass
($\,M_{\rm J}$) - $82.2^{+4.9}_{-4.4}$ $R_{b}$ Radius ($\,R_{\rm J}$) -
$0.95^{+0.09}_{-0.06}$ $P$ Period (days) - $10.980303^{+0.000011}_{-0.000011}$
$T_{C}$ Time of conjunction - 2450000 ($\rm{BJD_{TDB}}$) -
$2458335.77067^{+0.00054}_{-0.00054}$ $a$ Semi-major axis (AU) -
$0.0973^{+0.0028}_{-0.0026}$ $i$ Inclination (Degrees) -
$87.03^{+0.11}_{-0.14}$ $e$ Eccentricity - $0.1985^{+0.0029}_{-0.0031}$
$\omega_{*}$ Argument of Periastron (Degrees) - $116.5^{+1.0}_{-1.0}$ $T_{eq}$
Equilibrium temperature (K) - $867^{+26}_{-25}$ $K$ RV semi-amplitude (m/s) -
$7565.0^{+21.0}_{-22.0}$ $\delta$ Transit depth (fraction) -
$0.01014^{+0.00140}_{-0.00091}$ $\tau$ Ingress/egress transit duration (days)
- $0.04163^{+0.00071}_{-0.00380}$ $T_{14}$ Total transit duration (days) -
$0.08340^{+0.00130}_{-0.00130}$ $b$ Transit Impact parameter -
$0.911^{+0.014}_{-0.010}$ $\rho_{P}$ Density (cgs) - $119.0^{+24.0}_{-27.0}$
log gP Surface gravity - $5.355^{+0.052}_{-0.075}$ $\langle F\rangle$ Incident
Flux (109 erg s-1 cm-2) - $0.12^{+0.01}_{-0.01}$
Wavelength Parameters Sloan $u$ Sloan $z$ TESS V $u_{1}$ linear limb-darkening
coeff $0.830^{+0.088}_{-0.095}$ $0.254^{+0.042}_{-0.042}$
$0.312^{+0.045}_{-0.045}$ $0.469^{+0.067}_{-0.065}$ $u_{2}$ quadratic limb-