# An eccentric Brown Dwarf eclipsing an M dwarf

Caleb I. Cañas NASA Earth and Space Science Fellow  Department of Astronomy &
Astrophysics, The Pennsylvania State University, 525 Davey Laboratory,
University Park, PA 16802, USA  Center for Exoplanets and Habitable Worlds,
The Pennsylvania State University, 525 Davey Laboratory, University Park, PA
16802, USA  Suvrath Mahadevan Department of Astronomy & Astrophysics, The
Pennsylvania State University, 525 Davey Laboratory, University Park, PA
16802, USA  Center for Exoplanets and Habitable Worlds, The Pennsylvania State
University, 525 Davey Laboratory, University Park, PA 16802, USA  Chad F.
Bender Steward Observatory, The University of Arizona, 933 N. Cherry Ave,
Tucson, AZ 85721, USA  Noah Isaac Salazar Rivera Steward Observatory, The
University of Arizona, 933 N. Cherry Ave, Tucson, AZ 85721, USA  Andrew Monson
Department of Astronomy & Astrophysics, The Pennsylvania State University, 525
Davey Laboratory, University Park, PA 16802, USA  Corey Beard Department of
Physics & Astronomy, The University of California, Irvine, Irvine, CA 92697,
USA  Jack Lubin Department of Physics & Astronomy, The University of
California, Irvine, Irvine, CA 92697, USA  Paul Robertson Department of
Physics & Astronomy, The University of California, Irvine, Irvine, CA 92697,
USA  Arvind F. Gupta Department of Astronomy & Astrophysics, The Pennsylvania
State University, 525 Davey Laboratory, University Park, PA 16802, USA  Center
for Exoplanets and Habitable Worlds, The Pennsylvania State University, 525
Davey Laboratory, University Park, PA 16802, USA  William D. Cochran McDonald
Observatory and Center for Planetary Systems Habitability, The University of
Texas at Austin, Austin, TX 78730, USA  Connor Fredrick Associate of the
National Institute of Standards and Technology, 325 Broadway, Boulder, CO
80305, USA  Department of Physics, University of Colorado, 2000 Colorado
Avenue, Boulder, CO 80309, USA  Fred Hearty Department of Astronomy &
Astrophysics, The Pennsylvania State University, 525 Davey Laboratory,
University Park, PA 16802, USA  Center for Exoplanets and Habitable Worlds,
The Pennsylvania State University, 525 Davey Laboratory, University Park, PA
16802, USA  Sinclaire Jones Department of Astrophysical Sciences, Princeton
University, 4 Ivy Lane, Princeton, NJ 08540, USA  Shubham Kanodia Department
of Astronomy & Astrophysics, The Pennsylvania State University, 525 Davey
Laboratory, University Park, PA 16802, USA  Center for Exoplanets and
Habitable Worlds, The Pennsylvania State University, 525 Davey Laboratory,
University Park, PA 16802, USA  Andrea S.J. Lin Department of Astronomy &
Astrophysics, The Pennsylvania State University, 525 Davey Laboratory,
University Park, PA 16802, USA  Center for Exoplanets and Habitable Worlds,
The Pennsylvania State University, 525 Davey Laboratory, University Park, PA
16802, USA  Joe P. Ninan Department of Astronomy & Astrophysics, The
Pennsylvania State University, 525 Davey Laboratory, University Park, PA
16802, USA  Center for Exoplanets and Habitable Worlds, The Pennsylvania State
University, 525 Davey Laboratory, University Park, PA 16802, USA  Lawrence W.
Ramsey Department of Astronomy & Astrophysics, The Pennsylvania State
University, 525 Davey Laboratory, University Park, PA 16802, USA  Center for
Exoplanets and Habitable Worlds, The Pennsylvania State University, 525 Davey
Laboratory, University Park, PA 16802, USA  Christian Schwab Department of
Physics and Astronomy, Macquarie University, Balaclava Road, North Ryde, NSW
2109, Australia  Guðmundur Stefánsson Henry Norris Russell Fellow  Department
of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ
08540, USA

###### Abstract

We report the discovery of a $M=67\pm 2\mathrm{M_{J}}$ brown dwarf transiting
the early M dwarf TOI-2119 on an eccentric orbit ($e=0.3362\pm 0.0005$) at an
orbital period of $7.200861\pm 0.000005$ days. We confirm the brown dwarf
nature of the transiting companion using a combination of ground-based and
space-based photometry and high-precision velocimetry from the Habitable-zone
Planet Finder. Detection of the secondary eclipse with TESS photometry enables
a precise determination of the eccentricity and reveals the brown dwarf has a
brightness temperature of $2100\pm 80$ K, a value which is consistent with an
early L dwarf. TOI-2119 is one of the most eccentric known brown dwarfs with
$P<10$ days, possibly due to the long circularization timescales for an object
orbiting an M dwarf. We assess the prospects for determining the obliquity of
the host star to probe formation scenarios and the possibility of additional
companions in the system using Gaia EDR3 and our radial velocities.

Stars: Brown dwarfs, Eclipsing binary stars, Fundamental parameters of stars

††facilities: ASAS, Gaia, HET (HPF), PO:1.2m (ZTF), PO:1.5m (ZTF), Shane,
SuperWASP, TESS, WIYN (NESSI)††software:  allesfitter (Günther & Daylan,
2019), astroquery (Ginsburg et al., 2019), astropy (Astropy Collaboration et
al., 2018), barycorrpy (Kanodia & Wright, 2018), dynesty (Speagle, 2020), ellc
(Maxted, 2016), EXOFASTv2 (Eastman et al., 2019), HPF-SERVAL, HPF-SpecMatch,
juliet (Espinoza et al., 2019), matplotlib (Hunter, 2007), numpy (van der Walt
et al., 2011), pandas (McKinney, 2010), scipy (Virtanen et al., 2020), telfit
(Gullikson et al., 2014), thejoker (Price-Whelan et al., 2017)

##  1 Introduction

Brown dwarfs are objects with radii comparable to Jupiter and masses between
$13\sim 80\mathrm{M_{J}}$ (see Chabrier & Baraffe, 2000; Burrows et al.,
2001), although this lower limit is not well defined if these objects are
classified on the basis of their formation mechanism (e.g., Chabrier et al.,
2014). As isolated objects, brown dwarfs have traditionally been identified
via photometric surveys by their colors (e.g., Pinfield et al., 2008; Zhang et
al., 2009; Folkes et al., 2012; Reylé, 2018) because their spectral energy
distribution peaks in the near-infrared. Brown dwarfs contain complex spectral
features that are difficult to model and existing evolutionary models are
largely degenerate in age, radius, and metallicity. This makes it difficult to
determine fundamental properties, such as the mass and radius, for isolated
brown dwarfs. When these objects are eclipsing companions to a main-sequence
star, photometric and spectroscopic observations yield a measurement of the
mass and radius.

Brown dwarfs are infrequent companions ($\lesssim 1\%$) to main sequence stars
(e.g., Vogt et al., 2002; Patel et al., 2007; Wittenmyer et al., 2009;
Sahlmann et al., 2011; Nielsen et al., 2019), but previous radial velocity
(RV) surveys have facilitated their study (e.g., Campbell et al., 1988; Marcy
& Butler, 2000; Wittenmyer et al., 2009; Sahlmann et al., 2011; Bonfils et
al., 2013). These surveys have revealed the “brown dwarf desert” (e.g., Marcy
& Butler, 2000; Grether & Lineweaver, 2006) or the apparent paucity of brown
dwarf companions to main sequence stars within $\sim 3$ au. This feature has
been attributed to the different formation mechanisms between low and high-
mass companion brown dwarfs (see Ma & Ge, 2014; Chabrier et al., 2014) where
high-mass brown dwarfs ($\gtrsim 43\mathrm{M_{J}}$) are believed to form
through molecular cloud fragmentation, similar to a binary stellar companion,
while low-mass brown dwarfs form through gravitational instabilities in the
protoplanetary disk.

Another factor that may sculpt the brown dwarf desert is the orbital migration
and tidal in-spiral (e.g., Armitage & Bonnell, 2002; Pätzold & Rauer, 2002;
Damiani & Díaz, 2016) of brown dwarf companions. Damiani & Díaz (2016) note
that tidal interactions with the host star and angular momentum loss through
magnetic braking can lead to rapid in-spiral of a brown dwarf companion
orbiting main sequence dwarfs with outer convective envelopes. The in-spiral
time scale is a strong function of stellar radius, such that early M dwarfs
like TOI-2119, have larger in-spiral timescales than later main sequence
dwarfs. This enables close brown dwarf companions to exist for a longer time
despite the more efficient tidal dissipation and magnetic braking mechanisms
present in M dwarfs. Carmichael et al. (2020) noted that while there was no
obvious trend in the frequency of brown dwarfs with stellar host type, a large
percent of well-characterized (with mass and radius measurements) brown dwarfs
(6/23 or $\sim 26\%$ of the then known brown dwarfs) were found to transit M
dwarfs. This appears contrary to the occurrence of Jupiter-sized exoplanets,
in which the occurrence rate of these planets decreases for M dwarf host stars
(e.g.; Endl et al., 2006; Johnson et al., 2010; Bonfils et al., 2013;
Maldonado et al., 2020). Currently, there are 5 well-characterized Jupiter-
sized planets transiting M dwarfs and 8 transiting M dwarf - brown dwarf
systems (including TOI-2119; Carmichael et al., 2020; Artigau et al., 2021).
More masses and radii for brown dwarf companions are needed to probe any
dependence on stellar host type.

In this paper, we present a new M dwarf system, TOI-2119, hosting a high-mass
brown dwarf on a $\sim 7.2$-day eccentric orbit. We confirm the brown dwarf
nature of TOI-2119.01 using space-based photometry from the Transiting
Exoplanet Satellite (TESS Ricker et al., 2015), additional ground-based
photometry, adaptive optics (AO) imaging with the ShaneAO instrument (Srinath
et al., 2014) on the 3 m Shane Telescope at Lick Observatory, and near-
infrared (NIR) RVs with the northern spectrograph of the APO Galaxy Evolution
Experiment (APOGEE-2N; Majewski et al., 2017; Zasowski et al., 2017) and the
Habitable-zone Planet Finder Spectrograph (HPF; Mahadevan et al., 2012, 2014).

The paper is structured as follows: Section 2 presents the observations used
in this paper, Section 3 describes the method for spectroscopic
characterization and our best estimates of the stellar parameters, and Section
4 explains the analysis of the photometric and RV data. A discussion of the
bulk properties of TOI-2119 in context of other transiting brown dwarfs with
masses is presented in Section 5. We conclude the paper in Section 6 with a
summary of our key results.

##  2 Observations

###  2.1 TESS

TESS observed TOI-2119 (Gaia EDR3 1303675097215915264) in short-cadence mode
during Sectors 24 and 25 with data spanning 2020 Apr 16 through 2020 June 08.
It has one transiting candidate, TOI-2119.01, identified by the TESS Science
Processing Operations Center pipeline (SPOC Jenkins et al., 2016) with an
orbital period of $\sim 7.2$ days. The “quick-look pipeline” developed by
Huang et al. (2020) also detected TOI-2119.01 as a target of interest in the
full-frame image data of Sectors 24 and 25.

For this work, we use the pre-search data-conditioned (PDCSAP; Jenkins et al.,
2016) light curves available at the Mikulski Archive for Space Telescopes
(MAST). The PDCSAP photometry is corrected for instrumental systematics and
dilution from other objects contained within the aperture using algorithms
that were originally developed for the Kepler mission (Stumpe et al., 2012;
Smith et al., 2012). Observations with non-zero data quality flags that
indicate anomalous data due to various conditions, such as spacecraft events
or cosmic ray hits, are excluded from the analysis. The quality flags are
described in the TESS Science Data Products Description Document (Table 28 in
Tenenbaum & Jenkins, 2018). Figure 1 displays the photometry and the transits
observed by TESS. The TESS photometry reveals TOI-2119 to be an active,
flaring star and, to remove the flares, we reject any median normalized
observation larger than 1.01. We perform no additional outlier rejection
beyond the data quality flags and application of a threshold value.

Figure 1: (a) displays the PDCSAP photometry from TESS. The light curve
reveals a periodic $\sim 5\%$ signal around a flaring, active M dwarf. The
dashed line is the threshold of 1.01 which is used to flag data during flares.
(b) shows the transit after phasing the raw PDCSAP photometry from (a) to the
period and ephemeris determined by the SPOC pipeline. The large circles
represent 10-min bins of the phase-folded data. (c) is similar to (b) and
presents the TESS occultation. (d) shows the phase-folded TMMT photometry.

###  2.2 TMMT

We observed one transit of TOI-2119.01 using the robotic Three-hundred
MilliMeter Telescope (TMMT; Monson et al., 2017) at Las Campanas Observatory
(LCO) on the night of 2021 April 13. The observations were performed slightly
out of focus in the Bessell $I$ filter (Bessell, 1990) with a point spread
function FWHM of $4\arcsec$. We obtained 107 frames using an exposure time of
100s while operating in a 1x1 binning mode. In this mode, TMMT has a 13s
readout time between exposures, resulting in an effective cadence of 113s and
an observing efficiency of 90%. The observations began at airmass 5.29 and
ended at airmass 1.76.

We processed the photometry using AstroImageJ (Collins et al., 2017) following
the procedures described in Stefánsson et al. (2017). The light curve was
extracted using simple aperture photometry with an object aperture radius of 6
pixels (7.2″), and inner and outer sky annuli of 10 pixels (12″) and 15 pixels
(17.9″), respectively, because these values minimized the standard deviation
in the residuals. Following Stefánsson et al. (2017), we added the expected
scintillation-noise errors in quadrature to the photometric error (including
photon, readout, dark, sky background, and digitization noise). Figure 1(d)
displays the photometry from TMMT.

###  2.3 Doppler Spectroscopy with APOGEE-2N

TOI-2119 was observed from the Apache Point Observatory on 11 and 12 May 2018
using APOGEE-2N, a multiplexed, high-resolution ($R\sim 22,500$, NIR
($\lambda\sim 1.5-1.7$ micron) fiber-fed spectrograph (Wilson et al., 2012,
2019) that is mounted on the Sloan 2.5-meter telescope (Gunn et al., 2006).
The APOGEE-2N spectrograph was used as part of a survey in SDSS-IV (Blanton et
al., 2017) with the primary goal of studying the galactic evolution of the
Milky Way through the chemical and dynamical analysis of various stellar
populations and Galactic regions.

For this work, we use the publicly available DR16 (Jönsson et al., 2020) data
of TOI-2119. The APOGEE data pipeline (Nidever et al., 2015) performs sky
subtraction, telluric and barycentric correction, and wavelength and flux
calibration for each observation of TOI-2119. The RVs were derived following
the procedure described in Cañas et al. (2019). Briefly, we identified the
best-fit synthetic spectrum by cross-correlating the highest S/N spectra using
synthetic spectra generated from MARCs models (Gustafsson et al., 2008) that
were specifically generated for the APOGEE-2N survey (see Mészáros et al.,
2012; Zamora et al., 2015; Holtzman et al., 2018). The synthetic spectrum with
the largest correlation was used in the final cross-correlation to obtain the
reported radial velocities in Table 1. The uncertainties for each observation
were calculated by following the maximum-likelihood approach presented by
Zucker (2003). The derived RVs, the $1\sigma$ uncertainties, and the S/N per
resolution element ($\sim 2$ pixels) are presented in Table 1.

###  2.4 High-resolution Doppler Spectroscopy with HPF

We obtained eight 945-second visits of TOI-2119 using HPF with a median
signal-to-noise ratio (S/N) per 1D extracted pixel of 168 at
$1000\,\mathrm{nm}$. HPF is a high-resolution ($R\sim 55,000$), fiber-fed
(Kanodia et al., 2018), NIR ($\lambda\sim 8080-12780$ Å) spectrograph located
on the 10m Hobby-Eberly Telescope (HET) at McDonald Observatory in Texas
(Mahadevan et al., 2012, 2014) that achieves a long-term temperature stability
of $\sim$1$\,\mathrm{mK}$ (Stefánsson et al., 2016). The observations span 19
September 2020 through 26 May 2021 and were executed in a queue by the HET
resident astronomers (Shetrone et al., 2007).

The HxRGproc tool was used to process the raw HPF data and perform bias noise
removal, nonlinearity correction, cosmic-ray correction, and slope/flux and
variance image calculation (Ninan et al., 2018). The one-dimensional spectra
were reduced using the procedures in Ninan et al. (2018), Kaplan et al.
(2019), and Metcalf et al. (2019). The wavelength solution and drift
correction applied to the data was extrapolated from laser frequency comb
(LFC) frames that were taken as part of standard evening and morning
calibrations and from LFC calibration frames obtained periodically throughout
the night. The extrapolation from LFC frames enables precise wavelength
calibration on the order of $<30\,\mathrm{cm/s}$ (Stefánsson et al., 2020), a
value which is smaller than the photon noise for TOI-2119 (median RV
uncertainty of $48.5$ m/s).

We used a modified version (see Stefánsson et al., 2020) of the SERVAL code
(SpEctrum Radial Velocity AnaLyser; Zechmeister et al., 2018) to calculate
RVs. SERVAL employs the template-matching technique to derive RVs (e.g.,
Anglada-Escudé & Butler, 2012) and creates a master template from the
observations to determine the Doppler shift by minimizing the $\chi^{2}$
statistic. The master template was generated from all observed spectra while
masking telluric regions identified using a synthetic telluric-line mask
generated from telfit (Gullikson et al., 2014). The barycentric correction for
each epoch was calculated using barycorrpy (Kanodia & Wright, 2018) which
implements the algorithms from Wright & Eastman (2014). The derived HPF RVs,
the $1\sigma$ uncertainties, and the S/N per pixel at 1000 nm for TOI-2119 are
presented in Table 1.

Table 1: RVs of TOI-2119.  $\,\mathrm{BJD_{TDB}}$ | RV | $\sigma$ | S/N
---|---|---|---
| $(\,\mathrm{m/s})$ | $(\,\mathrm{m/s})$ |
APOGEE-2N:
2458249.80011 | $-18688$ | 213 | 226aaThe APOGEE-2N S/N is the median value per resolution element ($\sim 2$ pixels). For comparison, HPF has a resolution $2.5-3$ times that of APOGEE-2N with a resolution element and PSF that each span $\sim 3$ pixels.
2458250.84530 | $-11816$ | 209 | 163
HPF:
2459111.58596 | $-17407$ | 15 | 108bbThe HPF S/N is the median value per 1D extracted pixel at 1000 nm. All exposure times for HPF are 945 s.
2459117.57945 | $-12063$ | 17 | 93
2459231.02335 | 1908 | 10 | 164
2459232.02920 | $-4353$ | 9 | 175
2459238.00846 | $-319$ | 9 | 169
2459247.00784 | $-10639$ | 8 | 197
2459300.84858 | $-16666$ | 13 | 124
2459360.90067 | 2871 | 7 | 226

###  2.5 Adaptive Optics Imaging

TOI-2119 was observed in the $K_{s}$ band with the ShARCS camera on the Shane
3m telescope at Lick Observatory (Srinath et al., 2014). It was observed under
natural guide star mode using the 5-point dither process described in Furlan
et al. (2017). The seeing was $\sim 2\arcsec{}$ during the observations. The
data were reduced using a custom AO pipeline developed that rejects all
overexposed or underexposed images and excludes data that are flagged as
erroneous (e.g., due to lost guiding, shutters closed early due to weather,
etc.). The pipeline applies standard dark correction, flat correction, and a
sigma clipping process to all images. A master sky image is produced from the
5-point dither process which is subtracted from each image. The final image is
produced by interpolating all images onto a single centroid. A $5\sigma$
contrast curve is generated from the final image using the algorithms
described in Espinoza et al. (2016) and is presented in Figure 2. The poor
seeing during the night TOI-2119 was observed prevents any constraints
$<0.83\arcsec{}$ (marked as the hatched region in Figure 2). There are no
bright companions ($\Delta K_{s}<4$) that could be a source of contamination
in the photometry at separations of $0.83\arcsec{}-6.5\arcsec{}$ from
TOI-2119.

Figure 2: Above is the $5\sigma$ contrast curve obtained using the ShARCS
camera in the $K_{s}$ filter. ShaneAO cannot place constraints within the
hatched region ($<0.83\arcsec{}$) due to poor seeing ($\sim 2\arcsec{}$)
during the observation. The data show there are no bright companions ($\Delta
K_{s}<4$) at separations of $0.83\arcsec{}-6.5\arcsec{}$ from the host star.
The inset image is a cutout centered on TOI-2119 where the scale bar reflects
1″.

###  2.6 Speckle Imaging

We used NESSI (Scott et al., 2018) on the 3.5 m WIYN Telescope at KPNO to
perform speckle imaging on 2021 October 26. TOI-2119 was observed in two
narrowband filters centered at 562nm and 832nm. The images in each filter were
reconstructed following the procedures outlined in Howell et al. (2011). The
NESSI contrast curves in both filters are shown in Figure 3, along with an
inset of the image in the 832nm narrowband filter. The NESSI data show no
evidence of blending from a bright companion $\Delta\mathrm{Mag}<4$ at
separations of $0.15-1.2\arcsec$.

Figure 3: The $5\sigma$ contrast curve obtained using NESSI in the narrowband
filters centered at 562nm and 832nm showing no bright companions
($\Delta\mathrm{Mag}<4$) between $0.15-1.2^{\prime\prime}$ from the host star.
NESSI cannot place constraints within the hatched region ($<0.05\arcsec{}$)
The inset image is the 832nm narrowband filter centered on TOI-2119 where the
scale bar reflects 1″.

###  2.7 Non-detection of Spectroscopic Companions within 2”

The fibers for APOGEE-2N have a field-of-view of 2″ (see Wilson et al., 2019)
and we use the $H$-band APOGEE-2N spectra to search for light from secondary
stars around TOI-2119. We employ the software binspec_plus, which is based on
binspec (El-Badry et al., 2018b, a), to search for the faint spectrum of a
second star by modeling the observed spectrum as the sum of two model spectra.
binspec was designed to fit both single and double-lined spectra, but its
sensitivity is limited to the detection of moderate-mass ratio binaries
($0.4\lesssim q\lesssim 0.85$) because of the limited temperature regime of
the spectral models.
binspec_plus111https://github.com/tingyuansen/binspec_plus/ extends the
spectral model to include redder dwarfs and giants. We fit the APOGEE-2N
spectrum of the TOI-2119 with a neural network spectral model (see Ting et
al., 2019) trained on the Kurucz stellar library (Kurucz, 1979) that is valid
for slowly rotating ($v\sin i<45\,\mathrm{km\ s^{-1}}$) main-sequence stars in
the regime of $3000\mathrm{K}<T_{e}<7000\,\mathrm{K}$, $4.0<\log g<5.0$, and
$-1<\mathrm{[Fe/H]}<0.5$. The model selection criterion from Table B1 of El-
Badry et al. (2018b) relies on two values,
$\Delta\chi^{2}=\chi^{2}_{\mathrm{single}}-\chi^{2}_{\mathrm{binary}}$, which
quantifies how better a fit is obtained by the binary model, and the
improvement fraction, $f_{imp}$, which describes how better the binary model
fit is relative to how different it is from a single-star model. TOI-2119 is
classified as a single-lined spectroscopic binary (SB1) because both
$\Delta\chi^{2}$ and $f_{imp}$ are improved relative to a single-star model,
but a binary component fit is disfavored and shows negligible improvement in
the fit when compared to the SB1 fit ($\Delta\chi^{2}<3000$ and $f_{imp}<0$).
This analysis of the APOGEE-2N data reveals no evidence for secondary light
within 2″ from companion or background dwarf stars with
$3000\mathrm{K}<T_{e}<7000\,\mathrm{K}$.

##  3 Stellar Parameters

###  3.1 Spectroscopic Parameters

The spectroscopic stellar parameters ($T_{e}$, $\log g$, and [Fe/H]) for
TOI-2119 were calculated using the HPF-
SpecMatch222https://gummiks.github.io/hpfspecmatch/ package (Stefánsson et
al., 2020, S. Jones et. al. 2022, in prep.), which employs the empirical
template matching methodology discussed in Yee et al. (2017). HPF-SpecMatch
derives the stellar properties by comparing the highest S/N observed spectra
to a library of high quality ($\,\mathrm{S/N}>100$) HPF stellar spectra with
well-determined properties (values adopted from Yee et al., 2017). It
identifies the best-matching library spectrum using $\chi^{2}$ minimization,
creates a composite spectrum from a weighted, linear combination of the five
best-matching library spectra, and derives the stellar properties using these
weights. The reported uncertainty for each stellar parameter is the standard
deviation of the residuals from a leave-one-out cross-validation procedure
applied to the entire HPF library in the chosen spectral order.

The library contains 166 stars and spans the following parameter space:
$2700\,\mathrm{K}<T_{e}<6000\,\mathrm{K}$, $4.3<\log g<5.4$, and
$-0.5<\mathrm{[Fe/H]}<0.5$. We used HPF order index 17 (spanning $10460-10570$
Å) for the spectral matching of TOI-2119 because it has little to no telluric
contamination. Table 2 lists the derived spectroscopic parameters with their
uncertainties.

Table 2: Summary of Stellar Parameters.

Parameter | Description | Value | Reference
---|---|---|---
Main identifiers:
TIC | $\cdots$ | 236387002 | TIC
Gaia EDR3 | $\cdots$ | 1303675097215915264 | Gaia EDR3
Equatorial Coordinates, Proper Motion, Distance, and Maximum Extinction:
$\alpha_{\mathrm{J2016}}$ | Right Ascension (RA) | 16:17:43.17 | Gaia EDR3
$\delta_{\mathrm{J2016}}$ | Declination (Dec) | 26:18:15.16 | Gaia EDR3
$\mu_{\alpha}$ | Proper motion (RA, $\,\mathrm{mas/yr}$) | $-29.27\pm 0.02$ | Gaia EDR3
$\mu_{\delta}$ | Proper motion (Dec, $\,\mathrm{mas/yr}$) | $6.86\pm 0.03$ | Gaia EDR3
$d$ | Distance in pca | $31.46\pm 0.03$ | Bailer-Jones
$A_{V,max}$ | Maximum visual extinction | $0.01$ | Green
Optical and near-infrared magnitudes:
$B$ | Johnson $B$ mag | $13.86\pm 0.03$ | APASS
$V$ | Johnson $V$ mag | $12.37\pm 0.04$ | APASS
$g^{\prime}$ | Sloan $g^{\prime}$ mag | $13.07\pm 0.02$ | APASS
$r^{\prime}$ | Sloan $r^{\prime}$ mag | $11.76\pm 0.02$ | APASS
$i^{\prime}$ | Sloan $i^{\prime}$ mag | $10.75\pm 0.02$ | APASS
$J$ |  $J$ mag | $8.98\pm 0.02$ | 2MASS
$H$ |  $H$ mag | $8.39\pm 0.03$ | 2MASS
$K_{s}$ |  $K_{s}$ mag | $8.14\pm 0.02$ | 2MASS
$W1$ | WISE1 mag | $8.05\pm 0.02$ | WISE
$W2$ | WISE2 mag | $7.97\pm 0.02$ | WISE
$W3$ | WISE3 mag | $7.88\pm 0.02$ | WISE
$W4$ | WISE4 mag | $7.8\pm 0.2$ | WISE
Spectroscopic Parametersb:
$T_{e}$ | Effective temperature in $\,\mathrm{K}$ | $3553\pm 67$ | This work
$\mathrm{[Fe/H]}$ | Metallicity in dex | $0.1\pm 0.1$ | This work
$\log(g)$ | Surface gravity in cgs units | $4.74\pm 0.04$ | This work
Model-Dependent Stellar SED and Isochrone fit Parametersc:
$M_{\star}$ | Mass in $M_{\odot}$ | $0.53\pm 0.02$ | This work
$R_{\star}$ | Radius in $R_{\odot}$ | $0.51\pm 0.01$ | This work
$\rho_{\star}$ | Density in $\,\mathrm{g/cm^{3}}$ | $5.7\pm 0.4$ | This work
$A_{v}$ | Visual extinction in mag | $0.005\pm 0.003$ | This work
Other Stellar Parameters:
$P_{\mathrm{rot}}$ | Rotation period in days | $13.2\pm 0.2$ | This work
$v\sin i_{\star}$ | Rotational broadening in km/s | $<2$ | This work
Age | Age in Gyrs | $0.7-5.1$ | This work
RV | Systemic radial velocity in km/s | $-15.72\pm 0.02$ | This work

††footnotetext: References are: TIC (Stassun et al., 2019), Gaia EDR3 (Gaia
Collaboration et al., 2021), Bailer-Jones (Bailer-Jones et al., 2021), Green
(Green et al., 2019), APASS (Henden et al., 2018), 2MASS (Cutri et al., 2003),
WISE (Wright et al., 2010)

aafootnotetext: Geometric distance from Bailer-Jones et al. (2021).

bbfootnotetext: Derived using the HPF-SpecMatch algorithm.

ccfootnotetext: EXOFASTv2 derived values using MIST isochrones.

###  3.2 Spectral Energy Distribution Fitting

We modeled the spectral energy distribution (SED) to derive model-dependent
stellar parameters using the EXOFASTv2 analysis package (Eastman et al.,
2019). Our analysis uses the MIST model grid (Dotter, 2016; Choi et al., 2016)
which is based on the ATLAS12/SYNTHE stellar atmospheres (Kurucz, 1970, 1993).
EXOFASTv2 calculates the bolometric corrections for the SED fit by linearly
interpolating the precomputed bolometric corrections provided by the MIST team
in a grid of $\log g$, $\mathrm{T_{eff}}$, [Fe/H], and
$A_{V}$333http://waps.cfa.harvard.edu/MIST/model_grids.html#bolometric.

The fit uses Gaussian priors on the (i) 2MASS $JHK$ magnitudes, Sloan
$g^{\prime},r^{\prime},i^{\prime}$ magnitudes and Johnson $BV$ magnitudes from
Henden et al. (2018), and Wide-field Infrared Survey Explorer magnitudes
(Wright et al., 2010); (ii) host star surface gravity, temperature, and
metallicity derived from HPF-SpecMatch; and (iii) the geometric distance
calculated from Bailer-Jones et al. (2021). We apply a uniform prior for the
visual extinction in which the upper limit is determined from estimates of
Galactic dust (Green et al., 2019) calculated at the distance determined by
Bailer-Jones et al. (2021). The $R_{v}=3.1$ reddening law from Fitzpatrick
(1999) is used by EXOFASTv2 to convert the extinction determined by Green et
al. (2019) to a visual magnitude extinction. Table 2 contains the stellar
priors and derived stellar parameters with their uncertainties. The model-
dependent mass and radius for TOI-2119 are $0.53\pm 0.02~{}\mathrm{M_{\odot}}$
and $0.51\pm 0.01~{}\mathrm{R_{\odot}}$, respectively.

###  3.3 Rotation Period

TOI-2119 is a flaring star exhibiting photometric modulations of $<1\%$ that
persist throughout the TESS photometry (see Figure 1(a)). It is
chromospherically active as the calcium II infrared triplet lines are observed
to be in emission in each HPF observation. We therefore attribute the
variability in the light curve to activity-induced photometric modulation and
attempt to constrain the rotation period of TOI-2119 using TESS photometry.
For this search, we excise all transit events in the TESS data within a window
of 0.107 days (1.25 times the transit duration) from the expected mid-transit.
We analyzed the TESS data using the generalized Lomb-Scargle periodogram
(Zechmeister & Kürster, 2009), the wavelet power spectra (e.g., Bravo et al.,
2014), and the auto-correlation function (e.g., McQuillan et al., 2013a, b),
and estimated the rotation period to be in the range of 5-20 days.

To further constrain the rotation period, we used publicly available data from
the (i) Zwicky Transient Facility (ZTF; Masci et al., 2019) in the $zg$ band,
(ii) All-Sky Automated Survey for SuperNovae (ASAS-SN; Shappee et al., 2014;
Kochanek et al., 2017) in the $V$ and $g^{\prime}$ bands, and (iii) SuperWASP
(Butters et al., 2010). We modeled the ground-based photometry using the
juliet analysis package (Espinoza et al., 2019), which performs the parameter
estimation using dynesty (Speagle, 2020), a dynamic nested-sampling algorithm.
The photometric model is a Gaussian process that uses the approximate quasi-
periodic covariance function from the celerite package (Equation 56 in
Foreman-Mackey et al., 2017) because it has been used to reliably infer
stellar rotation rates (e.g., Angus et al., 2018; Robertson et al., 2020). We
used our constraints from the TESS photometry to place a uniform prior on the
rotation period of $5-20$ days. The fit yields a rotation period of $13.2\pm
0.2$ days and is included in Table 2. Figure 4 displays the ground-based
photometry used for this analysis and the posterior distribution on the
rotation period.

Figure 4: (a) is the phased ground-based photometry that was modeled with a
Gaussian process. The large black points represent 1-day bins of the phased
photometry. (b) presents the posterior distribution of the rotation period of
the Gaussian process model. We derive a rotation period of $13.2\pm 0.2$ days.

With a period of $13.2\pm 0.2$ days, TOI-2119 has intermediate rotation period
based on the classification scheme of Newton et al. (2016). Newton et al.
(2016) could not provide an age range for M dwarfs with rotation periods
spanning 10–70 days but showed that M dwarfs with $P_{\mathrm{rot}}<10$ days
have a mean age of $0.7\pm 0.3$ Gyr while those with $P_{\mathrm{rot}}>70$
days have mean ages of $5.1^{+4.2}_{-2.6}$ Gyr. TOI-2119 most probably has an
age between $0.7-5.1$ Gyr. This is age range is also consistent with the
rotation period and age relationship from Engle & Guinan (2018).

##  4 Photometric and RV Modeling

We use allesfitter (Günther & Daylan, 2021) to jointly model the photometry
and RVs. allesfitter calculates the transit and RV models using the ellc
package (Maxted, 2016) and performs the parameter estimation using dynesty.
The RV model is a standard Keplerian model while the photometric model is the
sum of a transit model, an occultation model, and the same Gaussian process
noise model described in Section 3.3 to account for correlated noise in the
TESS photometry. The transit model adopts a quadratic limb-darkening law where
the limb-darkening coefficients are parameterized following Kipping (2013a)
while the occultation model assumes uniform limb darkening. Both the
photometric and RV models also include a simple white-noise model in the form
of a jitter term that is added in quadrature to the error bars of each
instrument.

Figure 5: Joint Photometry and RV fit for TOI-2119. (a) displays the detrended
TESS photometry phased to the derived ephemeris in Table 3 in the top panel a
with the residuals to the best fit transit model in the bottom panel. (b) is
identical to (a) but shows the occultation. (c) is similar to (a) and presents
the transit fit to the TMMT data. Panels (a)-(c) are plotted in units of
orbital phase (from 0-1) where the black points represent 20-min bins of the
phase-folded data. (d) shows the phased RVs plotted with the best fit RV model
and the corresponding residuals. For all panels, the best-fitting model is
plotted as a dashed line while the shaded regions denote the $1\sigma$ extent
of the derived posterior solution.

Table 3 provides a summary of the inferred system parameters and respective
confidence intervals and Figure 5 displays the model posteriors. The data
reveal a high-mass brown dwarf ($M_{2}=67\pm 2\mathrm{M_{J}}$ and
$R_{2}=1.11\pm 0.03\mathrm{R_{J}}$) orbiting TOI-2119 on an eccentric orbit
($e=0.3362\pm 0.0005$) with a period of $7.200861\pm 0.000005$ days. The
eccentricity of the orbit is determined with exquisite precision because of
the powerful constraint on $e$ and $\omega$ from the presence of both a
transit and occultation (see Winn, 2010).

Table 3: System Parameters for TOI-2119

Parameter | Units | Prior | Value
---|---|---|---
Photometric Parameters |  |  | TESS | TMMT
Linear Limb-darkening Coefficienta | $q_{1}$ | $\mathcal{U}(0,1)$ | $0.18_{-0.03}^{+0.05}$ | $0.6\pm 0.1$
Quadratic Limb-darkening Coefficienta | $q_{2}$ | $\mathcal{U}(0,1)$ | $0.8_{-0.2}^{+0.1}$ | $0.06_{-0.04}^{+0.06}$
Photometric Jitter |  $\sigma_{phot}$ (ppm) | $\mathcal{J}(10^{-4},10^{6})$ | $0.004^{+0.769}_{-0.004}$ | $10\pm 10$
RV Parameters |  |  | APOGEE-2N | HPF
RV Offset |  $\gamma$ (km/s) | $\mathcal{U}(-20,-10)$ | $-14.5\pm 0.1$ | $-11.27\pm 0.01$
RV Jitter |  $\sigma_{RV}$ (m/s) | $\mathcal{J}(10^{-3},10^{3})$ | $1\pm 1$ | $10_{-10}^{+20}$
Orbital Parameters:
Orbital Period |  $P$ (days) | $\mathcal{N}(7.2,0.1)$ | $7.200861\pm 0.000005$
Time of Conjunction |  $T_{C}$ (BJDTDB) | $\mathcal{N}(2458958.6,0.1)$ | $2458958.67756\pm 0.00006$
$\sqrt{e}\cos\omega$ |  | $\mathcal{U}(-1,1)$ | $0.5798\pm 0.0004$
$\sqrt{e}\sin\omega$ |  | $\mathcal{U}(-1,1)$ | $-0.009\pm 0.003$
Semi-amplitude velocity |  $K$ (km/s) | $\mathcal{U}(1,20)$ | $10.59\pm 0.02$
Scaled Radius | $R_{2}/R_{\star}$ | $\mathcal{U}(0,1)$ | $0.226\pm 0.001$
$\left(R_{\star}+R_{2}\right)/a$ |  | $\mathcal{U}(0,1)$ | $0.0454\pm 0.0003$
$\cos i$ |  | $\mathcal{U}(0,1)$ | $0.0259\pm 0.0005$
Surface brightness ratio | $J$ | $\mathcal{U}(0,1)$ | $0.027_{+0.004}^{-0.003}$
TESS Gaussian Process Hyperparameters:
$B$ | Amplitude ($10^{-6}\,\mathrm{ppm}$) | $\mathcal{J}(10^{-6},10^{6})$ | $6^{+2}_{-1}$
$C$ | Additive Factor | $\mathcal{J}(10^{-6},10^{6})$ | $90\pm 90$
$L$ | Length scale (days) | $\mathcal{J}(10^{-}6,10^{6})$ | $1.5_{-0.3}^{+0.5}$
$P_{GP}$ | Period (days) | $\mathcal{J}(1,100)$ | $20_{-10}^{+30}$
Derived Parameters:
Scaled Semi-major Axis | $a/R_{\star}$ | $\cdots$ | $27.0\pm 0.2$
Impact Parameter | $b$ | $\cdots$ | $0.623\pm 0.009$
Impact Parameter of occultation | $b_{s}$ | $\cdots$ | $0.62\pm 0.01$
Time of Pericenter |  $T_{p}$ (BJDTDB) | $\cdots$ | $2458963.790\pm 0.002$
Time of Occultation |  $T_{s}$ (BJDTDB) | $\cdots$ | $2458963.790\pm 0.002$
Eccentricity | $e$ | $\cdots$ | $0.3362\pm 0.0005$
Argument of Periastron |  $\omega$ (degrees) | $\cdots$ | $-0.9\pm 0.3$
Orbital Inclination |  $i$ (degrees) | $\cdots$ | $88.51\pm 0.03$
Transit Duration |  $T_{14}$ (hours) | $\cdots$ | $2.039\pm 0.007$
Occultation Duration |  $T_{14}$ (hours) | $\cdots$ | $2.025\pm 0.009$
Mass |  $M_{2}$ ($\,\mathrm{M_{J}}$) | $\cdots$ | $67\pm 2$
Mass ratio | $q=M_{2}/M_{\star}$ | $\cdots$ | $0.12\pm 0.02$
Radius |  $R_{2}$ ($\,\mathrm{R_{J}}$) | $\cdots$ | $1.11\pm 0.03$
Surface Gravity |  $\log g_{2}$ (cgs) | $\cdots$ | $5.158\pm 0.008$
Density |  $\rho_{2}$ (g/cm3) | $\cdots$ | $60\pm 5$
Semi-major Axis |  $a$ (au) | $\cdots$ | $0.064\pm 0.002$
Transit Depth (TESS bandpass) | (%) | $\cdots$ | $5.09\pm 0.05$
Occultation Depth (TESS bandpass) | ppm ($\times 10^{-6}$) | $\cdots$ | $1400\pm 200$
$T_{2}$ | Brightness Temperature (K) | $\cdots$ | $2100\pm 80$

aafootnotetext: Using the $q1$ and $q2$ parameterization from Kipping (2013a).

##  5 Discussion

###  5.1 Brightness Temperature

The depth of the secondary eclipse observed in TESS can be modeled as a
function of various fundamental properties (e.g., Charbonneau et al., 2005;
Esteves et al., 2013; Shporer, 2017):

$\mathrm{Depth}=\left(\frac{R_{2}}{R_{\star}}\right)^{2}\frac{\int\tau\left(\lambda\right)F_{2,\nu}\left(\lambda,T_{2}\right)d\lambda}{\int\tau\left(\lambda\right)F_{\star,\nu}\left(\lambda,T_{e}\right)d\lambda}+A_{g}\left(\frac{R_{2}}{a}\right)^{2},$
(1)

where $\tau\left(\lambda\right)$ is the TESS transmission
function444https://heasarc.gsfc.nasa.gov/docs/tess/the-tess-space-
telescope.html#bandpass, $T_{e}$ and $F_{\star,\nu}\left(\lambda,T_{e}\right)$
are the effective temperature and flux of the host star, $T_{2}$ and
$F_{2,\nu}\left(\lambda,T_{2}\right)$ is the brightness temperature and flux
of TOI-2119.01, and $A_{g}$ is the geometric albedo. The value of
$\left(R_{2}/a\right)^{2}=70$ ppm and, even if the geometric albedo were
unity, this is a small fraction of the eclipse depth ($1400\pm 200$ ppm).
Marley et al. (1999) provide a more realistic geometric albedo of
$A_{g}\approx 0.1$ for a massive brown dwarf transiting an early M dwarf. This
value of $A_{g}$ would limit the contribution from the second term of Equation
1 to $\sim 7$ ppm. For TOI-2119, we ignore any contribution to the eclipse
depth from reflected light because the contribution from these terms are
$\lesssim 10$ ppm, a value which is below the precision of TESS. The
contribution from ellipsoidal variations (e.g., Shporer, 2017) is similarly
negligible and would have an amplitude $\lesssim 10$ ppm. To solve for the
brightness temperature of TOI-2119.01, we use our posterior distribution of
the eclipse depth and estimate the fluxes of TOI-2119 and its brown dwarf
companion using the BT-Settl models (Allard et al., 2012a, b) based on the
Caffau et al. (2011) solar abundances. To account for the uncertainties in the
stellar parameters, we calculate the posterior distribution of the brightness
temperature with a Monte Carlo sampling method where we use the stellar
parameters derived from our HPF-SpecMatch analysis as Gaussian priors and
allow them to vary while deriving the temperature.

This analysis yields a temperature of $T_{2}=2100\pm 80$ K for TOI-2119.01.
The measured temperature of TOI-2119.01 spans the M-L transition (between
2000-2500 K; Allard et al., 2013) and is comparable to those of early L-dwarfs
from field (e.g., Helling & Casewell, 2014; Zhang et al., 2017) and
astrometric discoveries (Dupuy & Liu, 2017). Future observations of TESS in
Sectors 51 and 52 will provide additional eclipses to further improve the
eclipse depth and temperature determination. Additional observations of the
secondary eclipse in different bandpasses (e.g., Beatty et al., 2014; Croll et
al., 2015; Beatty et al., 2017) are necessary to probe the dayside eclipse
spectrum of TOI-2119.01 and compare it to theoretical atmospheric models
(e.g., Beatty et al., 2020).

###  5.2 Comparison to the existing brown dwarf population

An analysis of the Kepler (Santerne et al., 2016) and CoRoT (Csizmadia & CoRot
Team, 2016) samples of short-period transiting brown dwarfs revealed that they
are rare with an occurrence rate of $\sim 0.2-0.3\%$ around Sun-like stars.
Including TOI-2119.01, there are 48 known transiting brown dwarfs, 9 of which
have M dwarf host stars. Figure 6 shows the location of TOI-2119.01 on a mass-
radius diagram of transiting brown dwarfs compiled from the literature
(Carmichael et al., 2020; Mireles et al., 2020; Casewell et al., 2020; Grieves
et al., 2021). For comparison, we include the cloudless, solar metallicity
evolutionary models by Marley et al. (2021) and the evolutionary models by
Phillips et al. (2020), each calculated in chemical equilibrium, at age of
0.5, 5 and 10 Gyr.

TOI-2119.01 is located in a cluster of other high-mass brown dwarfs and
appears to be consistent (within $2\sigma$) with brown dwarf models for ages
$<1$ Gyr. This age is within the range of $0.7-5.1$ Gyr determined from the
rotation period (see Section 3.3). The small ($<2\sigma$) discrepancy between
the observed mass and radius and the predicted values for models between
$0.7-5.1$ Gyrs is also seen with different evolutionary tracks, such as the
models from Baraffe et al. (2003) and Saumon & Marley (2008). Figure 6 shows
that the brown dwarf models evolve quickly for objects $<5$ Gyr, emphasizing
the need for precise ages to accurately discriminate between these models. A
small discrepancy is not surprising because of the approximate age
determination and the complexity of model atmospheres and the equation of
state for these ultracool objects (see Burrows et al., 2011; Chabrier et al.,
2019; Phillips et al., 2020; Marley et al., 2021). Some of the observed
inflation in radii for very low-mass stars and brown dwarfs may be attributed
to strong magnetic activity, which would inhibit efficient convection (e.g.,
López-Morales, 2007; Torres et al., 2010; Stassun et al., 2012; MacDonald &
Mullan, 2017) and result in a larger radius when compared to evolutionary
models. We have also ignored the role of the stellar insolation for the
shortest period brown dwarfs. Additional well characterized transiting brown
dwarfs, particularly those with known ages, are necessary to further improve
evolutionary tracks of brown dwarfs.

Figure 6: The brown dwarf mass-radius diagram showing TOI-2119.01 and all
substellar companions from the literature with masses between
$10-90\mathrm{M_{J}}$ and radii $<2\mathrm{R_{J}}$. Grey circles are systems
with non-M dwarf hosts while red diamonds are brown dwarfs transiting M
dwarfs. TOI-2119 is plotted as the blue star. Brown dwarfs with radii
$>2\mathrm{R_{J}}$ are found in young clusters with ages $\ll 1$ Gyr. The
solid lines (Sonora) are the cloudless, solar metallicity evolutionary tracks
from Marley et al. (2021) and the dash-dotted lines (ATMO) are the
evolutionary tracks from Phillips et al. (2020) at ages 0.5, 5, and 10 Gyr.
Contour lines of fixed $\log g$ values are included for reference.

From a statistical analysis of the brown dwarf population, Ma & Ge (2014)
postulated the brown dwarf sample is comprised of two populations: (i) a low-
mass group with $M<42.5\mathrm{M_{J}}$ with an eccentricity distribution
comparable to gas giants and (ii) a high-mass group with an eccentricity
distribution comparable to binary stars. Figure 7 compares TOI-2119.01 on the
period-eccentricity diagrams with the transiting brown dwarfs described above
and from the catalogue compiled by Ma & Ge (2014). TOI-2119.01 is the most
eccentric high-mass brown dwarf with a period $<10$ days. The period and
eccentricity of TOI-2119 is inconsistent with the $\sim 10$ day
circularization period (plotted as a dashed line in Figure 7) observed in M
dwarf binaries (e.g., Udry et al., 2000; Mayor et al., 2001) and the $\sim
10-12$ day circularization period observed in sun-like binaries (e.g.,
Duquennoy & Mayor, 1991; Meibom & Mathieu, 2005; Raghavan et al., 2010). We
note that two systems in young clusters with ages $<1$Gyr, the 2M0535-05
(Stassun et al., 2006) and AD 3116 (Gillen et al., 2017) systems, host massive
brown dwarfs with non-zero eccentricities with $P<10$ days, but this is not
surprising given their young ages. TOI-2119.01 is consistent with the shorter
circularization period of $\sim 3-5$ days that has been suggested for the
giant exoplanet population (e.g., Halbwachs et al., 2005; Pont et al., 2011;
Bonomo et al., 2017).

Figure 7: The eccentricity as a function of the period for brown dwarfs from
the catalogues of Ma & Ge (2014), Carmichael et al. (2020), Mireles et al.
(2020), Casewell et al. (2020), and Grieves et al. (2021). Triangles denote
the brown dwarfs with masses smaller than 42.5 $\mathrm{M_{J}}$ while the
squares are larger than this mass. Systems in young clusters: 2M0535-05A/B
(Stassun et al., 2006), AD 3116 (Gillen et al., 2017), RIK 72 (David et al.,
2019), and 2M1510Aa/b (Triaud et al., 2020) are denoted with yellow markers.
The dashed line indicates the maximum eccentricity for systems unaffected by
tides when adopting a circularization period of 10 days. TOI-2119.01, the blue
square, is most eccentric high-mass brown dwarf discovered with a period $<10$
days.

###  5.3 Potential Formation Mechanisms

There are various mechanisms of formation for brown dwarfs (see Whitworth et
al., 2007; Chabrier et al., 2014; Whitworth, 2018) including gravitational
instability and turbulent fragmentation of a molecular cloud (Padoan &
Nordlund, 2002, 2004; Hennebelle & Chabrier, 2008), disk instability and
migration (e.g., Helled et al., 2014; Kratter & Lodato, 2016; Nayakshin, 2017;
Müller et al., 2018), and core accretion for low-mass brown dwarfs (e.g.,
Lambrechts & Johansen, 2012; Mollière & Mordasini, 2012). The mass of
TOI-2119.01 means it may have been formed through gravitational instability in
a disk, and simulations by Forgan et al. (2018) show that dynamical
interactions and scattering between fragments in a gravitationally unstable
disk can readily form brown dwarf systems in a variety of configurations.
Subsequent fragment-fragment interactions during formation can lead to inward
scattering and produce a population of low semi-major axis, high-eccentricity
objects. As such, the observed eccentricity of TOI-2119.01 may be an imprint
of high-eccentricity migration.

###  5.4 Astrometric Constraints on Additional Companions

The high eccentricity of TOI-2119.01 may be the result of dynamical
interactions with a long-period companion. We use Gaia EDR3 to probe the
existence of a possible tertiary companion in the system. TOI-2119 is not
listed as a likely wide binary from the study of proper motions by El-Badry et
al. (2021). Despite no clear bound companion among other Gaia sources, the
precision of Gaia EDR3 allows us to probe binarity using the re-normalized
unit weight error (RUWE), which is the square root of the reduced $\chi^{2}$
statistic that has been corrected for calibration errors, and the excess
astrometric noise ($\epsilon$), a measure of the additional noise required to
explain the scatter from the derived astrometric solution (Lindegren et al.,
2018, 2021). Lindegren et al. (2021) note that these values are sensitive to
the photocentric motions of unresolved objects.

For orbital periods much shorter than the baseline of observations, the
astrometric wobble of the primary star around the center of mass may appear as
noise when adopting a single-star astrometric solution (e.g., Kervella et al.,
2019; Kiefer et al., 2019). A large excess astrometric noise with a
significance value, $D>2$, or a large RUWE has been shown to be a likely
indicator of unresolved companions in recent studies (e.g., Belokurov et al.,
2020; Penoyre et al., 2020; Gandhi et al., 2020; Stassun & Torres, 2021).
TOI-2119 has an RUWE of 1.9314 and $\epsilon=0.2644$ mas with a significance
of $D=161.3$ in Gaia EDR3. Penoyre et al. (2020) note that an RUWE $>1.4$
could reliably be used to identify binary systems in an analysis of mock and
real data of short period binaries. We use the analytical expression in
Equation 17 of Penoyre et al. (2020) to calculate the projected astrometric
scatter from a single-body astrometric fit, $\delta\theta$, assuming that many
periods of the binary are observed, as

$\delta\theta=\varpi\frac{a\lvert
q-l\rvert}{\left(1+q\right)\left(1+l\right)}\sqrt{1-\frac{\sin^{2}i}{2}-\frac{3+\sin^{2}i\left(\cos^{2}\omega-2\right)}{4}e^{2}},$
(2)

where $a$ is the semi-major axis in au, $q=M_{2}/M_{\star}$ is the mass ratio,
$l=L_{2}/L_{\star}$ is the luminosity ratio, $e$ is the eccentricity, $i$ is
the inclination, $\omega$ is the argument of pericenter, and $\varpi$ is the
parallax in mas. Equation 2 should be a suitable approximation for the
expected scatter due to TOI-2119.01 because Gaia EDR3’s temporal baseline (34
months) is much larger than the orbital period (7.2 days). The luminosity
ratio is estimated as $l\approx 0.00065$ in the Gaia
bandpass555https://www.cosmos.esa.int/web/gaia/edr3-passbands using the BT-
Settl models from Section 5.1. The expected astrometric noise from all
observations contained in Gaia EDR3 is $\delta\theta=0.1420$ mas. Even if we
use the Gaia Observation Scheduling Tool666https://gaia.esac.esa.int/gost/ to
obtain the timestamps for the Gaia EDR3 observations (79 different scans) and
calculate the two-dimensional deviations at each Gaia observation following
Appendix B from Penoyre et al. (2020), we obtain a time averaged
$\delta\theta=0.1406$ mas. This value is more than half of the observed
$\epsilon$ and we have ignored other sources of error, such that that the
observed $\epsilon$ may be completely consistent with the presence of
TOI-2119.01 ($q=0.12\pm 0.02$). The larger $\epsilon$ may also be a potential
indicator of an additional, long-distance companion, but we note that other
scenarios, such as a close (within 0.15″), faint on-sky companion (e.g.,
Ziegler et al., 2020; Belokurov et al., 2020) could enhance the value of
$\epsilon$. Future releases from Gaia will allow a proper motion analysis
(e.g., Kervella et al., 2019) of TOI-2119 to evaluate the possibility of a
third body in the system.

###  5.5 RV Constraints on Additional Companions

We use thejoker (Price-Whelan et al., 2017) to perform a rejection sampling
analysis on the residuals of our fit to the HPF RVs to constrain the potential
mass of a third companion in the TOI-2119 system. The HPF data have a temporal
baseline of 249 days and, for the rejection sampling we consider any orbits
with periods $P<10000$ days. The analysis with thejoker uses a log-uniform
prior for the period (between $8<P<10000$ days), the Beta distribution from
Kipping (2013b) as a prior for the eccentricity, and a uniform prior for the
argument of pericenter and the orbital phase. Out of the $>\times 10^{8}$
($2^{27}$) samples analyzed with thejoker, a total of 56653 samples survived
($\sim 0.05\%$ acceptance rate). The masses from the surviving samples let us
reject the presence of any additional low-inclination ($\sin i\sim 1$) brown
dwarfs ($M<11\mathrm{M_{J}}$) within 7.4 au of TOI-2119. Any tertiary
companion, even on an inclined orbit, would need to have a period short enough
for Gaia to detect binary motion ($\ll 100$ years, see Penoyre et al., 2020).

###  5.6 Tidal Evolution of TOI-2119

TOI-2119.01 is on a short-period orbit with non-zero eccentricity and we may
expect that tides have affected its orbit (e.g., Mazeh, 2008; Damiani & Díaz,
2016). Changes to the orbit may be due to tidal torques that emerge either
from the deformation of the brown dwarf by the host star or from the
deformation of the host star by a brown dwarf (Hut, 1981). Tidal dissipation
and magnetic braking from the spin-down of TOI-2119 should cause orbital decay
of the brown dwarf (e.g., Damiani & Lanza, 2015). To estimate the timescales
for circularization and inspiral, we adopt the tidal model presented in
Equations 1 and 2 of Jackson et al. (2008) and, similar to Persson et al.
(2019), we define the following timescales for inspiral, $\tau_{a}$, and
circularization, $\tau_{e}$:

$\displaystyle\frac{1}{\tau_{a}}$ $\displaystyle=$
$\displaystyle\frac{1}{\tau_{a,\star}}+\frac{1}{\tau_{a,\mathrm{BD}}}$ (3)
$\displaystyle\frac{1}{\tau_{e}}$ $\displaystyle=$
$\displaystyle\frac{1}{\tau_{e,\star}}+\frac{1}{\tau_{e,\mathrm{BD}}}$ (4)
$\displaystyle\frac{1}{\tau_{a,\star}}$ $\displaystyle=$ $\displaystyle
a_{\mathrm{BD}}^{-13/2}\frac{9}{2}\sqrt{\frac{G}{M_{\star}}}\frac{R_{\star}^{5}M_{\mathrm{BD}}}{Q_{\star}},$
(5) $\displaystyle\frac{1}{\tau_{a,\mathrm{BD}}}$ $\displaystyle=$
$\displaystyle
a_{\mathrm{BD}}^{-13/2}\frac{63}{2}\sqrt{GM_{\star}^{3}}\frac{R_{\mathrm{BD}}^{5}e_{\mathrm{BD}}^{2}}{Q_{\mathrm{BD}}M_{\mathrm{BD}}},$
(6) $\displaystyle\frac{1}{\tau_{e,\star}}$ $\displaystyle=$ $\displaystyle
a_{\mathrm{BD}}^{-13/2}\frac{171}{16}\sqrt{\frac{G}{M_{\star}}}\frac{R_{\star}^{5}M_{\mathrm{BD}}}{Q_{\star}},$
(7) $\displaystyle\frac{1}{\tau_{e,\mathrm{BD}}}$ $\displaystyle=$
$\displaystyle
a_{\mathrm{BD}}^{-13/2}\frac{63}{4}\sqrt{GM_{\star}^{3}}\frac{R_{\mathrm{BD}}^{5}}{Q_{\mathrm{BD}}M_{\mathrm{BD}}}$
(8)

where $\tau_{e,\star}$ and $\tau_{e,\mathrm{BD}}$ represent the contributions
to the circularization timescale and $\tau_{a,\star}$ and
$\tau_{a,\mathrm{BD}}$ are the contributions to the inspiral timescale due to
tides raised on the star and the BD, respectively. For the tidal quality
factors, we assume the brown dwarf is comparable to Jupiter and adopt a value
of $Q_{\mathrm{BD}}=10^{5}$ (see Goldreich & Soter, 1966; Lainey et al., 2009;
Lainey, 2016). This choice of $Q$ is also supported by observational evidence
that brown dwarfs have $Q_{\mathrm{BD}}>10^{4.5}$ (Heller et al., 2010). We
adopt a nominal value of $Q_{\star}=10^{7}$ for TOI-2119 based on the modeling
of Gallet et al. (2017) and, for simplicity, assume the tidal dissipation
factors remain constant. We note that $Q$ will change as the star or brown
dwarf evolve (e.g., Barker & Ogilvie, 2009; Gallet et al., 2017). Using the
system parameters from Table 3, we estimate a timescale for circularization of
$\sim 56$ Gyr and a timescale for in-spiral of $\sim 221$ Gyr. In each case,
the tides raised on the star by the brown dwarf ($\tau_{\star}$) dominate the
timescales. The circularization timescale is $\sim 180$ Gyr even with a second
order expansion to account for the moderate eccentricity of the orbit
(Equation 2 in Adams & Laughlin, 2006). The orbit of TOI-2119 is not evolving
due to tides and should remain unperturbed for the main sequence lifetime of
TOI-2119.

Equations 5-8 have a large dependency on the radii of each object ($\propto
R^{5}$) and the timescales should change as both the host star and brown dwarf
evolve. We use the evolutionary models of Baraffe et al. (2015) to obtain the
radii of TOI-2119 and TOI-2119.01 as a function of time to explore the
evolution of the circularization and inspiral timescales. Figure 8 shows that
for the lifetime of TOI-2119, the ages for circularization and inspiral are
orders of magnitude larger than the system age, except for ages of a few Myr
when the system age is comparable to the timescale for circularization. If the
observed eccentricity is primordial, TOI-2119.01 may have briefly begun
circularization early in the system but then stopped as the host star
contracted. The circularization timescale is only comparable to the system age
for a few million years and the eccentricity of the system has probably not
changed significantly due to tides.

Figure 8: Above are the timescales for inspiral, $\tau_{a}$, and
circularization, $\tau_{e}$, derived using Equations 3 and 4, adopting
$Q_{\star}=10^{7}$ and $Q_{\mathrm{BD}}=10^{5}$, and using the radii for the M
dwarf and brown dwarf from evolutionary models by Baraffe et al. (2015). The
dashed line is plotted for reference and corresponds where the time scale is
equal to the system’s age.

###  5.7 Potential for Measuring the True Spin-Orbit Alignment

The projected spin-orbit angle ($\lambda$), or the projected angle between the
stellar rotation axis and the normal to the planet of the orbit, can shed
light on the dynamical and formation history of a system (e.g., Winn &
Fabrycky, 2015; Dawson & Johnson, 2018). Measurements of $\lambda$ for massive
($>3M_{\mathrm{J}}$), hot ($T_{e}>6000$K) planets and brown dwarfs have
revealed that most of these systems are less likely to be retrograde and have
lower values of $|\lambda|$ (e.g., Hébrard et al., 2010, 2011; Triaud, 2018;
Zhou et al., 2019). There are only a few measurements of $\lambda$ for
transiting objects in the mass range $10-80~{}\mathrm{M_{J}}$: HAT-P-2 b
Loeillet et al. (2008), CoRoT-3 b (Triaud et al., 2009), XO-3 b (Hirano et
al., 2011), KELT-1 b (Siverd et al., 2012), WASP-18 b (Albrecht et al., 2012),
and HATS-70 b (Zhou et al., 2019). These objects orbit hot stars above the
Kraft break (Kraft, 1967), the region where stars become fully-radiative
($T_{e}\sim 6100$ K) and are observed to have low projected stellar
obliquities $|\lambda|$ (see Zhou et al., 2019). The lack of high $|\lambda|$
for these massive substellar companions is thought to be a result of tidal
realignment, as the realignment timescale is dependent on the mass ratio
$\propto q^{-2}$ (e.g., Barker & Ogilvie, 2009; Dawson, 2014; Triaud, 2018).

Unlike the current set of brown dwarfs orbiting FGK dwarfs with obliquity
measurements, TOI-2119 orbits a much cooler M dwarf and any primordial
misalignment should still be present because the expected timescale for spin-
orbit alignment $\tau_{i}>10^{12}$ years (e.g., Barker & Ogilvie, 2009) if we
adopt $Q_{\star}=10^{7}$ and $Q_{\mathrm{BD}}=10^{5}$. With only an upper
limit of $v\sin i_{\star}<2$ km/s, we have no constraint on the stellar
inclination and we recover a uniform distribution for $\cos i_{\star}$ when
using the formalism of Masuda & Winn (2020) to estimate the stellar
inclination. If the stellar equator is well-aligned with a viewer such that
$\sin i_{\star}=1$, we expect a rotational velocity of $v\sin
i_{\star}=1.95\pm 0.05$ km/s from our measured rotation period and stellar
radius. TOI-2119 is an early M dwarf with a peak in its SED at around $\sim
0.9-1$ microns which makes it possible to determine the value of $v\sin i$
using any precise optical spectrograph with a higher resolution than HPF
($R\sim 55000$), such as MAROON-X (Seifahrt et al., 2016), EXPRES (Jurgenson
et al., 2016), CARMENES (Quirrenbach et al., 2014, 2018), or NEID (Schwab et
al., 2016).

Observations with many of these precise spectrographs would also enable a
detection of the Rossiter-McLaughlin effect (RM effect; Winn, 2010; Triaud,
2018) to measure $\lambda$. For TOI-2119, the possibility of independent
measurements of $v\sin i_{\star}$, $\lambda$, and $P_{\mathrm{rot}}$ would
allow for an estimate of the spin-orbit angle, $\psi$. $\psi$ is one of a few
fundamental orbital parameters and can serve as a potential diagnostic of
theories of migration (e.g., Fabrycky & Winn, 2009). A first order estimate
for the amplitude of the RM effect is $\Delta
V=2/3\left(R_{1}/R_{\star}\right)^{2}v\sin i_{\star}\sqrt{1-b^{2}}$ (Equation
1, Triaud, 2018). We estimate an amplitude of $\sim 50$ m/s for TOI-2119.01,
if we assume $v\sin i_{\star}=1.95$ km/s, and this precision can be achieved
with current spectrographs (e.g., MAROON-X, EXPRES, CARMENES, NEID). A
measurement of $\psi$ in the TOI-2119 system will enable a complete dynamical
characterization to inform us how this system could have formed.

##  6 Summary

We report the discovery of a brown dwarf ($M_{2}=67\pm 2\mathrm{M_{J}}$ and
$R_{2}=1.11\pm 0.03\mathrm{R_{J}}$) on an eccentric (e=$0.3362\pm 0.0005$),
short period orbit ($P=7.200861\pm 0.000005$ days) transiting and occulting
the M dwarf TOI-2119. The rotation period of $13.2\pm 0.2$ days suggests the
system probably has an age between $0.7-5.1$ Gyrs while evolutionary models
for brown dwarfs favor ages $<1$ Gyr. The difficulty in constraining the age
of TOI-2119 limits our ability to use the brown dwarf companion to further
constrain evolutionary models. The secondary eclipses observed by TESS reveal
a temperature of $2100\pm 80$ K for TOI-2119.01, which is consistent with
measured temperatures of L0-L2 dwarfs. The high eccentricity and excess
astrometric noise from Gaia EDR3 are suggestive of an additional companion in
this system, but we can only exclude the existence of massive brown dwarfs on
low-inclination ($\sin i\sim 1$) orbits with our RVs. The precision of the
orbital parameters of TOI-2119 will enable detailed astrometric analysis of
future Gaia releases to confirm the existence of a distant, tertiary
companion. The precise determination of the orbital inclination and rotation
period make this system amenable to a measurement of the true spin-orbit angle
with observations from high resolution spectrometers. A measurement of $\psi$
would be the first for a massive substellar companion around a cool host star
and will further our understanding of the dynamical history of TOI-2119.

## Acknowledgments

We thank the anonymous referee for a thoughtful reading of the manuscript, and
for useful suggestions and comments which made for a clearer manuscript. This
work was supported by NASA Headquarters under the NASA Earth and Space Science
Fellowship Program through grant 80NSSC18K1114 and by the Alfred P. Sloan
Foundation’s Minority Ph.D. Program through grant G-2016-20166039. The Center
for Exoplanets and Habitable Worlds is supported by the Pennsylvania State
University and the Eberly College of Science.

These results are based on observations obtained with the Habitable-zone
Planet Finder Spectrograph on the HET. We acknowledge support from NSF grants
AST 1006676, AST 1126413, AST 1310875, AST 1310885, AST 2009889, AST 2108512
and the NASA Astrobiology Institute (NNA09DA76A) in our pursuit of precision
radial velocities in the NIR. We acknowledge support from the Heising-Simons
Foundation via grant 2017-0494. The Hobby-Eberly Telescope is a joint project
of the University of Texas at Austin, the Pennsylvania State University,
Ludwig-Maximilians-Universität München, and Georg-August Universität
Gottingen. The HET is named in honor of its principal benefactors, William P.
Hobby and Robert E. Eberly. The HET collaboration acknowledges the support and
resources from the Texas Advanced Computing Center. We are grateful to the HET
Resident Astronomers and Telescope Operators for their valuable assistance in
gathering our HPF data. We would like to acknowledge that the HET is built on
Indigenous land. Moreover, we would like to acknowledge and pay our respects
to the Carrizo & Comecrudo, Coahuiltecan, Caddo, Tonkawa, Comanche, Lipan
Apache, Alabama-Coushatta, Kickapoo, Tigua Pueblo, and all the American Indian
and Indigenous Peoples and communities who have been or have become a part of
these lands and territories in Texas, here on Turtle Island.

Computations for this research were performed on the Pennsylvania State
University’s Institute for Computational and Data Sciences’ Roar
supercomputer, including the CyberLAMP cluster supported by NSF grant
MRI-1626251.

Some of the data presented in this paper were obtained from from the Mikulski
Archive for Space Telescopes (MAST) at the Space Telescope Science Institute.
The specific observations analyzed can be accessed via
https://doi.org/10.17909/t9-v3f8-w427 (catalog 10.17909/t9-v3f8-w427). Support
for MAST for non-HST data is provided by the NASA Office of Space Science via
grant NNX09AF08G and by other grants and contracts. This work includes data
collected by the TESS mission, which are publicly available from MAST. Funding
for the TESS mission is provided by the NASA Science Mission directorate. This
research made use of the NASA Exoplanet Archive, which is operated by Caltech,
under contract with NASA under the Exoplanet Exploration Program. This
research has made use of the SIMBAD database, operated at CDS, Strasbourg,
France, and NASA’s Astrophysics Data System Bibliographic Services. 2MASS is a
joint project of the University of Massachusetts and IPAC at Caltech, funded
by NASA and the NSF.

These results are based on observations obtained with the 3 m Shane Telescope
at Lick Observatory. We acknowledge support from NSF grant AST 1910954. The
authors thank the Shane telescope operators, AO operators, and laser operators
for their assistance in obtaining these data.

Some of the observations in this paper made use of the NN-EXPLORE Exoplanet
and Stellar Speckle Imager (NESSI). NESSI was funded by the NASA Exoplanet
Exploration Program and the NASA Ames Research Center. NESSI was built at the
Ames Research Center by Steve B. Howell, Nic Scott, Elliott P. Horch, and
Emmett Quigley. The authors thank Mark E. Everett for assistance in obtaining
these data.

These results are based on observations obtained with the Samuel Oschin
Telescope 48-inch and the 60-inch Telescope at the Palomar Observatory as part
of the Zwicky Transient Facility project. ZTF is supported by the National
Science Foundation under Grant No. AST-2034437 and a collaboration including
Caltech, IPAC, the Weizmann Institute for Science, the Oskar Klein Center at
Stockholm University, the University of Maryland, Deutsches Elektronen-
Synchrotron and Humboldt University, the TANGO Consortium of Taiwan, the
University of Wisconsin at Milwaukee, Trinity College Dublin, Lawrence
Livermore National Laboratories, and IN2P3, France. Operations are conducted
by COO, IPAC, and UW. This work makes use of data from the first public
release of the WASP data (Butters et al., 2010) as provided by the WASP
consortium and services at the NASA Exoplanet Archive, which is operated by
the California Institute of Technology, under contract with NASA under the
Exoplanet Exploration Program.

This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

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