An Eccentric Brown Dwarf Eclipsing an M dwarf

TESS observed TOI-2119 (Gaia EDR3 1303675097215915264) in short-cadence mode during Sectors 24 and 25 with data spanning 2020 April 16 through June 8. 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 ∼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 presearch 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 (Smith et al. 2012; Stumpe et al. 2012). Observations with nonzero 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.

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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''. We obtained 107 frames using an exposure time of 100 s while operating in a 1 × 1 binning mode. In this mode, TMMT has a 13 s readout time between exposures, resulting in an effective cadence of 113 s 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 (72), and inner and outer sky annuli of 10 pixels (12'') and 15 pixels (179), 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.

TOI-2119 was observed from the Apache Point Observatory on 2018 May 11 and 12 using APOGEE-2N, a multiplexed, high-resolution (R ∼ 22,500, NIR (λ ∼ 1.5–1.7 μm)) fiber-fed spectrograph (Wilson et al. 2012, 2019) that is mounted on the Sloan 2.5 m 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 signal-to-noise ratio (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 1σ uncertainties, and the S/N per resolution element (∼2 pixels) are presented in Table 1.

We obtained eight 945 s visits of TOI-2119 using HPF with a median S/N per 1D extracted pixel of 168 at 1000 nm. HPF is a high-resolution (R ∼ 55,000), fiber-fed (Kanodia et al. 2018), NIR (λ ∼ 8080–12780 Å) spectrograph located on the 10 m Hobby–Eberly Telescope (HET) at McDonald Observatory in Texas (Mahadevan et al. 2012, 2014) that achieves long-term temperature stability of ∼1 mK (Stefánsson et al. 2016). The observations span 2020 September 19 through 2021 May 26 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 were 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 cm s⁻¹ (Stefánsson et al. 2020), a value that is smaller than the photon noise for TOI-2119 (median RV uncertainty of 48.5 m s⁻¹).

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 χ² 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 1σ uncertainties, and the S/N per pixel at 1000 nm for TOI-2119 are presented in Table 1.

TOI-2119 was observed in the K_s band with the ShARCS camera on the Shane 3 m telescope at Lick Observatory (Srinath et al. 2014). It was observed under natural guide star mode using the five-point dither process described in Furlan et al. (2017). The seeing was ∼2'' 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 five-point dither process, which is subtracted from each image. The final image is produced by interpolating all images onto a single centroid. A 5σ 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 <083 (marked as the hatched region in Figure 2). There are no bright companions (ΔK_s < 4) that could be a source of contamination in the photometry at separations of 083–65 from TOI-2119.

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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 562 and 832 nm. 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 832 nm narrowband filter. The NESSI data show no evidence of blending from a bright companion ΔMag < 4 at separations of 015–12.

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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, 2018a), 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 ≲ q ≲ 0.85) because of the limited temperature regime of the spectral models. binspec_plus ¹² extends the spectral model to include redder dwarfs and giants. We fit the APOGEE-2N spectrum of 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 () main-sequence stars in the regime of 3000K < T_e < 7000 K, , and −1 < [Fe/H] < 0.5. The model selection criterion from Table B1 of El-Badry et al. (2018b) relies on two values, , 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 Δχ² 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 (Δχ² < 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 K < T_e < 7000 K.

The spectroscopic stellar parameters (T_e , , and [Fe/H]) for TOI-2119 were calculated using the HPF-SpecMatch ¹³ package (Stefánsson et al. 2020; S. Jones et. al. 2022, in preparation), 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 (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 χ² 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 K < T_e < 6000 K, , and −0.5 < [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	⋯	236387002	TIC
Gaia EDR3	⋯	1303675097215915264	Gaia EDR3
Equatorial Coordinates, Proper Motion, Distance, and Maximum Extinction:
αJ2016	R.A. (R.A.)	16:17:43.17	Gaia EDR3
δJ2016	decl. (decl.)	26:18:15.16	Gaia EDR3
μα	Proper motion (RA, mas yr−1)	−29.27 ± 0.02	Gaia EDR3
μδ	Proper motion (Dec, mas yr−1)	6.86 ± 0.03	Gaia EDR3
d	Distance in parsec a	31.46 ± 0.03	Bailer-Jones
	Maximum visual extinction	0.01	Green
Optical and Near-infrared Magnitudes:
B	Johnson B mag	13.86 ± 0.03	APASS
V	Johnson V mag	12.37 ± 0.04	APASS
	Sloan mag	13.07 ± 0.02	APASS
	Sloan mag	11.76 ± 0.02	APASS
	Sloan mag	10.75 ± 0.02	APASS
J	J mag	8.98 ± 0.02	2MASS
H	H mag	8.39 ± 0.03	2MASS
Ks	Ks mag	8.14 ± 0.02	2MASS
W1	WISE1 mag	8.05 ± 0.02	WISE
W2	WISE2 mag	7.97 ± 0.02	WISE
W3	WISE3 mag	7.88 ± 0.02	WISE
W4	WISE4 mag	7.8 ± 0.2	WISE
Spectroscopic Parameters b :
Te	Effective temperature in Kelvin	3553 ± 67	This work
[Fe/H]	Metallicity in dex	0.1 ± 0.1	This work
	Surface gravity in cgs units	4.74 ± 0.04	This work
Model-dependent Stellar SED and Isochrone Fit Parameters c :
M⋆	Mass in M⊙	0.53 ± 0.02	This work
R⋆	Radius in R⊙	0.51 ± 0.01	This work
ρ⋆	Density in g cm−3	5.7 ± 0.4	This work
Av	Visual extinction in mag	0.005 ± 0.003	This work
Other Stellar Parameters:
Prot	Rotation period in days	13.2 ± 0.2	This work
	Rotational broadening in km s−1	<2	This work
Age	Age in Gyr	0.7–5.1	This work
RV	Systemic radial velocity in km s−1	−15.72 ± 0.02	This work

Notes. 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), and WISE (Wright et al. 2010).

^a Geometric distance from Bailer-Jones et al. (2021). ^b Derived using the HPF-SpecMatch algorithm. ^c EXOFASTv2 derived values using MIST isochrones.

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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 (Choi et al. 2016; Dotter 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 , T_eff, [Fe/H], and A_V . ¹⁴

The fit uses Gaussian priors on the (i) 2MASS JHK magnitudes, Sloan 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 ± 0.02 M_⊙ and 0.51 ± 0.01 R_⊙, respectively.

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 Ca 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 midtransit. 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 autocorrelation function (e.g., McQuillan et al. 2013a, 2013b), 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 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 ± 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.

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With a period of 13.2 ± 0.2 days, TOI-2119 has an 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_rot < 10 days have a mean age of 0.7 ± 0.3 Gyr while those with P_rot > 70 days have mean ages of Gyr. TOI-2119 most probably has an age between 0.7 and 5.1 Gyr. This age range is also consistent with the rotation period and age relationship from Engle & Guinan (2018).

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):

where is the TESS transmission function, ¹⁵ T_e and are the effective temperature and flux of the host star, T₂ and are the brightness temperature and flux of TOI-2119.01, and A_g is the geometric albedo. The value of , and, even if the geometric albedo were unity, this is a small fraction of the eclipse depth (1400 ± 200 ppm). Marley et al. (1999) provide a more realistic geometric albedo of A_g ≈ 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 ∼7 ppm. For TOI-2119, we ignore any contribution to the eclipse depth from reflected light because the contribution from these terms is ≲10 ppm, a value that is below the precision of TESS. The contribution from ellipsoidal variations (e.g., Shporer 2017) is similarly negligible and would have an amplitude of ≲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, 2012b) 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 T₂ = 2100 ± 80 K for TOI-2119.01. The measured temperature of TOI-2119.01 spans the M–L transition (between 2000 and 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).

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 ∼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 (Casewell et al. 2020; Carmichael et al. 2020; Mireles 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 ages of 0.5, 5, and 10 Gyr.

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TOI-2119.01 is located in a cluster of other high-mass brown dwarfs and appears to be consistent (within 2σ) 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 (<2σ) discrepancy between the observed mass and radius and the predicted values for models between 0.7 and 5.1 Gyr 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 the evolutionary tracks of brown dwarfs.

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 < 42.5M_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 catalog compiled by Ma & Ge (2014). TOI-2119.01 is the most eccentric high-mass brown dwarf with a period of <10 days. The period and eccentricity of TOI-2119 is inconsistent with the ∼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 ∼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 nonzero 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 ∼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).

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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-semimajor-axis, high-eccentricity objects. As such, the observed eccentricity of TOI-2119.01 may be an imprint of high-eccentricity migration.

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 renormalized unit weight error (RUWE), which is the square root of the reduced χ² statistic that has been corrected for calibration errors, and the excess astrometric noise (), 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; Gandhi et al. 2021; Penoyre et al. 2020; Stassun & Torres 2021). TOI-2119 has an RUWE of 1.9314 and = 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, δ θ, assuming that many periods of the binary are observed, as

where a is the semimajor axis in astronomical units, q = M₂/M_⋆ is the mass ratio, l = L₂/L_⋆ is the luminosity ratio, e is the eccentricity, i is the inclination, ω is the argument of pericenter, and ϖ is the parallax in milliarcseconds. 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 ≈ 0.00065 in the Gaia bandpass ¹⁶ using the BT-Settl models from Section 5.1. The expected astrometric noise from all observations contained in Gaia EDR3 is δ θ = 0.1420 mas. Even if we use the Gaia Observation Scheduling Tool ¹⁷ 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 δ θ = 0.1406 mas. This value is more than half of the observed , and we have ignored other sources of error, such that that the observed may be completely consistent with the presence of TOI-2119.01 (q = 0.12 ± 0.02). The larger may also be a potential indicator of an additional, long-distance companion, but we note that other scenarios, such as a close (within 015), faint on-sky companion (e.g., Belokurov et al. 2020; Ziegler et al. 2020) could enhance the value of . 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.

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 period P < 10,000 days. The analysis with thejoker uses a log-uniform prior for the period (between 8 < P < 10, 000 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 >×10⁸ (2²⁷) samples analyzed with thejoker, a total of 56,653 samples survived (∼0.05% acceptance rate). The masses from the surviving samples let us reject the presence of any additional low-inclination () brown dwarfs (M < 11M_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 (≪100 yr; see Penoyre et al. 2020).

TOI-2119.01 is on a short-period orbit with nonzero 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 the 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, τ_a , and circularization, τ_e :

where τ_e,⋆ and τ_e,BD represent the contributions to the circularization timescale and τ_a,⋆ and τ_a,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_BD = 10⁵ (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_BD Heller et al. (2010). We adopt a nominal value of Q_⋆ = 10⁷ 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 ∼56 Gyr and a timescale for inspiral of ∼221 Gyr. In each case, the tides raised on the star by the brown dwarf (τ_⋆) dominate the timescales. The circularization timescale is ∼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 (∝R⁵) 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.

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The projected spin–orbit angle (λ), 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 λ for massive (>3M_J), hot (T_e > 6000K) planets and brown dwarfs have revealed that most of these systems are less likely to be retrograde and have lower values of ∣λ∣ (e.g., Hébrard et al. 2010, 2011; Triaud 2018; Zhou et al. 2019). There are only a few measurements of λ for transiting objects in the mass range 10−80 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 ∼ 6100 K) and are observed to have low projected stellar obliquities ∣λ∣ (see Zhou et al. 2019). The lack of high ∣λ∣ for these massive substellar companions is thought to be a result of tidal realignment, as the realignment timescale is dependent on the mass ratio ∝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 the spin–orbit alignment τ_i > 10¹² yr (e.g., Barker & Ogilvie 2009) if we adopt Q_⋆ = 10⁷ and Q_BD = 10⁵. With only an upper limit of km s⁻¹, we have no constraint on the stellar inclination and we recover a uniform distribution for 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 , we expect a rotational velocity of km s⁻¹ from our measured rotation period and stellar radius. TOI-2119 is an early M dwarf with a peak in its SED at around ∼0.9–1 μm, which makes it possible to determine the value of using any precise optical spectrograph with a higher resolution than HPF (R ∼ 55, 000), 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 λ. For TOI-2119, the possibility of independent measurements of , λ, and P_rot would allow for an estimate of the spin–orbit angle, ψ. ψ 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 (Equation (1), Triaud 2018). We estimate an amplitude of ∼50 m/s for TOI-2119.01, if we assume km s⁻¹, and this precision can be achieved with current spectrographs (e.g., MAROON-X, EXPRES, CARMENES, and NEID). A measurement of ψ in the TOI-2119 system will enable a complete dynamical characterization to inform us how this system could have formed.