Verification of Gaia Data Release 3 Single-lined Spectroscopic Binary Solutions With Three Transiting Low-mass Secondaries

While secondary mass inferences based on single-lined spectroscopic binary (SB1) solutions are subject to sini degeneracies, this degeneracy can be lifted through the observations of eclipses. We combine the subset of Gaia Data Release 3 SB1 solutions consistent with brown dwarf-mass secondaries with the Transiting Exoplanet Survey Satellite (TESS) Object of Interest (TOI) list to identify three candidate transiting brown dwarf systems. Ground-based precision radial velocity follow-up observations confirm that TOI-2533.01 is a transiting brown dwarf with M=72−3+3MJup=0.069−0.003+0.003M⊙ orbiting TYC 2010-124-1 and that TOI-5427.01 is a transiting very low-mass star with M=93−2+2MJup=0.088−0.002+0.002M⊙ orbiting UCAC4 515-012898. We validate TOI-1712.01 as a very low-mass star with M=82−7+7MJup=0.079−0.007+0.007M⊙ transiting the primary in the hierarchical triple system BD+45 1593. Even after accounting for third light, TOI-1712.01 has a radius nearly a factor of 2 larger than predicted for isolated stars with similar properties. We propose that the intense instellation experienced by TOI-1712.01 diminishes the temperature gradient near its surface, suppresses convection, and leads to its inflated radius. Our analyses verify Gaia DR3 SB1 solutions in the low Doppler semiamplitude limit, thereby providing the foundation for future joint analyses of Gaia radial velocities and Kepler, K2, TESS, and PLAnetary Transits and Oscillations light curves for the characterization of transiting massive brown dwarfs and very low-mass stars.


Introduction
While isochrones can be used to infer the masses and radii of isolated low-mass stars and brown dwarfs, the theoretical models underlying those isochrones have difficulties reproducing the measured masses and radii of such objects (Kraus et al. 2011;Birkby et al. 2012).On the other hand, the minimum masses of the secondary stars and brown dwarfs in single-lined spectroscopic binary systems (SB1s) can be measured relative to the masses of the primaries in such systems.If the photospheres of the primaries in such systems are much, much hotter than the temperatures of the secondaries' "night" sides and the secondaries have significantly smaller radii (both of which apply for the lowest-mass stellar secondaries), then the eclipses of such systems can be treated like the transits and occultations of exoplanet systems.In that case, the depth of an eclipse of the primary by the secondary can be used to measure the radius of the low-mass secondary relative to the radius of the primary.The eclipsing nature of such a system lifts the i sin degeneracy of an SB1 solution as well.If the primary is a Sunlike star, then isochrone-inferred masses and radii can be both accurate and precise.Consequently, a homogeneous analysis of a large sample of transiting single-lined spectroscopic binaries would be a powerful way to infer accurate and precise masses and radii for a large population of low-mass stars and brown dwarfs.
Gaia Data Release (DR) 3ʼs nonsingle stars catalog (Pourbaix et al. 2022;Gaia Collaboration et al. 2023a;Babusiaux et al. 2023;Katz et al. 2023) presented a list of 181,327 single-lined spectroscopic binary solutions.This collection of SB1s is almost 2 orders of magnitudes larger than previous catalogs (e.g., Pourbaix et al. 2004).Of these solutions, 32,455 have Sun-like primaries (F5V through K5V according to Pecaut & Mamajek 2013) based on absolute Gaia G-band magnitudes and effective temperatures T eff from Gaia DR3ʼs astrophysical parameters data product (Creevey et al. 2023;Fouesneau et al. 2023).Of these, 2490 secondaries have minimum masses in the brown dwarf regime defined by an upper mass cutoff of 78.5 Jupiter masses (Chabrier et al. 2023).Because of Gaia's limited time baseline and Doppler precision, these systems usually have short periods and relatively high transit probabilities.These SB1 solutions have been validated down to the brown dwarf-mass regime (Gaia Collaboration et al. 2023b).The infrequent sampling of light curves based on Gaia photometry leaves them insensitive to all but the shortestperiod eclipsing systems.
NASA's Transiting Exoplanet Survey Satellite (TESS) mission has observed most of the sky in search of exoplanets and other transiting objects (Ricker et al. 2014).TESS light curves have been exhaustively searched for candidate transiting planets (Guerrero et al. 2021).Now in its Second Extended Mission, TESS data has led to the discovery of thousands of eclipsing binaries (Prša et al. 2022) and over a dozen transiting very-low-mass stars and brown dwarfs (e.g., Grieves et al. 2021;Carmichael et al. 2022;Psaridi et al. 2022;Lin et al. 2023;Vowell et al. 2023).The population of TESS-discovered eclipsing or transiting systems is biased toward periods shorter than about 10 days due to TESS's observing strategy and the smaller transit probabilities of systems with longer periods.
The combination of Gaia SB1 solutions and TESS light curves would be a powerful resource for the accurate and precise characterization of low-mass stars and brown dwarfs.In this article, we seek out systems with Gaia SB1 solutions consistent with brown dwarf-mass secondaries that have also been observed by TESS to transit their primaries.We identify three such systems for which the SB1 period is well matched by the TESS-inferred period: BD+45 1593 (TOI-1712), TYC 2010-124-1 (TOI-2533), and UCAC4 515-012898 (TOI-5427).Our ground-based follow-up analysis subsequently reveals that BD+45 1593 Ab (TOI-1712.01) is a very-low-mass star transiting the primary in a hierarchical triple, TYC 2010-124-1 b (TOI-2533.01) is a transiting brown dwarf, and UCAC4 515-012898 b (TOI-5427.01) is a transiting very-low-mass star.We describe the initial identification of these three objects as potential brown dwarfs in Section 2. We describe our follow-up observations for the systems and our subsequent analysis to confirm or validate the three objects in Section 3. We discuss the implications of these discoveries in Section 4 and summarize our conclusions in Section 5.

Candidate Brown Dwarf Identification
We first cross-match Gaia DR3ʼs nonsingle stars product with the TESS object of interest (TOI) catalog and the TESS eclipsing binary catalog (Prša et al. 2022).We next focus on systems where the orbital period from the Gaia SB1 solution is within 0.3% of the period found by TESS.We then use the binary mass function in the M 2 = M 1 limit to calculate a preliminary minimum mass for each secondary: The inputs to Equation (2) are a primary mass M 1 in Solar masses from Gaia's Final Luminosity Age Mass Estimator (FLAME) and a system's Gaia DR3 SB1 solution orbital parameters Doppler semiamplitude K 1 in meters per second and period P in years.In cases in which a FLAME-derived mass is unavailable, we use the primary mass from the TESS Followup Observing Program (TFOP) instead.For systems in which secondary mass is comparable to that of a brown dwarf, we refine our preliminary mass estimates by calculating more precise stellar parameters for the primary.This procedure yields three systems with candidate brown dwarfs: BD+45 1593 (Gaia DR3 917823348536224768/TOI-1712), TYC 2010-124-1 (Gaia DR3 1259922196651254272/ TOI-2533), and UCAC4 515-012898 (Gaia DR3 33414010621 25577088/TOI-5427).We illustrate these systems in Figure 1 and describe them in detail below.These SB1 solutions are based on Gaia R ≈ 11, 500 Radial Velocity Spectrometer (RVS) spectra that cover the wavelength range 846 nm λ 870 nm (Katz et al. 2023).The SB1 solutions for BD+45 1593 used 18 "good" radial velocity (RV) measurements, TYC 2010-124-1 used 47 "good" RV measurements, and UCAC4 515-012898 used 25 "good" RV measurements.We refer to these systems by their TESS Object of Interest designations TOI-1712, TOI-2533, and TOI-5427 in the context of analyses based on data sourced solely from TESS or TFOP.In all other contexts, we refer to these systems by their Simbad designations BD+45 1593, TYC 2010-124-1, and UCAC4 515-012898.
TOI-1712 and TOI-5427 were discovered by the TESS Science Office, while TOI-2533 was first discovered by Rafael Brahm.TOI-2533 then became a community TESS object of interest (CTOI), and later was adopted as a TOI by the TESS Science Office.TOI-1712 and TOI-2533 were identified by the TESS quick-look pipeline (QLP; Huang et al. 2020aHuang et al. , 2020b)), while TOI-5427 was identified by the TESS QLP Faint-star Search (Kunimoto et al. 2022).We give in Table 1 the details of the TESS observations of the three objects.For stars like the primaries in these systems that were not allocated postage stamps, TESS collected observations with a 30 minute cadence during its Prime Mission and a 10/2 minute cadence during its First/Second Extended Mission.
Because of TESS's large pixels, third light can make it difficult to interpret transit depths directly as secondary-toprimary radius ratios.To investigate the possibility of third light in these systems, we do two things.We first confirm that the TESS contamination ratios 17 are small for each system: 0.00054 for TOI-1712, 0.039224 for TOI-2533, and 0.263055 for TOI-5427.We next use the high spatial resolution Gaia DR3 source catalog and the plotting function within the giants pipeline (Grunblatt et al. 2022a;Saunders et al. 2022) to show that there are no bright sources within the TESS lightkurve-generated (Collaboration et al. 1812) full-frame image (FFI) point-spread function of any of these three systems (Figure 2).
(2021) lower and upper bounds on geometric distances.We report the photospheric stellar parameters in Table 3 and compare the isochrone-derived magnitudes to each star's observed magnitudes in Figure 3.
As we will show in the next section, there is evidence that BD+45 1593 is a double-lined spectroscopic binary.To determine the properties of both luminous stars in the system, we use an isochrones binary star model that requires both the primary and secondary to have the same age, composition, and distance.We use the full set of inputs mentioned previously.In Section 3.1, we will use the TESS T-band flux ratio that is inferred to show that the dilution of the transit in the BD+45 1593 system is small.The modeled photometry that results from the isochrones is consistent with the observed photometry, and this consistency supports the accuracy of the binary star model output (Figure 3).
Our isochrone analysis gives us several reasons to believe that the low-mass object in the BD+45 1593 system orbits the most massive component BD+45 1593 A. We infer T-band magnitudes 9.95 0.03 0.05 -+ for the primary BD+45 1593 A and 13.90 1.12 2.47 -+ for the secondary BD+45 1593 B. Given that the posterior-derived Gaia DR2 G magnitudes for the two stars are 10.300.02 0.05 -+ and 14.46 1.25 2.81 -+ , we argue that this flux difference would have left Gaia insensitive to the possible RV variation of BD+45 1593 B. As we will show, the second set of lines in the Tillinghast Reflector Echelle Spectrograph reconnaissance spectra of BD+45 1593 do not move on the timescale of months.On the other hand, the agreement of the Gaia DR3 SB1 period and the transit-inferred TOI period suggests that the object of interest in the system orbits BD+45 1593 A rather than BD+45 1593 B. Therefore, we refer to the primary of this system as BD+45 1593 Aa and report its parameters in Table 3. partially transparent blue lines to represent individual solutions sampled from normal distributions of the Gaia Doppler semiamplitude, eccentricity, and argument of periastron, with the standard deviation of each distribution representing the reported error on its respective parameter.Gaia's reported uncertainties on each parameter are derived from the variance-covariance matrix of the solution, but the matrix itself is not reported; we therefore do not correct for it in this plot.We plot the individual precision ground-based radial velocity measurements and their uncertainties as light blue circles with black borders and error bars.We plot the Doppler curves inferred from these data as dashed black lines.The agreement between the Gaia and precision ground-based SB1 solutions demonstrates the fidelity of the Gaia SB1 solutions at low Doppler semiamplitude. .It has been shown that the rotation period of a subgiant is proportional to its mass and therefore age (van Saders & Pinsonneault 2013).Assuming an aligned orbit, our inferred mass for BD+45 1593 Aa is large enough that Gaia should be able to detect the rotational broadening of its absorption lines.Indeed, the Gaia DR3 vbroad parameter for BD+45 1593 is 30 ± 6 km s −1 .We assume that all of the line broadening measured by the Gaia DR3 vbroad parameter is a result of rotation and use it to calculate the rotation period of BD+45 1593 Aa.We divide the isochrone-inferred circumference of BD+45 1593 Aa by its Gaia DR3 vbroad parameter, resulting in a rotation period P rot ≈ 5 days.It is possible that angular momentum exchange between the system's revolution and the rotation of BD+45 1593 Aa would lead to its faster rotation, though in that case, one would expect that the system's orbital period P = 3.566276 ± 0.0000044 days and the rotation period of the primary P rot ≈ 5 days would be synchronized.The agreement between our inferred rotation period P rot ≈ 5 and the van Saders & Pinsonneault (2013)predicted slow-launch rotation period P slow ≈ 6 days for a star of the mass, composition, and temperature of BD+45 1593 Aa supports our inference that BD+45 1593 Aa is massive.

Light Curve Analysis
The Box-fitting Least Squares (BLS- Kovács et al. 2002) algorithm-based transit depths reported in the TOI catalog are only indicative of true transit depths.We therefore reanalyze the TESS light curves of TOI-1712, TOI-2533, and TOI-5427 with the juliet Python package (Espinoza et al. 2019) to obtain more accurate and precise radius ratio posteriors for these three systems.We retrieve the light curve data products originally reduced by the TESS Science Processing Operations Center (SPOC- Jenkins et al. 2016) for the three systems from the Mikulski Archive for Space Telescopes (MAST).For each system, we use the available 30 minute cadence light curves produced from TESS Full-Frame Images by the TESS-SPOC High Level Science Products (HLSP) project (Caldwell et al. 2020).For TOI-1712, we additionally use the 2 minute cadence Presearch Data Conditioned (PDC-SAP; Smith et al. 2012;Stumpe et al. 2012Stumpe et al. , 2014) ) light curve from Sector 47 produced by the SPOC.Likewise, for TOI-5427 we additionally use 10 minute cadence light curves from Sectors 43, 44, and 45 also produced from TESS FFIs by the TESS-SPOC HLSP project.
We mask the transits in each light curve based on the ephemeris from the TOI catalog and use the Gaussian Process (GP) modeling tool in juliet to model out the stellar variability.We use a simple approximate Matern kernel for this process.For the dilution factor, we use a fixed prior at 1, for the mean out-of-transit flux we use a Gaussian prior centered at 0 with a standard deviation of 0.1, for the jitter term σ w and amplitude of the GP σ GP we use logarithmic uniform priors between 10 −6 and 10 6 , and for the Matern timescale of the GP ρ GP we use a logarithmic uniform prior between 10 −3 and 10 3 .We plot the systems' original TESS light curves along with the Gaussian process stellar variability fit in Figure 4.
After removing stellar variability, for each light curve, we unmask the transits and use the TOI ephemeris as a prior on the juliet fit to extract inclination and radius ratio posteriors.We use similar priors as before, except we use the Kipping (2013) quadratic limb-darkening parameterization with q1 and q2 0, 1 ( )priors appropriate for TESS.We plot in Figure 5 the detrended light curves for the systems with their transit fits, while in Figure 6 we plot the phase-folded 30 minutes-cadence light curves and transit fit for each system.We report the inclinations and radius ratios in Table 3.

Doppler Analysis
We present in Table 2 27 ground-based precision radial velocity measurements we obtained for TOI-2533 and TOI-5427.We collected 11 spectra for TOI-2533 between 2021 March 5 and 2021 April 8 using the Tillinghast Reflector Echelle Spectrograph (TRES-Fűrész 2008) on the 1.5 m Tillinghast Reflector telescope, situated on Mt.Hopkins in Arizona, USA.TRES has R ≈ 44, 000 over a wavelength range of approximately 3900-9100 Å.The exposure times ranged from 2200 to 3600 s with signal-to-noise per resolution element (S/N) between 23 and 35.We visually reviewed each order to remove cosmic rays.Depending on the S/N, we used 10-14 echelle orders within this wavelength range for each spectrum to measure each order's relative radial velocity.We used the spectrum with the highest S/N per resolution element as the reference value for these relative radial velocities.and UCAC4 515-012898).For each filter, we plot filled circles to represent the observed magnitudes and unfilled circles to represent the isochrone-inferred magnitudes.We plot the relative transmission for each filter obtained from the SVO Filter Profile Service (Rodrigo et al. 2012;Rodrigo & Solano 2020) above its photometric pair.There is a discontinuity on the wavelength axis at the top of each plot between the 2MASS magnitudes and AllWISE magnitudes.The Tycho-2 magnitudes for TYC 2010-124-1 are close to the catalog's limit of reliability (Høg et al. 2000).The B T magnitude difference corresponds to 2.1σ, which is unsurprising given the number of comparisons in our sample.However, the V T magnitude difference corresponds to 3.2σ, which we attribute to underestimated random uncertainties or systematic uncertainties at the faint end of the Tycho-2 photometric calibration.The consistency and overall small offsets between the observed and isochrone-inferred magnitudes demonstrate that our method of deriving the host stars' parameters is robust, especially when UV photometry is available.
We also collected three spectra for TOI-1712 between 2020 March 7 and 2023 February 3 using TRES.The exposure times ranged from 600 to 2160 s and with S/N between 35 and 67.These spectra revealed a cross-correlation function indicative of a double-lined spectroscopic binary.The evolution of the cross-correlation function suggests that (1) the primary shows some orbital motion as seen by Gaia and (2) the secondary appears stationary.Combined with the Gaia DR3 SB1 solution, this observation suggests that BD+45 1593 (TOI-1712) is a hierarchical triple system with an unresolved secondary diluting the transit observed by TESS.
We collected 11 spectra of TOI-5427 between 2022 September 25 and 2022 October 7 using the CTIO High Resolution Spectrometer (CHIRON; Tokovinin et al. 2013) high-resolution spectrograph, installed in the 1.5 m telescope at the Cerro Tololo International Observatory.We used an image In addition to the 30 minute cadence data for each of the objects, we include two-minute cadence data for TOI-1712 from TESS Sector 47 and ten-minute cadence data for TOI-5427 from Sectors 43, 44, and 45.We plot in red on top of the data the juliet-derived Gaussian process fits the light curves.We next use these fits to detrend the light curves before subsequently fitting the transits.
slicer that produces spectra with R ≈ 80, 000.The exposure times ranged between 3000 and 3650 s with S/N between 47 and 82 at 550 nm.We calibrated each science spectrum with a thorium-argon (ThAr) spectrum taken immediately beforehand to account for instrumental spectral drift and to compute a new wavelength solution automatically from this calibration with the CHIRON pipeline (Paredes et al. 2021).To extract the radial velocities from these CHIRON observations, we used a least squares deconvolution (Donati et al. 1997) approach where we deconvolved each spectrum against an ATLAS9 synthetic template (Kurucz 1992) following the technique described by Zhou et al. (2020).
We collected five spectra of TOI-5427 between 2022 November 14 and 2023 February 11 using the NEID spectrograph (Halverson et al. 2016;Schwab et al. 2016), a stabilized fiber-fed optical spectrograph on the WIYN 3.5 m telescope at Kitt Peak National Observatory (KPNO).We used the high-resolution (HR) mode that produces spectra with In addition to the 30 minute cadence data for each of the objects, we include two-minute cadence data for TOI-1712 from TESS Sector 47 and ten-minute cadence data for TOI-5427 from Sectors 43, 44, and 45.We overlay the data with red lines representing our juliet-derived transit fits.These fits demonstrate that the periods and transit shape parameters reported in the TOI catalog accurately reflect the data and are sufficient for comparison to external catalogs.R ≈ 110, 000 with exposure times of 480 s.The data were reduced using v1.2.0 of the standard NEID Data Reduction Pipeline (NEID-DRP),18 which derives radial velocities by cross-correlating the observed spectra with a weighted stellar mask (Baranne et al. 1996;Pepe et al. 2002).The median radial velocity precision attained was approximately 26 m s −1 .
To fit Keplerian orbits to these ground-based radial velocity data for TOI-2533 and TOI-5427, we use the thejoker Python package (Price-Whelan et al. 2017).We do not fit the TRES spectra for TOI-1712.For each system, we use the default priors in thejoker: a log-uniform prior in a period set to be between the 1σ confidence interval provided by TESS, a Gaussian prior in Doppler semiamplitude described by σ K = 1 km s −1 , and a Gaussian prior in systemic velocity described by σ v = 1 km s −1 .We sample this prior 200,000 times and conduct rejection sampling to obtain a set of initial parameters for use in a pymc3 (Salvatier et al. 2016) MCMC simulation.Using 10 chains, we generate a posterior distribution of 5000 samples with a burn-in of 20,000 samples.The resulting posterior distributions are both symmetric and unimodal.As suggested by the thejoker documentation,19 this unimodality suggests that these posterior samples are independent and represent a unique solution without the need for convergence tests due to the MCMC sampling method used by thejoker.We then take the 16th, 50th, and 84th percentiles of the resulting Doppler semiamplitude and eccentricity posteriors to obtain the values and uncertainties reported in Table 3.
Zero-point offsets between different precision radial velocity spectrographs with amplitudes of a few m s −1 are common.We therefore verify that any zero-point offsets have not affected our analysis of TOI-5427.We fit the radial velocities from each instrument with thejoker using the same process described above.We then compare the systemic velocity distributions between the two in Figure 7 and obtain the 16th, 50th, and 84th percentiles of the offset distribution by subtracting the systemic velocity posterior from NEID from the systemic velocity posterior from CHIRON.This results in an offset of 0.6 20.5 21.0 -- + m s −1 that is smaller than the uncertainties of the individual radial velocity measurements.This supports our decision to analyze both data sets without including zero-point offsets between them.We therefore combine the data from CHIRON and NEID to simultaneously fit the ensemble of radial velocities for TOI-5427.

Determination of the Companions' Properties
We solve the binary star mass function assuming that i sin 3 ≈1 and re-parameterize Equation (1) as a cubic equation where the coefficient B is defined as Taking the real root of Equation (3) results in a mass ratio that can then be used to determine companion masses given primary masses.Using the inclinations from each system's 30 minute cadence light curve juliet transit fit, we find that the i sin corrections for the companions result in adjustments  We use the 30 minute cadence light curve juliet-inferred radius ratio posteriors to calculate the secondary radii R 2 in Jupiter radii.In the TOI-1712 system, the flux from the eclipsing pair is diluted by an unresolved secondary revealed by the TRES spectra.We correct the dilution in the TOI-1712 light curve by incorporating into a juliet transit fit the TESS T-band flux ratio from our isochrones binary star fit posterior.We first take each point in the isochrones posterior and calculate the flux ratio of the secondary to the primary where T Aa and T B are the TESS T-band magnitudes of the primary and secondary.We next calculate the dilution D in the light curve for each point

This Work
Note.We derive the secondary mass for TYC 2010-124-1 and UCAC4 515-012898 using ground-based radial velocity data from TRES and both CHIRON and NEID, respectively.We use Lallement et al. (2022) and Vergely et al. (2022) for the A V extinctions.
We then fit the 30 minute cadence light curve of TOI-1712 for each point using the same procedure described in Section 3.1, but with the dilution prior set to be the posterior point's calculated dilution.We obtain the median radius ratio from each point's individual juliet posterior and use these points as our full radius ratio posterior for BD+45 1593.We then use the same procedure as with TYC 2010-124-1 and UCAC4 515-012898 to obtain the companion radius for BD+45 1593.
We use a Monte Carlo simulation to infer the mass and radius uncertainties for these three systems.We generate normal distributions for each thejoker Doppler analysisderived (for TYC 2010-124-1 and UCAC4 515-012898) or Gaia/TESS-derived (for BD+45 1593) parameter.The number of Monte Carlo trials is equal to the lesser of the number of data points in the mass and radius posterior distributions from isochrones and the number of data points in the radius ratio posterior from juliet (about 3000 samples).For the posterior with more data points, we randomly select a number of posterior points equal to the number of data points in the smaller posterior without replacement.For each set of points in the combined posteriors, we calculate a mass and radius inference for the companion, resulting in distributions that we characterize with their 16th, 50th, and 84th percentiles reported in Table 3.This approach captures the covariance between the stellar parameters from the isochrone fit in order to generate an accurate uncertainty for the companion mass and radius inferences.A caveat is that our reported uncertainties only include random uncertainties.The inclusion of systematic uncertainties would likely result in larger overall uncertainties (e.g., Tayar et al. 2022).
We account for contamination in the TESS light curve for UCAC4 515-012898 (TOI-5427), where the TESS contamination ratio is 26.3055%.This level of light curve contamination corresponds to a radius underestimate of 5.13%, so we increase our inferred radius for UCAC4 515-012898 b (TOI-5427) by 5.13% to account for this effect.BD+45 1593 (TOI-1712) and TYC 2010-124-1 (TOI-2533) have TESS contamination ratios indicative of radii underestimates that are smaller than our report uncertainties, so we do not increase uncertainties in either case.We provide corner plots illustrating this process and visualizing the covariances for each system in Figure 8.

Discussion
Our synthesis of Gaia DR3 SB1 solutions and TESS transit discoveries described in this article has revealed a new transiting brown dwarf and two very-low-mass eclipsing binary companions.We confirm that TOI-2533.very-low-mass star in a hierarchical triple system.The Gaia DR3 SB1 solutions for brown dwarfs and verylow-mass stars are consistent with the ground-based precision radial velocity-based SB1 solutions.While the Gaia Doppler semiamplitude for TYC 2010-124-1 is in good agreement with ground-based follow-up observations, it appears that Gaia has underestimated by about 2 km s −1 the Doppler semiamplitude of UCAC4 515-012898.The Gaia DR3 SB1 solutions also suggest a higher eccentricity for UCAC4 515-012898 and a slight phase shift for TYC 2010-124-1.We are unable to further investigate this issue, as the individual Gaia radial velocity measurements are not publicly available.For these two systems, the agreement between the Gaia DR3 and groundbased precision radial velocity SB1 solutions suggests that Gaia DR3 SB1 solutions are sufficiently precise to characterize massive brown dwarfs and low-mass stars.
It seems possible that the quality of the Gaia DR3 SB1 solution is proportional to the number of "good" radial velocity observations available by the time of Gaia DR3.The brown dwarf TYC 2010-124-1 b has 47 "good" Gaia DR3 radial velocities, while the very-low-mass stars BD+45 1593 Ab and UCAC4 515-012898 b only have 18 and 25, respectively.We suggest that the number of "good" Gaia radial velocities may be a useful metric for assessing future Gaia SB1 solutions.The fact that BD+45 1593 is an SB2 system may have affected Gaia's SB1 fit to its radial velocity variations.BD+45 1593 A is both hot and rotating quickly, and all of these facts make it a challenging target for Doppler observations.We plot our inferred masses and radii for the three secondaries in Figure 9 , is more than 80% larger than the radius R ≈ 1.0 R Jup predicted by the Baraffe et al. (2015) models for an isolated star with similar mass, composition, and age.Because the MIST and PAdova TRieste Stellar Evolutionary Code (PARSEC; Bressan et al. 2012;Nguyen et al. 2022) isochrone grids do not extend to these objects' mass ranges, we are unable to use them for comparison.Given the precisions of our mass, age, composition, and radius inferences, we find at over 9σ significance that BD+45 1593 Ab is inflated.We note that this estimate accounts for dilution from BD+45 1593 B, and in any case, dilution typically would lead to an underestimated radius.
Observations of radii about 10% larger than predicted by theoretical models appear to be ubiquitous among K and M dwarfs (Kraus et al. 2011;Birkby et al. 2012).These larger observed radii correspond to observed temperatures typically 5% cooler than predicted by models, though this effect is poorly studied due to the difficulty of determining late-type stellar temperatures (Ribas et al. 2008;Morales et al. 2009;Torres 2013).Magnetic are the most-favored explanation for this "radius inflation problem" (and its parallel "temperature suppression problem"), as they can increase the radii of stars yet are rarely included in stellar models.Strong magnetic fields are responsible for the significant starspot coverage of late-type dwarfs and may inhibit convective energy transport (Feiden & Chaboyer 2013).The net result of these two physical mechanisms is an increase in the photospheric radii of K and M dwarfs.
To empirically correct for radius underestimates, attempts have been made in the past to relate magnetic activity with proxies like rotation (Somers & Stassun 2017;Jaehnig et al. 2019), X-ray emission (López-Morales 2007), and Hα emission (Stassun et al. 2012).On the other hand, Mann et al. (2015) found no correlation between radius discrepancy and either Hα or X-ray emission.While models have had some success including magnetic fields in the context of X-ray emission (MacDonald & Mullan 2014), the magnetic field strengths required in this context might not be realistic (Feiden & Chaboyer 2014).More quantitative predictions from Browning et al. (2016) provided an upper bound for the possible strength of these magnetic fields via magnetohydrodynamic simulations, and MacDonald & Mullan (2015) provided a constraint based on lithium abundance.While this remains an active area of research, it appears that magnetic fields contribute to radius inflation in low-mass stars without accounting for all aspects of the radius inflation problem.
The eventual solution of the radius inference problem is important, as accurate and precise radii for low-mass stars are required for the inference of accurate and precise radii for the apparently common planets transiting low-mass stars (Cassan et al. 2012).As low-mass stars are also the most common type of star in the galaxy (Bochanski et al. 2010), we expect that a sizable portion of the Milky Way's exoplanet population orbits low-mass stars.Because of their small separations and high transit probabilities, habitable zone terrestrial planets are easier to find orbiting low-mass stars than solar-type stars.Low-mass stars are therefore the preferred target for habitable transiting planet search programs (Gould et al. 2003)  We propose that the intense instellation experienced by BD +45 1593 Ab is primarily responsible for its inflated radius.It has been suggested that in binary systems with two very-lowmass stars, instellation-driven radius inflation is limited to 5% (Lucy 2017).In this situation though, BD+45 1593 Ab is experiencing 500 times more flux than in the situation investigated by Lucy (2017).The increased surface temperature resulting from this instellation could decrease the temperature gradient of BD+45 1593 Ab near its surface, thereby limiting the ability of convection to transport energy in the same manner as magnetic fields.This diminished efficiency of convective energy transport would then lead to the inflated radius of    BD+45 1593 Ab.Indeed, the photospheric temperature of an isolated star with similar properties to BD+45 1593 Ab is expected to be T eff ≈ 2300 (Baraffe et al. 2015).Given its instellation, the "day side" equilibrium temperature of BD+45 1593 Ab could be as high as T eq ≈ 4400 K assuming a Bond albedo A B = 0 and no redistribution of heat.
Tidal effects may also play a role in the inflated radius of BD +45 1593 Ab, perhaps in a process analogous to the shear mixing that may occur in massive binaries (Song et al. 2013).The fully convective nature of BD+45 1593 Ab would make shear mixing inefficient, and its small eccentricity likely minimizes the importance of tidal dissipation for its inflated radius.The probable fast rotation of BD+45 1593 Ab resulting from its circular orbit, short circularization time, and therefore likely spin-orbit synchronization could contribute to its inflated radius, though the relationship between rotation and radius inflation is unclear (Jackson et al. 2019).Consequently, we conclude that instellation is the best candidate to explain the inflated radius of BD+45 1593 Ab.
We searched the light curves of TOI-1712 and TOI-5427 for secondary eclipses perfectly opposite the transits of TOI-1712.01and TOI-5427.01as expected for circular orbits.We were unable to identify a secondary eclipse in either case.This is not surprising, as the detection of a secondary eclipse would have eliminated these objects from consideration for inclusion in the TOI catalog.Given the precision of the TESS data for TOI-1712 and TOI-5427 and the expected secondary eclipse durations of TOI-1712.01and TOI-5427.01,we would have been able to identify secondary eclipses above 0.003% for TOI-1712 and above 0.01% for TOI-5427.This lack of a secondary eclipse detection does not constrain the "day side" temperature for UCAC4 515-012898 b, as we expect its photospheric temperature to have been undetectable given our limits.On the other hand, the nondetection of a secondary eclipse for TOI-  2023) models.The models we use assume solar metallicity, while our systems have slightly subsolar metallicities.However, these differences in metallicity are too small to produce a radius offset as large as we observe for BD+45 1593 Ab.Indeed, at the low-mass end of the MIST isochroe grid at M * ≈ 0.11 M e ≈ 110 M Jup a 0.2 dex decrease in [Fe/H] corresponds to no more than a 5% decrease in stellar radius.
1712.01 limits the "day side" temperature of BD+45 1593 Ab to less than 3200 K.The "day side" of BD+45 1593 Ab could be as hot as 4400 K if its albedo is zero and heat is not redistributed, so our nondetection of a secondary eclipse implies that either its albedo is nonzero or the redistribution of heat is efficient.
We compare TYC 2010-124-1 b to the Chabrier et al. (2023) brown dwarf isochrones in Figure 9. Isolated brown dwarfs cool and contract to settle into a typical mass range of between 0.7 and 1.4 Jupiter radii (Deleuil et al. 2008;Šubjak 2020;Carmichael et al. 2020) after at least 100 Myr.Objects younger than this tend to be larger Stassun et al. 2006;David et al. 2019.According to isolated brown dwarf evolution models (e.g., Baraffe et al. 2003;Saumon & Marley 2008;Phillips et al. 2020;Marley et al. 2021;Carmichael 2023), the rate of this contraction should decrease over time.However, the details of this process are unclear (Carmichael 2023).We find that the radius of TYC 2010-124-1 b is 9% bigger than the model prediction for an isolated brown dwarf, but this offset is only significant at the 1.9σ level.
The radius inflation we observe in BD+45 1593 Ab potentially parallels the processes responsible for the inflation of some hot Jupiters (e.g., Grunblatt et al. 2016Grunblatt et al. , 2017Grunblatt et al. , 2022b;;Wittenmyer et al. 2022).Hot Jupiters orbiting evolved stars are sometimes observed with larger radii than hot Jupiters orbiting main sequence stars (Grunblatt et al. 2019).In this case, the inflated radii of mature hot Jupiters orbiting evolved stars have been "reinflated" due to the rapid transport of energy deposited into their surface layers by their evolved host star into their interiors (e.g., Lopez & Fortney 2016;Thorngren & Fortney 2018;Thorngren et al. 2021).Intense instellation may therefore be capable of inflating radii from the giant planet regime up to the very-low-mass star regime.
Because theoretical models have struggled to explain the data that is currently available, a much larger sample of massive brown dwarfs and very-low-mass stars with precisely inferred radii relative to their solar-type primaries could lead to useful empirical radius calibrations.Our approach that combines Gaia SB1 solutions with transit discoveries from Kepler, K2, TESS, and the future PLAnetary Transits and Oscillations (PLATO) mission has the potential to precisely characterize over 400 brown dwarfs and low-mass stars.Such a catalog of radii precisely inferred relative to the radii of their primaries could be the basis of future empirical brown dwarf and low-mass star mass-radius relations.The masses inferred in this way using the Doppler technique with a known inclination are more precise and likely more accurate than other currently employed methods of mass inference such as astrometry or atmospheric fitting. 20As transit surveys typically focus on low-mass stars to find small-radius planets, these empirical stellar radii could lead to better planet radii which would lead to better atmospheric and interior structure inferences for terrestrial planets like those in the TRAPPIST-1 system.

Conclusion
We characterized three transiting systems: one brown dwarf and two low-mass stars in the TYC 2010-124-1, UCAC4 515-012898, and BD+45 1593 systems identified by TESS as TOI-2533.01, TOI-5427.01, andTOI-1712.01.We showed that the synthesis of Gaia DR3 SB1 solutions and TESS TOI discoveries offers a promising path to the large-scale, homogeneous characterization of low-mass stars and massive brown dwarfs.Gaia DR3 SB1 solutions and TESS transits indicated that the masses of the transiting objects in all three systems were consistent with the brown dwarf-mass range.Ground-based precision radial velocity measurements confirmed that TOI-2533.01 is a transiting brown dwarf with M M M 72 0.069 transiting a massive subgiant primary in the hierarchical triple system BD+45 1593.The star BD+45 1593 Ab has a radius nearly 80% larger than predicted by theoretical models for an isolated star with similar masses, solar composition, and age equal to that of the primary BD+45 1593 Aa.While the observation of very-low-mass stars with radii larger than predicted by theoretical models seems to be ubiquitous and often attributed to magnetic fields, radius inflation as large as we observe in BD+45 1593 Ab cannot be attributed to the effect of magnetic fields alone.We suggest that the intense instellation experienced by BD+45 1593 Ab heats its photosphere beyond the photospheric temperature expected for an isolated star with similar parameters.This increased photospheric temperature diminishes the temperature gradient in the outer parts of BD+45 1593 Ab, suppresses convection, and leads to its inflated radius.Future studies of systems with Gaia SB1 solutions and Kepler, K2, TESS, or PLATO transit detections have the potential to provide hundreds of precise radius inferences for brown dwarfs and very-low-mass stars.These latter data would be critical for the calibration of empirical mass-radius relations for very-low-mass stars that would be very useful for the calculation of the radii of planets transiting very-low-mass stars like those in the TRAPPIST-1 system.

Figure 1 .
Figure 1.Doppler curves for BD+45 1593, TYC 2010-124-1, and UCAC4 515-012898 based on their Gaia DR3 and ground-based SB1 solutions.We plot 2000partially transparent blue lines to represent individual solutions sampled from normal distributions of the Gaia Doppler semiamplitude, eccentricity, and argument of periastron, with the standard deviation of each distribution representing the reported error on its respective parameter.Gaia's reported uncertainties on each parameter are derived from the variance-covariance matrix of the solution, but the matrix itself is not reported; we therefore do not correct for it in this plot.We plot the individual precision ground-based radial velocity measurements and their uncertainties as light blue circles with black borders and error bars.We plot the Doppler curves inferred from these data as dashed black lines.The agreement between the Gaia and precision ground-based SB1 solutions demonstrates the fidelity of the Gaia SB1 solutions at low Doppler semiamplitude.

Figure 2 .
Figure 2. TESS FFI approximately 2048 × 2048 pixel postage stamps for TOI-1712, TOI-2533, and TOI-5427.TESS collected the FFI for TOI-1712 during Sector 20, the FFI for TOI-2533 during Sector 23, and the FFI for TOI-5427 during Sector 6.We center each postage stamp on the target and mark each G < 15 Gaia DR3 source with a white circle of radius inversely proportional to the Gaia G magnitude.These FFIs show that blending is not a concern for the light curves of the objects.

Figure 3 .
Figure3.Comparison between the observed magnitudes for the three systems and the isochrone-derived magnitudes of the combined binary system (in the case of BD +45 1593) or the primaries (in the case of TYC 2010-124-1 and UCAC4 515-012898).For each filter, we plot filled circles to represent the observed magnitudes and unfilled circles to represent the isochrone-inferred magnitudes.We plot the relative transmission for each filter obtained from the SVO Filter Profile Service(Rodrigo et al. 2012;Rodrigo & Solano 2020) above its photometric pair.There is a discontinuity on the wavelength axis at the top of each plot between the 2MASS magnitudes and AllWISE magnitudes.The Tycho-2 magnitudes for TYC 2010-124-1 are close to the catalog's limit of reliability(Høg et al. 2000).The B T magnitude difference corresponds to 2.1σ, which is unsurprising given the number of comparisons in our sample.However, the V T magnitude difference corresponds to 3.2σ, which we attribute to underestimated random uncertainties or systematic uncertainties at the faint end of the Tycho-2 photometric calibration.The consistency and overall small offsets between the observed and isochrone-inferred magnitudes demonstrate that our method of deriving the host stars' parameters is robust, especially when UV photometry is available.

Figure 4 .
Figure 4. TESS Science Processing Operations Center (SPOC)-reduced light curves for TOI-1712, TOI-2533, and TOI-5427.In addition to the 30 minute cadence data for each of the objects, we include two-minute cadence data for TOI-1712 from TESS Sector 47 and ten-minute cadence data for TOI-5427 from Sectors 43, 44, and 45.We plot in red on top of the data the juliet-derived Gaussian process fits the light curves.We next use these fits to detrend the light curves before subsequently fitting the transits.

Figure 5 .
Figure5.Detrended light curves for TOI-1712, TOI-2533, and TOI-5427.In addition to the 30 minute cadence data for each of the objects, we include two-minute cadence data for TOI-1712 from TESS Sector 47 and ten-minute cadence data for TOI-5427 from Sectors 43, 44, and 45.We overlay the data with red lines representing our juliet-derived transit fits.These fits demonstrate that the periods and transit shape parameters reported in the TOI catalog accurately reflect the data and are sufficient for comparison to external catalogs.

Figure 6 .
Figure 6.Phased light curves for the 30 minute cadence data of TOI-1712, TOI-2533, and TOI-5427.We overlay the data with red lines representing the julietderived transit fits.The relative flux axes are consistent across the three objects to illustrate their differing transit depths.

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transiting brown dwarf, placing it in a class of only a few dozen such objects.We include in

Figure 7 .
Figure 7.Comparison between CHIRON and NEID velocity zero-point offsets for TOI-5427.We plot distribution medians as solid vertical lines and the 16th and 84th percentiles as dashed vertical lines.Left: Distributions of Monte Carlo samples from thejoker Doppler solution systemic velocities after fitting to radial velocity measurements taken by CHIRON and NEID.Right: Distribution of the differences between the two distributions in the left-hand panel.The resulting median offset is much smaller than the individual radial velocity uncertainties, suggesting that the data sets are consistent with each other.
. While we find that our mass and radius inferences for TYC 2010-124-1 b are consistent with the Chabrier et al. (2023) theoretical models for brown dwarfs, the radius of UCAC4 515-012898 b is about 6% larger than predicted by the Baraffe et al. (2015) theoretical models for isolated stars of the same mass, as is often the case for lowmass stars.In contrast, the radius of BD+45 1593 Ab R like MEarth (Nutzman & Charbonneau 2008), the TRAnsiting Planets and PlanetesImals Small Telescope (TRAPPIST; Jehin et al. 2011 ), the Next-Generation Transit Survey (NGTS; West et al. 2016), and TESS (Ricker et al. 2014).Unaccounted for, the radius inflation problem would lead to underestimated radii for planets transiting M dwarfs.An underestimated radius could cause a nonterrestrial, uninhabitable planet to be mistakenly classified as a terrestrial, possibly habitable planet.

Figure 9 .
Figure 9. Comparisons between predicted and observed masses and radii.Top: mass-radius relations assuming our isochrone-inferred system ages.We plot the massradius relation at each system's age as the solid line and indicate its 1σ uncertainty as the shaded region.Bottom: mass-radius relations assuming a range of ages.Thicker lines refer to older ages.BD+45 1593 Ab has a significantly larger radius than predicted by the Baraffe et al. (2015) theoretical models.UCAC4 515-012898 b is slightly bigger than predicted by the Baraffe et al. (2015) theoretical models as is frequently observed for low-mass stars.TYC 2010-124-1 b is consistent with the Chabrier et al. (2023) models.The models we use assume solar metallicity, while our systems have slightly subsolar metallicities.However, these differences in metallicity are too small to produce a radius offset as large as we observe for BD+45 1593 Ab.Indeed, at the low-mass end of the MIST isochroe grid at M * ≈ 0.11 M e ≈ 110 M Jup a 0.2 dex decrease in [Fe/H] corresponds to no more than a 5% decrease in stellar radius.

Table 3
Properties of the Objects and their Host Stars

Table 4
Literature Sample of Transiting Brown Dwarfs as of June 2023