TOI-503: The First Known Brown-dwarf Am-star Binary from the TESS Mission^*

TESS monitored TOI-503 at a 2-minute cadence from 2019 January 8 to February 1 (∼24.5 days). There is a gap of 1.7 days during this time due to the transfer of data from the spacecraft. The TESS Input Catalog (TIC) ID of the source is 186812530 (Stassun et al. 2018b), and it was observed in CCD 3 of camera 1 in Sector 7. TOI-503 will not be observed in any upcoming sectors of the primary TESS mission. We use the publicly available Pre-search Data Conditioning Simple Aperture Photometry (PDCSAP; Stumpe et al. 2014; Smith et al. 2012) light curves at Mikulski Archive for Space Telescopes (MAST)⁵³ that are provided by the TESS Science Processing Operations Center (SPOC). The PDCSAP light curves have the systematics of the spacecraft removed. The SPOC pipeline (Jenkins et al. 2016) was used to extract the light curve and associated uncertainties from the original scientific data. We normalize this light curve by dividing it by the median-smoothed flux, which can be seen in Figure 1. A total of 6 transits spaced at a period of ∼3.7 days are visible with depths of ∼4500 ppm. The TESS data validation reports (Jenkins et al. 2016) identify TOI-503 as the host of a planet candidate with an estimated radius of 1.13 ± 0.28 ${R}_{{\rm{J}}}$ by fitting the TESS light curve and using host-star parameters from Stassun et al. (2018b). The basic parameters of the star are listed in Table 1.

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As part of the TESS Follow-up Observation Program (TFOP), additional ground-based photometry was carried out by the Sinistro camera on the Las Cumbres Observatory (LCO), Siding Spring Observatory (SSO) 1.0 m on 2019 March 19, the Santa Barbara Instrument Group (SBIG) camera on the LCO 0.4 m on 2019 March 19, the Chilean Hungarian Automated Telescope (CHAT) 0.7 m on 2019 March 22, and the KeplerCam instrument on the Fred Lawrence Whipple Observatory (FLWO) 1.2 m on 2019 April 25. The LCO-SSO observations were taken in the Y-band and confirmed that there are no nearby or background eclipsing binaries within 25 that were blended in the aperture of camera 1 from TESS. The transit was not detected by LCO-SSO due to the insufficient amount of out-of-transit baseline flux. The observations with SBIG show a clear ingress but do not extend long enough to show the egress of the transit due to the target star reaching a high airmass. A full on-time transit was detected by CHAT in the ıband as well as the KeplerCam instrument in the z band. By independently fitting just the KeplerCam light curve using AstroImageJ (Collins et al. 2017), we find that the modeled transit center time is consistent with the time predicted by the public TESS ephemeris within 1σ uncertainty. We decide against incorporating any ground-based follow-up in our joint analysis due to the shallow nature of this transit and the low transit depth signal-to-noise ratio.

The TFOP was also responsible for observations of TOI-503 with Gemini/NIRI on 2019 March 22, and again with Keck/NIRC2 (Wizinowich et al. 2000) on 2019 April 7 (Figure 2). In each case, observations were taken in NGS mode in the Br-γ filter with the target as the guide star. Images were dithered, such that a sky background could be constructed, with a square dithering pattern for the NIRI data and a 3-point pattern for the NIRC2 data to avoid the known noisy fourth quadrant. For each instrument we used the same basic reduction procedure: images were flat-fielded and sky-subtracted, and the dithered frames were aligned and co-added.

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Sensitivity was determined by injecting simulated sources azimuthally around the primary target, at separations of integer multiples of the central source's full width at half maximum (Furlan et al. 2017). The brightness of each injected source was scaled until standard aperture photometry detected it with 5σ significance. The resulting brightness of the injected sources relative to the target set the contrast limits at that injection location. The final 5σ limit at each separation was determined from the average of all of the determined limits at that separation and the uncertainty on the limit was set by the rms dispersion of the azimuthal slices at a given radial distance. No nearby contaminating sources are identified in either image, and at 1'' we reach contrasts of Δmag = 8.0 mag in the NIRI data and Δmag = 7.2 mag in the NIRC2 data.

We obtained a total of 50 spectra of TOI-503 between 2019 March 18, and 2019 April 17 using KESPRINT observing time on the 2 m Perek telescope at the Ondřejov Observatory, the 2 m Alfred Jensch telescope at Tautenburg, and the 2.56 m Nordic Optical Telescope (NOT) at the Roque de Los Muchachos Observatory. Using the central Europe monitoring network with telescopes in Ondřejov and Tautenburg for simultaneous observations has the advantage of allowing a better coverage of observing data. Furthermore, both telescopes are capable of long-term monitoring of interesting objects (Kabáth et al. 2019b). For these reasons, such observations are often performed (Kabáth et al. 2019a; Sabotta et al. 2019; Skarka et al. 2019). RVs from all used telescopes beyond the KESPRINT are reported in Table 2.

We collected a set of 14 spectra using the Ondřejov Echelle Spectrograph, which has a spectral resolving power R ≈ 44,000 over the wavelength range of 370–850 nm (Kabáth et al. 2019b, 2020). All spectra have an exposure time of 3600 s resulting in a signal-to-noise (S/N) per pixel at 550 nm varying between 16 and 22, depending on the observing conditions and the airmass. We use the standard IRAF 2.16 routines (Tody 1993) to process the spectra, which were corrected for bias, flat field, and cosmic rays. The spectrum with the highest S/N was used as template for the cross-correlation done with the IRAF fxcor routine, allowing us to remove instrumental shift by measuring the shift in telluric lines, and to measure the relative RVs. The errors are standard deviations of values from eighteen 10 nm intervals that were considered.

2.5.1. FIES Spectra

2.5.2. Tautenburg Spectra and Doppler Tomography Analysis

We used the 2 m Alfred Jensch telescope of the Thüringer Landessternwarte Tautenburg to obtain 28 spectra of TOI-503. The telescope is equipped with an echelle spectrograph with spectral resolving power R ≈ 35,000 with the 2'' slit used. The spectra used for orbital analysis have an exposure time 1200 s, resulting in an S/N ratio between 23 and 27. We processed the spectra using the Tautenburg Spectroscopy pipeline (Sabotta et al. 2019) built upon PyRaf and the Cosmic Ray code by Malte Tewes based on the method by van Dokkum (2001). We use cross-correlation routines from IRAF to correct spectra for the shift in telluric lines and to measure the relative RVs. There are 17 spectra from the 28 that have an exposure time of 600 s and that were taken in an attempt to extract a Doppler tomography (DT; e.g., Hatzes 1998; Albrecht et al. 2007; Collier Cameron et al. 2010a) signal during the transit night of 2019 April 17. These are not used for the RV measurements to avoid the signal created by the BD blocking light from the host star, which creates an additional Doppler shift that is based on the orbital alignment and rotation rate of the star, and not the orbital motion of the BD.

The DT technique reveals the distortion of the stellar line profiles when a planet or BD blocks part of the stellar photosphere during a transit. This distortion is a tiny bump in the stellar absorption profile, scaled down in width according to the BD-to-star radius ratio. Additionally, the area of that bump corresponds to the BD-to-stellar disks area ratio. As the BD moves across the stellar disk, the bump produces a trace in the time series of line profiles, which reveals the spin–orbit alignment between the star and BD orbit. For this analysis, we first created a reference stellar absorption spectrum consisting of delta functions at the wavelength positions of the observed stellar absorption lines. Their positions and strengths were determined by fitting each stellar absorption line in the observed spectrum with the rotational profile of TOI-503 ($v\sin i=26\ \mathrm{km}\,{{\rm{s}}}^{-1}$). A total of 410 stellar absorption lines were identified in the wavelength range from 455.8 to 674.6 nm. We excluded those wavelength regions from our analysis which exhibited telluric lines, the Hydrogen Balmer absorption lines, and the Na II doublet around 589 nm.

By employing a least-squares deconvolution similar to what is shown in Collier Cameron et al. (2002) of the observed spectra with the reference spectrum, we summed up the 410 stellar absorption lines in each spectrum into one high S/N mean line profile. The resulting line profiles were scaled so that their height was one, and were interpolated onto a velocity grid of 2.65 km s⁻¹ increments, corresponding to the velocity range of one spectral pixel at 550 nm. We then summed up all the mean line profiles collected the nights before the transit and subtracted the resulting profile from the in-transit ones. Figure 3 shows the residuals of the line profiles and shows that we are unable to detect a trace of the transiting planet using this method.

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We used the Tillinghast Reflector Echelle Spectrograph (TRES) on Mount Hopkins, Arizona, to obtain spectra of TOI-503 between 2019 March 23 and April 14. The spectrograph has a resolving power of R ≈ 44,000 and covers wavelengths from 390 to 910 nm. Forty-three spectra of TOI-503 were taken with TRES with exposure times ranging from 195 to 300 s and S/N ranging from 35 to 59. The relative RVs that we derive from TRES spectra use multiple echelle orders from each spectrum that are cross-correlated with the highest S/N spectrum of the target star. We omit individual orders with poor S/N and manually remove obvious cosmic rays. Of these 43 spectra, 33 were taken in an attempt to extract a DT signal, but as with our analysis of the Tautenburg in-transit DT spectra, we do not find a noticeable signal.

We obtained seven spectra with the PARAS spectrograph (Chakraborty et al. 2014) coupled with the 1.2 m telescope at Gurushikhar Observatory, Mount Abu, India, between 2019 April 6 and 11 at a resolving power of R ≈ 67,000, in the wavelength range of 380–690 nm. Each night had a median seeing of around 15. The exposure time for each measurement was kept at 1800 s, which resulted in a S/N of 20–25 at the blaze peak wavelength of 550 nm. The spectra were extracted using a custom-designed automated pipeline written in IDL, based on the algorithms of Piskunov & Valenti (2002). The extracted spectra were cross-correlated with the template spectrum of an A-type star to calculate the relative RVs. Further details of the spectrograph and data-analysis procedure can be found in Chakraborty et al. (2014). The uncertainties reported here are the cross-correlation function fitting errors combined with the photon noise in the same way as described in Chaturvedi et al. (2016, 2018).

We use iSpec (Blanco-Cuaresma et al. 2014; Blanco-Cuaresma 2019) and the Stellar Parameter Classification (SPC) software Buchhave et al. (2012) to analyze the spectra of TOI-503. Then, with the spectral properties as well as an SED, a light curve, and a Gaia parallax of the star, we use EXOFASTv2 (Eastman et al. 2019), and a combination of PARAM 1.3 (to model the stellar parameters; da Silva et al. 2006), GeePea (to model the light curve; Gibson et al. 2012), and Systemic Console (to model the RV curve; Meschiari et al. 2009), to independently model the star and BD.

3.1.1. iSpec Stellar Parameters

We use iSpec to perform a detailed analysis of the host star from the FIES spectra. Specifically, we use the Synthe radiative transfer code (Kurucz 1993), the MARCS atmosphere models (Gustafsson et al. 2008), and version 5 of the GES atomic line list (Heiter et al. 2015) between 420 and 920 nm, which includes 35 different chemical species. These are incorporated into the framework of iSpec. We co-add all the eight FIES spectra (after the RV shift correction) to increase the S/N and use them to determine the effective temperature T_eff, metallicity [Fe/H], surface gravity $\mathrm{log}g$, and the projected stellar equatorial velocity $v\sin i$. We model the stellar parameters using the Bayesian parameter estimation code PARAM 1.3 and use the parallax measured by Gaia DR2 ($\varpi =3.8875\pm 0.0591$ mas; Lindegren et al. 2018) for the distance of the star and Tycho V magnitude (Høg et al. 2000). PARAM 1.3 code estimates stellar properties using the PARSEC isochrones (Bressan et al. 2012). We calculate the value of $\mathrm{log}g$ iteratively to ensure an agreement between iSpec and PARAM 1.3. We determine the effective temperature by fitting the Hα Balmer line (Cayrel et al. 2011), and the metallicity by fitting for 22 Fe i lines in the interval 597–643 nm. From this analysis, we find TOI-503 to be a metallic-line A star, or Am star, with a metallicity of $[\mathrm{Fe}/{\rm{H}}]=0.61\pm 0.07$.

The formation of Am stars is generally attributed to the slowing of the stellar rotation via tidal force caused by a binary star (Michaud et al. 1983). Am stars are generally slow rotators compared to typical A stars, with rotation rates below 120 km s⁻¹ (Abt & Morrell 1995). The study by Abt & Moyd (1973) suggests that all slowly rotating A-type main-sequence stars are chemically peculiar (i.e., those with high iron abundance or unusual depletion of key elements such as Ca). The rotation period of TOI-503 (P_rot = 3.64 days) is determined from the projected stellar equatorial velocity, the inclination derived from GeePea, and the radius of the star derived from PARAM 1.3. The rotation period of the star is similar to the orbital period of the BD (P_orb = 3.67 days), which is indicative of synchronism. This analysis assumes the alignment between the equatorial and orbital planes of the star. However, such an assumption is not surprising for the close binary system like TOI-503. For example, the paper by Hale (1994) suggests approximate alignment for solar-type binaries under the separation of 30–40 au. The paper by Hut (1980) shows that for close binary systems where the tidal evolution is the primary mechanism linked with temporal changes in orbital parameters, the tidal equilibrium can be established only under assumptions of coplanarity, circularity, and synchronized rotation. Furthermore, the similarity with the rotation period determined from the photometric light curve in Section 3.1.4 also reflects approximate alignment. Such a slow rotation rate would enable the onset of radiative diffusion within the stable atmosphere, which leads to the abundance of elements observed in the spectrum, as in Am stars (Michaud et al. 1983). In this context, comparing the TOI-503 spectrum with the templates of a normal A-type star, a magnetically peculiar Ap star, and an Am star from the ESO database⁵⁴ reveals the clear similarity between the observed spectrum of TOI-503 and that of the Am stars (Figure 4). However, the most persuasive argument would be that the overabundance (in context of A-type stars) of the iron group elements is coupled with an underabundance of key light elements, such as Ca, Sc, or Mg, which is the characteristic sign of Am stars. The abundances we derive point to this conclusion precisely, thereby confirming the Am classification. The stellar parameters and the abundances of selected species are reported in Table 3.

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Table 3.  Comparison of Parameters between Analysis Methods

Parameter	SPC/EXOFASTv2	iSpec/PARAM 1.3
M⋆ (M*)	1.80 ± 0.06	1.78 ± 0.02
R⋆ (R*)	1.70 ± 0.05	1.77 ± 0.04
$\mathrm{log}g$	4.23 ± 0.03	4.17 ± 0.02
Teff (K)	7650 ± 160	7639 ± 105
[Fe/H]	0.30 ± 0.09	0.61 ± 0.07
[Ni/H]	⋯	0.58 ± 0.09
[Ca/H]	⋯	−0.40 ± 0.11
[Sc/H]	⋯	0.10 ± 0.14
[Mg/H]	⋯	0.25 ± 0.15
${v}_{\mathrm{rot}}\sin {i}_{\star }$ (km s−1)	28.6 ± 0.4	25.0 ± 0.3
Prot (days)	3.01 ± 0.09	3.64 ± 0.13
Age (Gyr)	${0.18}_{-0.11}^{+0.17}$	0.14 ± 0.04
Parameter	EXOFASTv2	GeePea/Systemic Console
Mb (MJ)	53.7 ± 1.2	53.3 ± 1.1
Rb (RJ)	1.34 ± 0.26	1.28 ± 0.29
${R}_{b,\mathrm{mode}}$ (RJ)	1.27 ± 0.15	⋯
Period (days)	3.6772 ± 0.0001	3.6775 ± 0.0002
a/R*	7.22 ± 0.22	7.47 ± 0.19
Rb/R*	0.0805 ± 0.015	0.0724 ± 0.015
b	0.974 ± 0.022	0.956 ± 0.023
Inclination i (degree)	82.25 ± 0.41	82.65 ± 0.38
e	0 (adopted)	0 (adopted)

Note. The parameters here are the median values except for the EXOFASTv2 R_p, which shows both the median and the mode.

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3.1.2. Stellar Parameter Classification and EXOFASTv2 Modeling

We also use SPC with the TRES spectra to independently (from iSpec and FIES) derive effective temperature (T_eff), metallicity ([Fe/H]), surface gravity ($\mathrm{log}g$), and the projected stellar equatorial velocity ($v\sin i$) for TOI-503. We iteratively use SPC with EXOFASTv2 (Eastman et al. 2019) to determine values for T_eff and [Fe/H], meaning that we use the $\mathrm{log}g$ from EXOFASTv2 as a fixed parameter in SPC and then take the T_eff and [Fe/H] from SPC (with the fixed $\mathrm{log}g$ from EXOFASTv2) as starting values in a new EXOFASTv2 analysis. However, due to the upper limit of [Fe/H] ≤ +0.5 for the metallicity of the MIST isochrones (Paxton et al. 2015; Choi et al. 2016; Dotter 2016) that EXOFASTv2 utilizes, we rely on our measurements using iSpec for the metallicity. With SPC, we measure a metallicity of $[\mathrm{Fe}/{\rm{H}}]=0.34\pm 0.08$ with a fixed $\mathrm{log}g=4.23$ from an initial EXOFASTv2 analysis. The parameters T_eff, [Fe/H], and $\mathrm{log}g$ are not fixed in subsequent EXOFASTv2 analyses, and only $\mathrm{log}g$ is fixed in subsequent SPC analyses. The [Fe/H] value is about 0.27 dex lower than our value from iSpec, most likely because SPC explicitly measures [m/H], which is a good approximation for [Fe/H], assuming a Solar-like composition and chemical proportions (not the case for TOI-503). We use SPC on a co-added spectrum with the RV shifts corrected for. We do not co-add any spectrum with S/N < 15. With SPC, we use the 503–532 nm wavelength range (centered on the Mg b triplet) on a single co-added TRES spectrum.

We derive the mass and radius of the BD using EXOFASTv2, which uses the Monte Carlo-Markov Chain (MCMC) method. For each MCMC fit, we use N = 36 (N = 2 × n_parameters) walkers, or chains, and run for 50,000 steps, or links. We modeled the host star mass and radius using the MIST isochrones, which are integrated into the framework of EXOFASTv2. Figure 5 shows the orbital solution we derive with EXOFASTv2 with a joint fit of the RV and transit data. Our transit solution from this same joint fit agrees with that shown via the GeePea analysis (Figure 6). We account for interstellar extinction, A_V, using the Galactic dust and reddening extinction tool from IRAS and COBE/DIRBE,⁵⁵ and take this value of A_V = 0.0791 as an upper limit for our priors in EXOFASTv2. We also use the parallax of TOI-503 as measured by Gaia DR2 and the SPC results for T_eff and metallicity ([Fe/H] = 0.34) as starting points for our priors. The full list of free parameters we specify for each object is period P, time of conjunction (T_C in BJD), host star effective temperature T_eff, host star metallicity [Fe/H], RV semi-amplitude K, RV relative offset to the systemic velocity γ_rel, interstellar extinction A_V, parallax, orbital inclination i, and R_B/R_⋆. We initially allow the eccentricity e to be a free parameter and find it to be close to zero at e ≈ 0.007 ± 0.003 ($e\,\cos \,\omega =-0.0058\pm 0.0032$, $e\,\sin \,\omega =-0.0004\pm 0.0037$). In order to avoid the Lucy–Sweeney bias (Lucy & Sweeney 1971), we fix the eccentricity to zero in all subsequent analyses. The derived T_eff from EXOFASTv2 agrees well with the spectroscopic T_eff from SPC. We impose Gaussian priors on these free parameters in EXOFASTv2. The median value with 1σ uncertainties of the MCMC chains for each parameter is reported in Table 4. The parameters derived from EXOFASTv2 are consistent with those derived from our other independent analyses.

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3.1.3. Systemic Console and GeePea Modeling

3.1.4. Analysing the Surface Rotation

Even though it is not completely clear that A-type stars have spots, there are a variety of studies on the discovery of spots on the well-known star Vega (Balona 2017; Böhm et al. 2015; Petit et al. 2017) and more studies about the measurement of the rotation based on spot modulation for A-type stars (Balona 2011, 2013). There is even previous evidence of the detectable presence of spots on Am-type stars (Balona et al. 2015). Thus it is reasonable to search for the signature of the rotation period through the modulation caused by the star spots in TOI-503. To do this, we use the SPOC two-minute cadence light curve of TOI-503. We removed the signal of the primary and secondary transits using the known ephemerides and then filled all gaps, including the transits and the data-transfer gaps, using in-painting techniques based on a multi-scale discrete cosine transform as described in García et al. (2014b) and Pires et al. (2015).

We then search for modulation in the resulting light curve by performing the following steps. First, we perform a time-frequency analysis based on wavelets decomposition (Torrence & Compo 1998; Mathur et al. 2010; García et al. 2014a) to compute the wavelet power spectrum (WPS), which we subsequently project on the period axis to form the global wavelets power spectrum (GWPS). In the second step, we perform auto-correlation function analysis (ACF, McQuillan et al. 2014) to extract the most significant signal, which corresponds to a particular period. Finally, by a combination of previous two steps (specifically multiplying them), we create a function called the composite spectrum (CS; Ceillier et al. 2016, 2017). As these steps are sensitive to different types of artifacts in a light curve, by deriving the CS, we can mask such artifacts and highlight a periodic signal created by stellar activity such as star spots. The pipeline that combines these different techniques has been applied to simulated data (Aigrain et al. 2015) and has been already performed to a large number of solar-like stars and red giants (e.g., Santos et al. 2019) with reliable success.

The original light-curve analysis with the transits provides a period of ${P}_{\mathrm{GWPS}}=3.66$ days, corresponding to the orbital period of the BD. Once the transits are removed, we find a period of ${P}_{\mathrm{GWPS}}=3.24$ days with the wavelet analysis and ${P}_{\mathrm{ACF}}=3.55$ days with the ACF analysis. The height of the peak in the ACF (H_ACF, measured from the maximum to the adjacent minima) is  0.5, which fulfills our criteria for a reliable result (${H}_{\mathrm{ACF}\gt 0.4}$). We note that we detect the overtone of half of the real rotation period ${P}_{\mathrm{GWPS}}=1.8$ days using wavelets decomposition analysis, which can be seen in Figure 8. This period is detected in power spectra quite often and happens when we observe active regions on the visible side of the star and diametrically opposite side of the star. This period is absent in the CS power spectrum and reveals the final period of ${P}_{\mathrm{CS}}=3.50\pm 0.12$ days. These results are slightly lower than the BD orbital period, but still quite close to it. The rotation period found (Table 3) also agrees with the values obtained spectroscopically from the iSpec and SPC analyses.

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However, given the close values of the rotation period with the orbital period, we cannot completely rule out that the modulation we measure is affected by the orbital motion of the BD. Such an effect would project to LC in the form of additional signals, which are the ellipsoidal deformation signal on the primary star, and the optical reflection plus thermal phase curve signal. We try to distinguish these signals to find the real rotation period. To do so, we apply LS periodograms to the SPOC LC and fit the most significant periods by using the Levenberg–Marquardt minimization method. In Figure 9 we provide the ellipsoidal deformation signal with a period of half of the orbital period with maxima corresponding to phases 0.25 and 0.75 and rotational signal with a period of 3.3 days. We are not able to see any other signals in the LC. That is possibly linked with the nature of this BD. However, future investigation is needed to find an answer.

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3.1.5. Stellar Parameters from Gaia DR2

As an additional independent check on the derived stellar parameters, we performed an analysis of the broadband spectral energy distribution (SED) together with the Gaia DR2 parallax in order to determine an empirical measurement of the stellar radius, following the procedures described in Stassun & Torres (2016) and Stassun et al. (2017, 2018a). We pulled the ${B}_{T}{V}_{T}$ magnitudes from Tycho-2, the Strömgren ubvy magnitudes from Paunzen (2015), the BVgri magnitudes from APASS, the JHK_S magnitudes from 2MASS, the W1–W4 magnitudes from WISE, and the G magnitude from Gaia. We also used the GALEX NUV and/or FUV fluxes, which are available in this case. Together, the available photometry spans the full stellar SED over the wavelength range 0.35–22 μm, and extends down to 0.15 μm when GALEX data are available (see Figure 10). We performed a fit using Kurucz stellar atmosphere models, with the priors on effective temperature (T_eff), surface gravity ($\mathrm{log}g$), and metallicity ([Fe/H]) from the spectroscopically determined values. The remaining free parameter is the extinction (A_V), which we restricted to the maximum line-of-sight value from the dust maps of Schlegel et al. (1998).

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The resulting fit is very good (Figure 10), with a reduced ${\chi }^{2}$ of 4.8. The best-fit extinction is ${A}_{V}={0.00}_{-0.00}^{+0.06}$, which is consistent with what we find with EXOFASTv2 (${A}_{V}={0.038}_{-0.026}^{+0.028}$). This zero extinction is consistent with the maximum line-of-sight extinction from the one-dimensional dust maps from Schlegel et al. (1998) of 0.09 mag, as well as the ${A}_{V}=0.12\pm 0.06$ value from Amôres & Lépine (2005). Integrating the (unreddened) model SED gives the bolometric flux at Earth of ${F}_{\mathrm{bol}}=4.18\,\pm 0.15\times {10}^{-9}$ erg s cm⁻². Taking the ${F}_{\mathrm{bol}}$ and T_eff together with the Gaia DR2 parallax, adjusted by $+0.08$ mas to account for the systematic offset reported by Stassun & Torres (2018), gives the stellar radius as $R=1.66\pm 0.05$ ${R}_{\odot }$. We note that when we do not account for this systematic offset (as with our values in Table 3 and Figure 11), we measure roughly $2.3 \%$ larger radii for the star and BD. This difference does not affect our final conclusions about this system. Finally, estimating the stellar mass from the empirical relations of Torres et al. (2010) gives $M=1.90\pm 0.11{M}_{\odot }$, which with the radius gives the density $\rho =0.58\pm 0.06$ g cm⁻³. We find that this independent check on the stellar mass and radius agrees with the values shown in Table 3.

We report an age of ${180}_{-110}^{+170}$ Myr for TOI-503 using the MIST models and EXOFASTv2. We find this consistent with the Yonsei-Yale (YY) isochrone models (Spada et al. 2013), from which we report an age of ${200}_{-130}^{+200}$ Myr. Both the MIST and YY isochrone grids are incorporated into the framework of EXOFASTv2. A stellar mass track is interpolated from the grids for the MIST or YY isochrones, and from this, an age is estimated (Eastman et al. 2019). We reiterate that the metallicity range of MIST isochrones is −5.0 $\leqslant$ [Fe/H] $\leqslant$ 0.5, which may influence the accuracy of the age estimate, given that we measure a spectroscopic [Fe/H] of 0.6 with iSpec. The YY isochrones have a metallicity range of −3.29 $\leqslant$ [Fe/H] $\leqslant$ 0.78, which makes this set of isochrones better suited to this system. Still, we find the stellar and BD properties to be consistent between the two isochrone models.

We now look at the Baraffe et al. (2003; COND03) and Saumon & Marley (2008; SM08) substellar evolutionary models to examine how well they serve as predictors of the age of TOI-503b (Figure 11). The COND03 models present evolutionary tracks for irradiated giant planets and BDs, making them useful in the study of short-period BDs. The Saumon & Marley (2008) models include details like metal-rich, metal-poor, and cloudy atmosphere models for low-mass stars and BDs, but do not include the effects of irradiation. However, both the COND03 and SM08 models are limited in their application to TOI-503b. The BD cooling models from Baraffe et al. (2003) indicate that an object with a mass on the order of $10{M}_{{\rm{J}}}$ and an age greater than 500 Myr may maintain a radius of at least 1.0–1.2 ${R}_{{\rm{J}}}$ while in close proximity (semimajor axis of a = 0.046 au) to a host star with ${T}_{\mathrm{eff}}\,=6000$ K. The difference between a non-irradiated and irradiated BD at ages up to 10 Gyr is roughly $0.1{R}_{{\rm{J}}}$ (Baraffe et al. 2003). However, this is not the most appropriate comparison to TOI-503b, primarily because of the large difference in the mass of the BD in this case ($53{M}_{{\rm{J}}}$ versus $10{M}_{{\rm{J}}}$ from the COND03 models), which means that TOI-503b has a higher internal luminosity that will affect its radius over time. We also expect a much hotter star at ${T}_{\mathrm{eff}}=7650\,{\rm{K}}$ (versus ${T}_{\mathrm{eff}}=6000$ K) to have the effect of slowing the natural contraction of the BD's radius over time.

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Lastly, given the grazing nature of the transit, which limits how well we may constrain the BD radius, we are limited in how thoroughly we may interpret what effects the BD mass and T_eff of the host star have on the radius of this substellar companion. This means that the COND03 models may only be used as a broad, qualitative check for the age of TOI-503b. The SM08 models should be treated in a similar, albeit less reliable, way, as these do not consider the effects of irradiation. However, we are confident that this is one of the youngest intermediate-mass BDs ever found.

The mass–period diagram of transiting BDs (Figure 12) shows a sparse but diverse population. The total number of published transiting BDs, including TOI-503b in this work, is 21 (see Table 5 or Table 6, respectively, for this list). The BD binary system, 2M0535-05 (Stassun et al. 2006), and the very young (∼5–10 Myr) RIK 72b, which transits a pre-main-sequence star (David et al. 2019), are not shown in Figure 11 because their radii are above $3{R}_{{\rm{J}}}$ and do not correspond to the Baraffe et al. (2003) and Saumon & Marley (2008) models, as discussed in Section 3.2. KOI-189b (Díaz et al. 2014) has a mass of $78.0\pm 3.4{M}_{{\rm{J}}}$ and is the most massive BD, while HATS-70b, with a mass of $12.9\pm 1.8{M}_{{\rm{J}}}$, is the least massive. This neatly places objects at the two extremes in mass of what is considered a BD, but Díaz et al. (2014) caution that KOI-189b may instead be a low-mass star.

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Table 4.  Median Values and 68% Confidence Interval for TOI-503, Created Using EXOFASTv2 Commit Number 65aa674

Parameter	Units	Values
Stellar Parameters:
M*	Mass (M⊙)	${1.80}_{-0.06}^{+0.06}$
R*	Radius (R⊙)	${1.70}_{-0.04}^{+0.05}$
L*	Luminosity (L⊙)	${8.96}_{-0.54}^{+0.54}$
${\rho }_{* }$	Density (cgs)	${0.51}_{-0.05}^{+0.04}$
$\mathrm{log}g$	Surface gravity (cgs)	${4.23}_{-0.03}^{+0.03}$
Teff	Effective temperature (K)	${7650}_{-160}^{+140}$
[Fe/H]	Metallicity (dex)	${0.30}_{-0.09}^{+0.08}$
Age	Age (Gyr)	${0.18}_{-0.11}^{+0.17}$
EEP	Equal evolutionary point	${292}_{-31}^{+22}$
AV	V-band extinction (mag)	${0.038}_{-0.026}^{+0.028}$
σSED	SED photometry error scaling	${3.9}_{-0.99}^{+1.7}$
ϖ	Parallax (mas)	${3.878}_{-0.058}^{+0.059}$
d	Distance (pc)	${257.9}_{-3.8}^{+3.9}$
Brown-dwarf Parameters:		b
P	Period (days)	3.67718 ± 0.00010
Rb	Radius (${R}_{{\rm{J}}}$)	${1.34}_{-0.15}^{+0.26}$
TC	Time of conjunction (BJDTDB)	2458492.05383 ± 0.00053
T0	Optimal conjunction time (BJDTDB)	2458506.76256 ± 0.00039
a	Semimajor axis (au)	0.05727 ± 0.00063
i	Inclination (Degrees)	${82.25}_{-0.41}^{+0.31}$
Teq	Equilibrium temperature (K)	${2011}_{-28}^{+27}$
Mb	Mass (${M}_{{\rm{J}}}$)	53.7 ± 1.2
K	RV semi-amplitude (m s−1)	${4640}_{-27}^{+30}$
logK	Log of RV semi-amplitude	${3.6673}_{-0.0026}^{+0.0028}$
Rb/R*	Radius of planet in stellar radii	${0.0805}_{-0.0090}^{+0.015}$
a/R*	Semimajor axis in stellar radii	${7.22}_{-0.22}^{+0.20}$
δ	Transit depth (fraction)	${0.0065}_{-0.0014}^{+0.0028}$
Depth	Flux decrement at mid transit	${0.00452}_{-0.00023}^{+0.00026}$
τ	Ingress/egress transit duration (days)	${0.03836}_{-0.00057}^{+0.00060}$
T14	Total transit duration (days)	${0.0767}_{-0.0011}^{+0.0012}$
b	Transit impact parameter	${0.974}_{-0.015}^{+0.022}$
${\delta }_{S,3.6\mu {\rm{m}}}$	Blackbody eclipse depth at 3.6 μm (ppm)	${700}_{-160}^{+320}$
${\delta }_{S,4.5\mu {\rm{m}}}$	Blackbody eclipse depth at 4.5 μm (ppm)	${860}_{-200}^{+390}$
ρb	Density (cgs)	${27}_{-11}^{+13}$
loggP	Surface gravity	${4.87}_{-0.17}^{+0.12}$
${M}_{P}\sin i$	Minimum mass (${M}_{{\rm{J}}}$)	53.2 ± 1.2
${M}_{P}/{M}_{* }$	Mass ratio	${0.02844}_{-0.00037}^{+0.00039}$
c1	Linear limb-darkening coeff	${0.146}_{-0.050}^{+0.049}$
c2	Quadratic limb-darkening coeff	${0.333}_{-0.048}^{+0.049}$
Telescope Parameters:		FIES	Ondřejov	PARAS	TRES	Tautenburg
γrel	Relative RV offset (m s−1)	${29468}_{-20}^{+22}$	${3549}_{-78}^{+77}$	$-{31}_{-84}^{+85}$	${4571}_{-23}^{+21}$	$-{2766}_{-35}^{+43}$
σJ	RV jitter (m s−1)	${46}_{-30}^{+41}$	120 ± 120	${230}_{-66}^{+100}$	${40}_{-40}^{+43}$	${0.00}_{-0.00}^{+93}$
${\sigma }_{{\rm{J}}}^{2}$	RV jitter variance	${2200}_{-1900}^{+5500}$	${13000}_{-22000}^{+40000}$	${53000}_{-26000}^{+57000}$	${1600}_{-2200}^{+5300}$	$-{1800}_{-3500}^{+11000}$
Transit Parameters:		TESS UT oi50-3.-TE (TESS)
σ2	Added variance	$-{0.0000000323}_{-0.0000000063}^{+0.0000000064}$
F0	Baseline flux	0.9999834 ± 0.0000059

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Table 5.  List of Published Transiting Brown Dwarfs as of 2019 June

Name	P (days)	MBD/MJ	RBD/RJ	e	M⋆/M⊙	R⋆/R⊙	Teff (K)	[Fe/H]	Reference
TOI-503b	3.677	53.7 ± 1.2	${1.34}_{-0.15}^{+0.26}$	0 (adopted)	1.80 ± 0.06	1.70 ± 0.05	7650 ± 160	+0.61 ± 0.07	this work
HATS-70b	1.888	${12.9}_{-1.6}^{+1.8}$	${1.38}_{-0.07}^{+0.08}$	$\lt 0.18$	1.78 ± 0.12	${1.88}_{-0.07}^{+0.06}$	${7930}_{-820}^{+630}$	+0.04 ± 0.11	(1)
KELT-1b	1.218	27.4 ± 0.9	1.12 ± 0.04	0.01 ± 0.01	1.34 ± 0.06	1.47 ± 0.05	6516 ± 49	+0.05 ± 0.08	(2)
NLTT 41135b	2.889	33.7 ± 2.8	1.13 ± 0.27	<0.02	0.19 ± 0.03	0.21 ± 0.02	3230 ± 130	−0.25 ± 0.25	(3)
LHS 6343c	12.713	62.9 ± 2.3	0.83 ± 0.02	0.056 ± 0.032	0.37 ± 0.01	0.38 ± 0.01	⋯	+0.02 ± 0.19	4
LP 261-75b	1.882	68.1 ± 2.1	0.90 ± 0.02	<0.007	0.30 ± 0.02	0.31 ± 0.01	3100 ± 50	⋯	(5)
WASP-30b	4.157	61.0 ± 0.9	0.89 ± 0.02	0 (adopted)	1.17 ± 0.03	1.30 ± 0.02	6201 ± 97	−0.08 ± 0.10	(6)
WASP-128b	2.209	37.2 ± 0.9	0.94 ± 0.02	<0.007	1.16 ± 0.04	1.15 ± 0.02	5950 ± 50	+0.01 ± 0.12	(7)
CoRoT-3b	4.257	21.7 ± 1.0	1.01 ± 0.07	0 (adopted)	1.37 ± 0.09	1.56 ± 0.09	6740 ± 140	−0.02 ± 0.06	(8)
CoRoT-15b	3.060	63.3 ± 4.1	1.12 ± 0.30	0 (adopted)	1.32 ± 0.12	1.46 ± 0.31	6350 ± 200	+0.10 ± 0.20	(9)
CoRoT-33b	5.819	59.0 ± 1.8	1.10 ± 0.53	0.070 ± 0.002	0.86 ± 0.04	0.94 ± 0.14	5225 ± 80	+0.44 ± 0.10	(10)
Kepler-39b	21.087	20.1 ± 1.3	1.24 ± 0.10	0.112 ± 0.057	1.29 ± 0.07	1.40 ± 0.10	6350 ± 100	+0.10 ± 0.14	(11)
KOI-189b	30.360	78.0 ± 3.4	1.00 ± 0.02	0.275 ± 0.004	0.76 ± 0.05	0.73 ± 0.02	4952 ± 40	−0.07 ± 0.12	(12)
KOI-205b	11.720	39.9 ± 1.0	0.81 ± 0.02	<0.031	0.92 ± 0.03	0.84 ± 0.02	5237 ± 60	+0.14 ± 0.12	(13)
KOI-415b	166.788	62.1 ± 2.7	0.79 ± 0.12	0.689 ± 0.001	0.94 ± 0.06	1.15 ± 0.15	5810 ± 80	−0.24 ± 0.11	(14)
EPIC 201702477b	40.737	66.9 ± 1.7	0.76 ± 0.07	0.228 ± 0.003	0.87 ± 0.03	0.90 ± 0.06	5517 ± 70	−0.16 ± 0.05	(15)
EPIC 212036875b	5.170	52.3 ± 1.9	0.87 ± 0.02	0.132 ± 0.004	1.29 ± 0.07	1.50 ± 0.03	6238 ± 60	+0.01 ± 0.10	(18), (21)
AD 3116b	1.983	54.2 ± 4.3	1.02 ± 0.28	0.146 ± 0.024	0.28 ± 0.02	0.29 ± 0.08	3200 ± 200	+0.16 ± 0.10	(17)
CWW 89Ab	5.293	39.2 ± 1.1	0.94 ± 0.02	0.189 ± 0.002	1.10 ± 0.05	1.03 ± 0.02	5755 ± 49	+0.20 ± 0.09	(16), (18)
RIK 72b	97.760	59.2 ± 6.8	3.10 ± 0.31	0.146 ± 0.012	0.44 ± 0.04	0.96 ± 0.10	3349 ± 142	⋯	(19)
NGTS-7Ab	0.676	${75.5}_{-13.7}^{+3.0}$	${1.38}_{-0.14}^{+0.13}$	0 (adopted)	0.48 ± 0.13	0.61 ± 0.06	3359 ± 106	⋯	(20)
2M0535-05a	9.779	56.7 ± 4.8	6.50 ± 0.33	0.323 ± 0.006	⋯	⋯	⋯	⋯	(22)
2M0535-05b	9.779	35.6 ± 2.8	5.00 ± 0.25	0.323 ± 0.006	⋯	⋯	⋯	⋯	(22)

References. (1) Zhou et al. (2019), (2) Siverd et al. (2012), (3) Irwin et al. (2010), (4) Johnson et al. (2011), (5) Irwin et al. (2018), (6) Anderson et al. (2011), (7) Hodžić et al. (2018), (8) Deleuil et al. (2008), (9) Bouchy et al. (2011b), (10) Csizmadia et al. (2015), (11) Bonomo et al. (2015), (12) Díaz et al. (2014), (13) Díaz et al. (2013), (14) Moutou et al. (2013), (15) Bayliss et al. (2017), (16) Nowak et al. (2017), (17) Gillen et al. (2017), (18) Carmichael et al. (2019), (19) David et al. (2019), (20) Jackman et al. (2019), (21) Persson et al. (2019), (22) Stassun et al. (2006).

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TOI-503b has an intermediate-mass of $53.7\pm 1.2{M}_{{\rm{J}}}$, an inclination angle of ${82.25}_{-0.41}^{+0.31}$ degrees ($b=0.97\pm 0.02$), and adds to the diversity of objects found in the BD desert, as it is one of the youngest BDs known to transit a main-sequence star. Past works have argued that there is a paucity of objects from 35–55 ${M}_{{\rm{J}}}\sin i$, $P\leqslant 100$ days, but this argument is difficult to support given the relatively small number of transiting BDs discovered and the fact that in recent years, five BDs (Gillen et al. 2017; Nowak et al. 2017; Hodžić et al. 2018; Carmichael et al. 2019; Persson et al. 2019, and this work) have been discovered in this intermediate-mass range, bringing new life, so to speak, to the desert. The recent growth in the discoveries of this type of BD could be a hint at an undisclosed population of intermediate-mass BDs in the BD desert. With the rise in the population of BDs in the intermediate-mass range, we cannot rule out further reforesting of the driest region of the BD desert. However, we note that this is mostly a qualitative assessment of the distribution of intermediate-mass BDs, but an interesting feature to highlight nonetheless.

Based on our estimate of the age of TOI-503 (roughly 180 Myr) and the circular orbit of TOI-503b, we now consider the role tidal interactions have played in the orbital evolution of this system—namely, whether or not tides could have circularized the orbit of the BD. This comparison of circularization timescale to the system's age has implications for how the BD may have formed.

In order for a binary system affected by tides to be in a stable equilibrium, it must satisfy two conditions: the orbital angular momentum must be at least three times the sum of the rotational angular momenta of the two components, and the total angular momentum of the system must be greater than the critical value,

$$\begin{eqnarray}&&{L}_{\mathrm{crit}}=4{\left[\displaystyle \frac{{G}^{2}}{27}\displaystyle \frac{{M}_{\star }^{3}{M}_{\mathrm{BD}}^{3}}{{M}_{\star }+{M}_{\mathrm{BD}}}({I}_{\star }+{I}_{\mathrm{BD}})\right]}^{\tfrac{1}{4}},\end{eqnarray} \tag{ 1 }$$

where I_⋆ and ${I}_{\mathrm{BD}}$ are the rotational moments of inertia of the star and BD, respectively (Hut 1980). We assume a value of ${I}_{\star }={\alpha }_{\star }{M}_{\star }{R}_{\star }^{2}$ where ${\alpha }_{\star }=0.24$, interpolating the stellar moments of inertia from Claret & Gimenez (1989) to the mass of TOI-503. For the BD we assume the same internal structure as Jupiter, such that ${\alpha }_{\mathrm{BD}}=0.275$ (Ni 2018). We additionally assume that the orbit of the BD is well-aligned to the stellar rotation (i.e., $\sin {i}_{\star }\approx 1$), in order to calculate the stellar rotation period from $v\sin {i}_{\star }$, and we assume the present-day stellar rotation rate for the quoted calculations. We find that ${L}_{\mathrm{tot}}=1.07\pm 0.07{L}_{\mathrm{crit}}$ and ${L}_{\mathrm{orb}}=5.0\pm 0.5{L}_{\mathrm{rot}}$. TOI-503 is thus Darwin stable; interestingly, the total angular momentum is consistent with being equal to the critical value, while the orbital angular momentum is close to twice the critical value relative to the rotational angular momentum, both much like KELT-1b (Siverd et al. 2012).

From Jackson et al. (2008), the timescale for orbital circularization timescale for a close-in companion is

$$\begin{eqnarray}&&\displaystyle \frac{1}{{\tau }_{e}}=\left[\displaystyle \frac{63}{4}\sqrt{{{GM}}_{\star }^{3}}\displaystyle \frac{{R}_{{\mathrm{BD}}^{5}}}{{Q}_{\mathrm{BD}}{M}_{\mathrm{BD}}}+\displaystyle \frac{171}{16}\sqrt{G/{M}_{\star }}\displaystyle \frac{{R}_{\star }^{5}{M}_{\mathrm{BD}}}{{Q}_{\star }}\right]{a}^{-\tfrac{13}{2}},\end{eqnarray} \tag{ 2 }$$

where Q_⋆ and ${Q}_{\mathrm{BD}}$ are the tidal quality factors of the star and BD, respectively. Jackson et al. (2008) did not provide an expression for the tidal synchronization timescale, but Goldreich & Soter (1966), from whom Jackson et al. (2008) obtained their expressions, did. Rewriting this expression to use the terminology of this work, the synchronization timescale is

$$\begin{eqnarray}&&\displaystyle \frac{1}{{\tau }_{{\rm{\Omega }}}}=\displaystyle \frac{9}{4}\displaystyle \frac{{{GR}}_{\star }^{3}{M}_{\mathrm{BD}}^{2}}{{\alpha }_{\star }{M}_{\star }{Q}_{\star }{\rm{\Omega }}{a}^{6}},\end{eqnarray} \tag{ 3 }$$

where Ω is the angular velocity of the star.

Tidal quality factors are difficult to measure. There are only three BDs with published constraints on Q, which indicate $\mathrm{log}{Q}_{\mathrm{BD}}\gt 4.15\mbox{--}4.5$ (Heller et al. 2010; Beatty et al. 2018). Furthermore, there is disagreement in the literature about the values of Q_⋆, with plausible values ranging from 10⁴ to 10⁸; furthermore, even for a single system the value of Q_⋆ may change over time as the tidal forcing changes due to the orbital evolution of the system as well as stellar evolution (e.g., Jackson et al. 2008; Penev et al. 2012). Nonetheless, in order to assess the effect of the uncertain value of Q_⋆ on the evolution of TOI-503, in Figure 13 we show the tidal damping timescales as a function of the tidal quality factors. As is apparent from the figure, the tidal timescales are shorter for the lower half of plausible values of Q_⋆ and longer for the upper half.

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We provide preferring values ${Q}_{\star }={10}^{8}$ and ${Q}_{\mathrm{BD}}={10}^{5}$ following Persson et al. (2019). These values have been chosen using the observational quantification of the dissipation of the stellar equilibrium tide by Collier Cameron & Jardine (2018) in hot-Jupiter systems and of the dissipation of tides in Jupiter by Lainey et al. (2009), respectively. Although EPIC 212036875 (Persson et al. 2019) is less massive than TOI-503, Collier Cameron & Jardine (2018) did not find any significant T_eff dependence of Q_⋆ for the stellar equilibrium tide, justifying this assumption. For the orbital period larger than half of the rotation period of the star, tidal inertial waves (i.e., one of the components of the dynamical tide; e.g., Ogilvie & Lin 2007) can be excited in convective regions (Bolmont & Mathis 2016). However, for a massive star such as TOI-503, the convective envelope should be very thin leading to a negligible dissipation of tidal inertial waves (Mathis 2015; Gallet et al. 2017), while this dissipation can also be neglected in the convective core because this is a full sphere (e.g., Ogilvie & Lin 2004; Wu 2005). At the same time, the presence of this core may prevent an efficient dissipation of tidal gravity waves propagating in the radiative layers of TOI-503 (Barker & Ogilvie 2010; Guillot et al. 2014). Therefore, the estimate we provide here using the equilibrium tide values should be reasonable. We also note that an alternative tidal model relying on dynamical tides within the radiative envelope of hot stars was presented by Zahn (1977); using this model, which may be more appropriate for a hot star like TOI-503, predicts tidal damping timescales more than an order of magnitude larger than the Jackson et al. (2008) model for the largest plausible values of Q_⋆. However, given this uncertainty in the appropriate tidal model and value of Q_⋆, we cannot draw any firm conclusions on the tidal evolution of the system.

Am stars are commonly found in binary systems (e.g., Carquillat & Prieur 2007) and rotate more slowly than is typical for field A stars (e.g., Abt & Morrell 1995). The Am nature of these stars is thought to be due to their slow rotation, and it has been hypothesized that there may be a link between the binarity and slow rotation, but the exact mechanisms involved are still not well known (e.g., Böhm-Vitense 2006). It has also been noted that not all slowly rotating A stars are Am stars (Abt 2009). While many short-period Am binary systems could have experienced tidal synchronization, a significant number of Am binaries are too widely separated to experience significant tidal effects within their main-sequence lifetimes (Carquillat & Prieur 2007). Due to the systematic uncertainty on the tidal timescales for TOI-503 (Section 4.2), we cannot make any firm conclusions as to how any tidal braking experienced by the TOI-503 primary contributed to its nature as an Am star.

Although it lies at the lower end of the envelope in mass ratio, the TOI-503 system does not otherwise stand out significantly from the known population of Am binaries. In Figure 14 we show TOI-503 in context in the RV semi-amplitude-period plane for known Am-star binaries. TOI-503 has among the lowest K value of any known such system, but not the lowest. Boffin (2010) showed that the mass ratio distribution of Am-star binaries is uniform, and in this context, the existence of TOI-503b at a very small mass ratio is not surprising. Future surveys more sensitive to very small mass ratio Am binaries will be necessary to determine whether the mass ratio distribution eventually tails off.

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Apart from TOI-503, other Am stars known to host a low-mass companion (${M}_{b}\lt 80{M}_{{\rm{J}}}$) are WASP-33 (Collier Cameron et al. 2010b) and KELT-19A (Siverd et al. 2018), but the mass ratio q for both the systems is even smaller than the TOI-503 system.

The age of TOI-503 is approximately 180 Myr. In Section 4.2, we have shown that given our consideration of the Jackson et al. (2008) and Zahn (1977) prescription of the tidal evolution of the system, we cannot say with certainty whether or not TOI-503 circularized the BD's orbit. Our interpretation of this is that TOI-503b may have formed at a larger orbital distance from its host star or also at a slightly larger eccentricity or more simply formed in situ in a nearly circular orbit.

Now the question becomes which formation mechanism (core accretion or fragmentation) is more plausible. To address this point, we can look at some of the nearest neighbors, in terms of mass, to TOI-503b: AD 3116b (${M}_{b}=54{M}_{{\rm{J}}}$), EPIC 212036875b (${M}_{b}=52{M}_{{\rm{J}}}$), and CWW 89Ab (${M}_{b}=39{M}_{{\rm{J}}}$). As shown in two independent studies (Carmichael et al. 2019; Persson et al. 2019), EPIC 212036875b is an eccentric (e = 0.132), short-period (P = 5.16 days) BD that orbits an F-type star. The Persson et al. (2019) study found EPIC 212036875b to likely have formed farther from its host star via gravitational disk instabilities and then quickly migrate to its current, close-in eccentric orbit. This is argued because core accretion is not effective to grow a $50{M}_{{\rm{J}}}$ object (Kratter & Lodato 2016), where fragmentation in the disk certainly could be, and this may be the case for TOI-503b.

For AD 3116b, the circularization timescale is challenging to interpret, as Gillen et al. (2017) caution, given the mass ratio of this system ($q\approx 0.18$), the very short ($\lt 2$ days) period, and the nature of the host M dwarf star. Though AD 3116b is young at a measured age of 600 Myr, given the nature of its orbit and host star, it is more difficult to infer a formation scenario. The narrative for CWW 89Ab is different still from these other examples, as Beatty et al. (2018) argue that it formed via core accretion in part of a triple system that includes a wide secondary star, CWW 89B. From these few examples, we see that a difference in mass of $39{M}_{{\rm{J}}}$ (CWW 89Ab) versus $52{M}_{{\rm{J}}}$ (EPIC 212036875b) may have origins in different formation scenarios. This highlights how the mass of a short-period BD may not as strongly dictate a formation scenario as any single discovery might imply and that there are plausible non-in-situ formation pathways that come from both core accretion or disk fragmentation.

On the other hand, the in situ formation scenario points to a possible way that Am stars can form. To our knowledge, this is the first time a BD has been detected orbiting an Am star in such a short period. Detailed studies of Am stars report a binary fraction around 60%–70% (Abt & Levy 1985; Carquillat & Prieur 2007). In some such systems, the stellar companions are too distant for the tidal braking to be effective (e.g., Siverd et al. 2018). It possibly suggests that other processes may need to be invoked to explain their small rotational velocities. However, this may also be linked to the fact that it is relatively difficult to detect such a low-mass companion as a BD around an Am star, and our discovery of one such BD around an Am star in the BD desert may reflect this. However, further similar discoveries are needed to confirm if this is the correct explanation. The BD orbiting an Am star is a bridge connecting two areas that are not fully understood: the formation mechanisms and ultimate classification of BDs, and the creation, evolution, and behavior of Am stars. Such an overlap enables us to look at these areas from an entirely new perspective.