The Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) is a NASA mission to monitor nearly the entire sky for brief decreases in brightness caused by transiting planetary objects. However, a significant number of these transits are astrophysical false positives, caused by stellar binary systems. Since the launch of TESS in 2018, there have been 234 confirmed planets and 1573 false positives detected (Guerrero et al. 2021).
Ground-based follow-up is essential to fully characterize these objects.
Eclipsing binary systems are important astrophysical benchmarks because they allow us to dynamically constrain the physical characteristics of the system including mass and radius (e.g., Torres et al. 2009;Kesseli et al. 2019;Serenelli et al. 2021) mostly independent of theoretical models. Thus, these stellar systems provide measurements that feedback into the calibration and evolution of stellar evolution models. Cataloging false positives in TESS data may also benefit the TESS data-processing pipeline to identify parameters that are correlated with erroneously classifying binary systems as exoplanets.
The TESS input catalog identified TIC 71268730 (TOI-5375, 2MASS J07350822+7124020, Gaia DR3 111058697833 9817728) as an early M dwarf with an effective temperature of 3865 ± 157 K. The TESS data-processing pipeline designated the companion of TOI-5375 as a candidate planet with a period of 1.72 days and a depth of 36.88 ± 0.58 mmag. Gan et al. (2023) classified TOI-5375 as a verified planet candidate after vetting by their photometric analysis pipeline. In this paper, we present our analysis of the TOI-5375 system augmenting the TESS photometry with ground-based observations to determine the Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. companion, TOI-5375 B, is a very low mass star (VLMS) at the hydrogen-burning mass limit. In Section 2, we describe the observational data collected; in Section 3, we discuss the stellar parameters; in Section 4, we discuss the resulting posteriors of our joint fit; in Section 5 we present an analysis of our results in the context of evolutionary models, age, temperature, and environment.
TOI-5375 was observed by TESS in Sector 20 from 2019 December 24-2020 January 21, and in Sector 26 from 2020 June 8-2020 July 4, at a 30 minute (1800 s) cadence. It was also observed in Sector 40 from 2021 June 24-2021 July 23, at 120 s cadence. Similar to the TOI-1899 (Cañas et al. 2020) and TOI-3629 (Cañas et al. 2022) systems, we identified TOI-5375 B as a planetary candidate using a custom pipeline to search for transiting candidates in short-and long-cadence TESS data orbiting M dwarfs that were amenable to radial-velocity (RV) observations with the Habitable-zone Planet Finder (HPF; see Cañas et al. 2022). TOI-5375 B was also independently identified by the TESS science-processing pipeline (Jenkins et al. 2016) with a period of about 1.72 days and a transit duration of 1.74 hr. For the short-cadence data, Sector 40, we obtained the Pre-search Data Conditioning SAP (PSDCSAP) flux data from the Mikulski Archive for Space Telescopes (MAST).
We used eleanor (Feinstein et al. 2019) to produce the light curves from the TESS full-frame images of Sectors 20 and 26. eleanor uses the TESScutfoot_0 service to obtain a cutout of 31 × 31 pixels from the calibrated full-frame images centered on the target. In order to derive the light curve, we used the CORRFLUX values, in which eleanor uses linear regression with pixel position, measured background, and time to remove signals correlated with these parameters. We set the aperture mode to "normal," which tests different apertures and is based on the magnitude of the target star and the contamination ratio from TESS (Feinstein et al. 2019). Figure 1 shows the original light curves of TOI-5375 in TESS Sectors 20, 26, and 40. Several strong flares are clearly seen in the light curves. We identified and masked these events by hand before carrying out subsequent analysis.
We observed TOI-5375 on the night of 2022 April 4 UT using the 0.6 m telescope at Red Buttes Observatory (RBO) in Wyoming (Kasper et al. 2016). RBO is equipped with an Andor Apogee Alta F16 camera and uses the 2 × 2 on-chip binning mode, which has a gain of 1.4 e -/ADU and a plate scale of 0 73 pixel -1 . All observations were obtained in the Bessell I filter (Bessell 1990). The target was defocused moderately and observed using an exposure time of 240 s. Observations ranged from an airmass of 1.18 to 2.15. We processed the RBO light curves using AstroImageJ (Collins et al. 2017). The final reductions used a photometric aperture radius of 12 pixels (8 76), an inner sky radius of 18 pixels (13 14), and an outer sky radius of 25 pixels (18 25).
From 2020 November to 2022 January, we used the HPF (Mahadevan et al. 2014) to obtain 12 exposures of TOI-5375. HPF is a high-resolution, near-infrared (8080-12780 Å) Doppler spectrograph at the 10 m Hobby-Eberly Telescope (HET) located in Texas (Ramsey et al. 1998;Bash 2001). We Variability in the host star's light curve evolves throughout the different sectors, which we infer to be due to varying stellar spots. The periodicity of the spot-induced variability is tied to the rotation of the primary star. We also see flares due to stellar activity, which are masked out in our analysis.
used the tool HxRGproc to convert the raw HPF data into flux images and correct nonlinearity and cosmic rays, remove bias noise, and calculate the slope/flux and variance image (Ninan et al. 2018).
We analyzed the HPF spectra to measure the RVs using the method in Stefansson et al. (2020), which uses a modified version of the SpEctrum Radial Velocity AnaLyser pipeline (SERVAL; Zechmeister et al. 2018) that has been optimized for HPF data. HPF-adapted SERVAL first creates a master template from the target star observations and then moves it in velocity space to determine the Doppler shift for each observation. SERVAL then compares the observation with the template and minimizes the χ 2 statistic. The telluric regions are identified by a synthetic telluric-line mask created by telfit (Gullikson et al. 2014), a Python wrapper to the Lineby-Line Radiative Transfer Model package (Clough et al. 2005).
After masking out the telluric and sky-emission lines, the master template is created using all of the HPF observations for this target. We used barycorrpy (Kanodia & Wright 2018) to account for the barycentric correction on each spectra. The RVs, 1σ RV uncertainty, signal-to-noise ratio, and exposure times are listed in Table 1. Orbital Parameters:
Effective temperature of the host star (K)
Quality factor for secondary oscillation ( ) 0.01, 500.0 dQ Difference between quality factor for primary and secondary model
b Each object in the binary system has an independent limb-darkening parameter associated with it. The limb-darkening parameters are used in the secondary eclipse function.
To investigate the possibility of bright background sources contaminating our RBO photometry, we observed TOI-5375 with the NN-Explore Exoplanet Stellar Speckle Imager (NESSI; Scott et al. 2018) on the WIYN 3.5 m telescope at Kitt Peak National Observatory on the night of 2022 April 21. A 9 minute sequence of 40 ms diffraction-limited speckle images was taken in the Sloan z' filter with NESSI's red camera. A reconstructed speckle image was generated following the procedures described in Howell et al. (2011). Figure 2 shows the contrast curve along with an inset of the NESSI speckle image in the z' filter. We conclude that there are no close by sources with magnitudes brighter than Δz' = 4.45 for separations > 0 5.
HPF -SpecMatch (Stefansson et al. 2020) uses the empirical template matching methodology discussed in Yee et al. (2017) to derive stellar parameters of the host star from HPF spectra. We used this package to calculate the stellar parameters effective temperature (T eff ), surface gravity (log(g)), metallicity ([Fe/H]), and v i sin A . HPF -SpecMatch identifies the spectra that best match well-characterized stars from a library using χ 2 minimization. Then, it creates a composite spectrum using a weighted, linear combination of the five best-matching library spectra and derives the stellar properties using these weights. While searching for the best-matching library spectra, HPF -SpecMatch uses a linear limb-darkening law to broaden the stellar templates. We determined TOI-5375 has a T eff of 3897 ± 88 K, a log(g) of 4.68 ± 0.046, a [Fe/H] of 0.29 ± 0.12, and a v i sin A of 16.7 ± 0.9 km s -1 . The reported uncertainty is the standard deviation of the residuals from a leave-one-out cross-validation procedure applied to the entire spectral library in the chosen spectral order.
We derived the model-dependent stellar parameters, mass and radius, using the spectral energy distribution (SED) that uses the EXOFASTv2 analysis package (Eastman et al. 2019). EXOFASTv2 calculates the bolometric corrections for the SED fit by linearly interpolating the precomputed bolometric corrections 18 We applied an upper limit to the visual extinction based on estimates of Galactic dust (Green et al. 2019) calculated at the distance determined by Bailer-Jones et al. (2021). We converted the extinction from Green et al. (2019) to a visual magnitude extinction using the Rv = 3.1 reddening law from Fitzpatrick 1999). Table 2 contains the priors used in the joint fit described in Section 4, and Table 3 contains the stellar parameters derived from our HPF SpecMatch analysis with their uncertainties. The model-dependent mass and radius are 0.649 ± 0.024 M ☉ and 0.620 ± 0.016 R ☉ , respectively. independent limb-darkening coefficient. For uninformative limb-darkening priors, we reparameterized the priors following the procedure described in Kipping (2013). We included a jitter term as a simple noise model for each photometric data set. We assumed a circular orbit and fix the eccentricity to zero. We also used a dilution term on the photometric model because we want to account for potentially blended background stars in the TESS data. We did not include the dilution term for the RBO data because the higher spatial resolution compared to TESS allows for the star to be isolated from background stars, and our NESSI data confirm that there are no background objects within the RBO point-spread function.
We used the standard Keplerian model for the RVs. The photometric model includes the quadratic limb-darkening law (Kipping 2013). We simultaneously fit a Gaussian Process (GP) to the photometric data to detrend the light curve and extracted the transits. Our GP kernel is a mixture of two simple harmonic oscillator terms that can be used to model stellar rotation as a stochastically driven, damped harmonic oscillator (Foreman-Mackey et al. 2017; Foreman-Mackey 2018). We used this kernel to model the quasiperiodic signal for our likelihood function for TESS photometry. We also assumed a linear trend for the RV data. Figure 3 shows the best-fit model overlaid on the RV data with the residuals plotted in the bottom left panel and shows the phase-folded RVs along with the bestfit model. We note that the jitter term is relatively high compared to other HPF measurements due to the stellar activity and variability of the star (as seen in Figure 1). Figure 4 shows the RBO photometry with the model overlaid. Table 2 contains a list of our priors used as inputs to exoplanet.
To test the validity of our joint fit, we used the simplest case of fitting the RV data with exoplanet. We adapted the recipe from Foreman-Mackey et al. (2021a) to fit a single companion using the same RV priors as the joint fit and to create a single Keplerian RV model fixing the eccentricity to zero. Our posterior result for the semiamplitude is 18.26 km s -1 with a σ of 0.17 km s -1 , which is consistent with our joint fit of the posterior values.
We built upon our initial joint fit model by adding an additional component to model the secondary eclipse in the TESS data. We adopted part of the recipe from Foreman-Mackey et al. (2021a) foot_3 by including normal priors of the ratios of the mass (q), radius R B /R A , and surface brightness (S). We applied the secondary eclipse function from exoplanet to the TESS sectors to model the secondary eclipse. We did not apply the secondary eclipse function to the RBO data as the duration does not include the secondary eclipse portion of the light curve. The secondary eclipse function models the transits using starry. As with our initial joint fit, we fixed the eccentricity to zero to improve the stability of the modeling calculation. Solving for eccentricity would be an interesting astrophysical parameter; however, our attempts at allowing this parameter to float caused the model to become unstable. We used two independent quadratic limb-darkening law parameters for the primary star and transiting companion and concluded that our results from this fit are consistent with our single quadratic limb-darkening model.
Figure 5 shows the photometric plot of TESS Sector 20 along with a stellar rotation GP kernel. The detrended photometry is shown in the bottom panel along with the optimized mapped eclipses overlaid before running the HMC. The optimized parameter estimates are then used as the initial conditions when running the HMC. Figure 6 shows the phasefolded photometry data from TESS Sector 20 with the best-fit model posteriors and 1σ interval (16th and 84th percentiles). Figure 7 shows the phase-folded photometric data of the secondary eclipse from TESS Sector 20 with the best-fit model and 1σ interval. Our analysis yields for the companion a mass of 0.080 ± 0.002M ☉ and a radius of
, making the companion, not a planet, but rather a very low mass star, which we designate as TOI-5375 B. Table 4 shows these and other parameters derived from our joint fit analysis.
Understanding the characteristics of companion objects requires knowledge of the host star. The contrast ratio of exoplanet systems makes secondary eclipse detection nearly impossible. Therefore, deriving the physical parameters for exoplanets is often reliant on the accuracy of stellar evolution models. Eclipsing binary systems, where the secondary's light can be detected, are important for constraining those stellar evolution models. In particular, objects near the hydrogenburning mass limit, like TOI-5375 B, are able to measure the mass and radius mostly independent of models. An estimate of the companion age would indeed make this a benchmark VLMS.
The simplest way to determine the age of the companion is to assume it is coeval with the primary star, for which we can constrain the age. Isochrone models and asteroseismology are less reliable for low-mass stars than for solar-type stars for determining ages, so age estimates for our M dwarf primary star are weakly constrained at best. One property of low-mass stars we can exploit is the rotation period. M dwarfs lose angular momentum as they age, which results in their rotation period increasing (Engle & Guinan 2011). Therefore, rotation periods can be used to estimate the ages of M dwarfs (see If we attribute the variability of the host star to evolving starspots over each sector of TESS data, we can use the starspots to extract the rotation period using the period of the GP of -+
1.9716 0.0083 0.0080 days. We independently measured the rotation period using the periodogram function from lightkurve (Lightkurve Collaboration et al. 2018) for each TESS sector and a joint periodogram. The joint periodogram yielded a rotation period of ∼1.99 days; this analysis is broadly consistent (2σ) with the rotation period extracted from the GP fit. This period is also visually consistent with the 4% modulation seen in Figure 1. Equation (1) suggests a rotation period derived age of ∼400 Myr. This value is consistent within 1σ of the expected age of an early M dwarf with a rotation period between 1 < P < 10 days as seen in Newton et al. (2016). However, we note that due to the complex nature of the close binary system, which has potentially significant tidal effects affecting the angular momentum of the system, rotation-based ages derived for single stars and widely separated binaries may not apply.
The depth of the secondary eclipse observed in TESS can be modeled as a function of various fundamental properties (e.g., Charbonneau et al. 2005;Esteves et al. 2013;Shporer 2017): Figure 8 shows TOI-5375 B plotted on a mass-radius distribution of substellar and other low-mass stars near the hydrogen-burning mass limit. We also show the solar metallicity ([M/H] = 0.0) evolutionary isochrone tracks from Baraffe (Baraffe et al. 2015) and Sonora (Marley et al. 2021). Our mass-radius results are consistent with the 0.4 Gyr model, and this is consistent with our rotation-based estimate of the age of the system. However, in this region of parameter space, isochrones corresponding to older ages begin to fall on top of each other as the stars settle on the main sequence, so at 2σ our radius measurement is consistent with a broad range of isochrone ages. TOI-5375 B is comparable in mass and radius to Kepler-503b (Cañas et al. 2018), although Kepler-503b's age is much older at ∼6.7 Gyr. It is gratifying to see that both objects are consistent with the isochrone tracks for their respective ages.
Our HPF -SpecMatch analysis measured a spectroscopic v i sin A of 16.7 ± 0.9 km s -1 . Combining this with the -+ 1.9716 0.0083 0.0080 day rotation period from our joint fit and stellar radius of 0.632 ± 0.019R ☉ allows an estimate of the stellar inclination. Using the methodology from Masuda & Winn (2020), and allowing inclination to range from 0°to 180°, yields a stellar inclination estimate of 90°± 13°. Our modeled orbital inclination posterior is -+ 88.41 0.86 0.97 °. Together, our joint fit, the v i sin A and rotation period, suggests both the stellar equator and orbit of TOI-5375 B are close to edge-on and most likely well aligned. Independent measurements of the obliquity using the Rossiter-McLaughlin (RM) effect (Triaud 2018) would directly confirm these results. However, due to the relative faintness and length of transit duration (1.74 hr), acquiring RV data from the HET would be nearly impossible, so a different spectrograph, such as MAROON-X (Seifahrt et al. 2022) at Gemini, would be required.
The modulation seen in the different TESS sectors in Figure 1 could be used to deduce the atmospheric circulation (e.g., Bourrier et al. 2020), and future efforts could explore the efficacy of heat circulation in the companion based on the temperature measured in transit and in the eclipse position; however, such an analysis is beyond the scope of this paper.
We present ground-based follow-up data from HPF, NESSI, and RBO and use it along with TESS photometry to carry out an HMC joint fit that characterizes the companion to TOI-5375. This analysis shows TOI-5375 B is a VLMS with a mass of 0.080 ± 0.002M ☉ , a radius of 1.9716 0.0083 0.0080 days, determined by the spot-induced periodicity in the light curve. The rotation period is suggestive of an age of ∼400 Myr measured using single-star evolution of wide binaries and is not associated with any nearby clusters. TOI-5375 is amenable to additional modeling including atmospheric circulation, RM observations to measure obliquity, and the 3D architecture of the orbit.
https://mast.stsci.edu/tesscut/
The Astronomical Journal, 165:218 (10pp), 2023 May Lambert et al.
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