Kepler-503b: An Object at the Hydrogen Burning Mass Limit Orbiting a Subgiant Star

The NASA Kepler space mission, in its search for transiting Earth analogs, provided nearly continuous observations of ∼200,000 stars with a photometric precision of a few parts per million (Borucki et al. 2010; Koch et al. 2010). The final Kepler data release (DR25) lists more than 8000 Kepler objects of interest (KOIs), or targets showing a transit that may be caused by an exoplanet (Thompson et al. 2017). Vetting these KOIs has revealed over 2000 eclipsing binaries with precise photometric data (Kirk et al. 2016). While high-resolution imaging (Furlan et al. 2017) and statistical methods (Morton et al. 2016) are useful for constraining the nature of a KOI, dynamical observations can provide an unambiguous classification for a given system.

Eclipsing binaries are important astrophysical systems because simultaneous modeling of spectroscopic and photometric observations yields precise dynamical masses and stellar radii (Torres et al. 2010). Precisely measured stellar parameters are valuable for calibrating and refining stellar evolution models (e.g., Fernandez et al. 2009; Torres et al. 2014) and even play a role in the cosmic distance scale. Furthermore, determining the precise properties of exoplanets requires an understanding of their host stars' parameters, particularly the masses and radii. The detection of false-positive KOIs has greater implications for the planet-hosting stellar population. The presence of eclipsing binaries quantifies the false-positive rate and can reveal any dependencies on parameters, such as the location within the Kepler field and the properties of the host star or planetary candidate.

In this Letter, we provide tight constraints on the age, radii, masses, and other properties of the low-mass-ratio (M₂/M₁ = q ∼ 0.07) eclipsing binary system Kepler-503 (KIC 3642741, 2MASS J19223275+3842276, Kp = 14.75, H = 13.14). The Letter is structured as follows: Section 2 presents the observational data, Section 3 discusses our data processing, and Section 4 describes our analysis. A discussion of our results is presented in Section 5.

Kepler-503 was observed from Apache Point Observatory (APO) between 2015 April 30 and 2017 April 7 as part of the APO Galaxy Evolution Experiment (APOGEE) Kepler object of interest (KOI) program (Fleming et al. 2015; Majewski et al. 2017; Zasowski et al. 2017) within Sloan Digital Sky Survey (SDSS)-IV (Blanton et al. 2017). We obtained 19 spectra of Kepler-503, using the high-resolution (R ∼ 22,500), near-infrared (1.514–1.696 μm), multi-object APOGEE spectrograph (Wilson et al. 2010, 2012), mounted on the Sloan 2.5 m telescope (Gunn et al. 2006). The observations are summarized in Table 1, which lists our derived radial velocities, their uncertainties (corresponding to a 1-σ error), and the signal-to-noise ratio (S/N) per pixel for each epoch. One observation with a S/N below 10 was not used for analysis.

Kepler-503 was observed for the entirety of the Kepler mission. The transiting companion, Kepler-503b, is listed as a planetary candidate in DR25 and was statistically validated as an exoplanet by Morton et al. (2016). The final data release lists a shallow, 0.37% transit signal with an orbital period of 7.258450123 days and an estimated physical radius of ${5.53}_{-0.53}^{+1.59}$ R_⊕. The stellar parameters in the DR25 stellar properties catalog (Mathur et al. 2017) were derived with photometric priors and inferred from stellar models. The DR25 parameters for Kepler-503 suggest a solar-like host star with an effective temperature of ${5638}_{-171}^{+154}$ K, a mass of ${1.006}_{-0.120}^{+0.090}$M_⊙, and a radius of ${0.920}_{-0.088}^{+0.264}$R_⊙.

3.1. Radial Velocities

The APOGEE data reduction pipeline (Nidever et al. 2015) performs sky subtraction, telluric and barycentric correction, and wavelength and flux calibration for each observation of a target. We focused our analysis on these individual spectra for dynamical characterization. While the APOGEE pipeline provides radial velocity measurements, we performed additional post-processing on the spectrum to remove residual telluric lines prior to analysis.

Radial velocities of Kepler-503 were derived using the cross-correlation method with uncertainties calculated via the maximum-likelihood approach presented by Zucker (2003). With this method, we account for uncertainty contributions from the spectral bandwidth, sharpness of the correlation peak, and the spectral line S/N but cannot exclude systematic uncertainties due to the instrument or poor template selection. Cross-correlation searches for the Doppler shift of an observed spectrum that maximizes the correlation with a template that adequately represents the observed spectrum without a Doppler shift. The best-fitting spectrum should have the highest correlation and it is common practice for this to be used as the template (e.g., Latham et al. 2002). We identified the best-fitting synthetic spectrum in the H-band from a grid of BT-Settl synthetic spectra (Allard et al. 2012) by cross-correlating the APOGEE epoch with the highest S/N against a grid spanning surface effective temperature (5100 ≤ T_e ≤ 6100, in intervals of 100 K), surface gravity ($3.5\leqslant \mathrm{log}g\leqslant 4.5$, in intervals of 0.5 dex), metallicity (−0.5 ≤ [M/H] ≤ 0.5, in intervals of 0.5 dex), and rotational broadening ($2\leqslant v\sin i\leqslant 50$, in intervals of 2 km s⁻¹). The synthetic spectrum with the largest correlation was used for the final cross-correlation to derive the reported radial velocities in Table 1. The properties of the best model are listed in Table 2 and were not used as priors for fitting the system.

Table 2.  Parameters for the Kepler-503 System

Parameter	Units	Median Value
Primary Synthetic Spectruma:
Effective Temperature	Te (K)	6000
Surface Gravity	$\mathrm{log}({g}_{1})$ (cgs)	4.0
Metallicity	[M/H]	0.0
Rotational Velocity	v sin i (km s−1)	2.0
Primary Stellar Priors:
Effective Temperatureb	Te (K)	5690 ± 150
Surface Gravityb	$\mathrm{log}({g}_{1})$ (cgs)	4.0
Metallicityb	[Fe/H]	0.17 ± 0.05
Maximum Visual Extinction	AV,max	0.43
Distance	(pc)	1628 ± 55
Primary Parameters:
Mass	M1 (M⊙)	${1.154}_{-0.042}^{+0.047}$
Radius	R1 (R⊙)	${1.764}_{-0.068}^{+0.080}$
Density	ρ1 (g cm−3)	${0.297}_{-0.037}^{+0.038}$
Surface Gravity	$\mathrm{log}({g}_{1})$ (cgs)	4.008 ± 0.038
Effective Temperature	Te (K)	${5670}_{-110}^{+100}$
Metallicity	[Fe/H]	${0.169}_{-0.045}^{+0.046}$
Age	(Gyr)	${6.7}_{-0.9}^{+1.0}$
Parallax	(mas)	${0.617}_{-0.019}^{+0.020}$
Secondary Parameters:
Mass	M2 (M⊙)	0.075 ± 0.003
Radius	R2 (R⊙)	${0.099}_{-0.004}^{+0.006}$
Density	ρ2 (g cm−3)	108 ± 17
Surface Gravity	$\mathrm{log}({g}_{2})$ (cgs)	${5.320}_{-0.050}^{+0.045}$
Equilibrium Temperature	Teq (K)	${1296}_{-23}^{+22}$
Orbital Parameters:
Orbital Period	P (days)	7.2584481 ± 0.0000023
Time of Periastron	TP (BJDTDB)	${2454970.27}_{-1.1}^{+0.63}$
Semimajor Axis	a (au)	0.0786 ± 0.0010
Orbital Eccentricity	e	${0.025}_{-0.012}^{+0.014}$
Argument of Periastron	ω (degrees)	${33}_{-54}^{+32}$
Semi-amplitude Velocity	K (km s−1)	7.17 ± 0.18
Mass Ratio	q	${0.0648}_{-0.0020}^{+0.0019}$
Systemic Velocity	γ (km s−1)	−45.93 ± 0.10
Radial Velocity Jitter	(σRV (m s−1)	${168}_{-92}^{+96}$
Transit Parameters:
Time of Mid-transit	TC (BJDTDB)	2454971.34494 ± 0.00026
Radius Ratio	R2/R1	${0.05619}_{-0.00060}^{+0.00069}$
Scaled Semimajor Axis	a/R1	${9.59}_{-0.42}^{+0.39}$
$e\cos \omega$		${0.017}_{-0.010}^{+0.009}$
$e\sin \omega$		${0.010}_{-0.015}^{+0.020}$
Linear Limb-darkening Coefficient	u1	0.419 ± 0.023
Quadratic Limb-darkening Coefficient	u2	${0.238}_{-0.045}^{+0.044}$
Orbital Inclination	i (degrees)	${88.04}_{-0.76}^{+1.0}$
Impact Parameter	b	${0.32}_{-0.17}^{+0.11}$

Notes.

^aThese parameters are for the best-fit template spectrum used for cross-correlation. ^bThese values are from ASPCAP.

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3.2. Photometry

We jointly modeled Kepler-503's radial velocities and light curve using the EXOFASTv2 analysis package (Eastman 2017). The light curve and Keplerian radial velocity models follow the parametrization described by Eastman et al. (2013). We adopted a quadratic limb-darkening law for the transit. The priors for the modeling included (i) 2MASS JHK magnitudes (Skrutskie et al. 2006), (ii) SDSS ugriz magnitudes (Alam et al. 2015), (iii) UBV magnitudes (Everett et al. 2012), (iv) WISE magnitudes (Wright et al. 2010), (v) surface gravity, temperature, and metallicity from the APOGEE Stellar Parameter and Chemical Abundances Pipeline (ASPCAP; García Pérez et al. 2016), (vi) the maximum visual extinction from estimates of Galactic dust extinction by Schlafly & Finkbeiner (2011), (vii) the photometric measurements from the second data release of the Gaia survey (Gaia Collaboration et al. 2018), and (viii) the distance estimate from Bailer-Jones et al. (2018). We validated the performance of our EXOFASTv2 implementation by analyzing the corresponding data products for KOI-189, and obtained very similar parameters to those published by Díaz et al. (2014) using the PASTIS planet-validation software. We repeated the analysis for Kepler-503 using the parallax from Gaia to determine if there were any significant effects from the nonlinearity of the parallax transformation or any asymmetry in the parallax posterior distribution. The results are consistent to within their 1-σ uncertainties, and herein we present values from the analysis using the distance prior. Figure 1 presents the result of the fit and Table 2 provides a summary of the stellar priors and the inferred systemic parameters, along with their confidence intervals. The minimum companion mass is ∼0.075 M_⊙, a value incompatible with the statistical validation and estimated parameters from DR25.

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The stellar parameters from EXOFASTv2 are derived using stellar models; the values suggest that Kepler-503 is an evolved star beyond the terminal age main sequence. Seager & Mallén-Ornelas (2003) proposed a diagnostic for a transiting system using transit parameters to obtain an estimate of the primary stellar density (ρ₁). With both photometry and velocimetry, one can determine that the observational data are consistent with the selected stellar models (e.g., von Boetticher et al. 2017). To determine if the deviation from the DR25 stellar parameters was justified, we used the MESA Isochrones & Stellar Tracks (MIST; Choi et al. 2016; Dotter 2016) to model the primary star and iteratively refine its parameters until the density derived from the photometry and velocimetry was within the uncertainty of the density from the models.

The result of the stellar modeling is shown in Figure 2 and demonstrates that the stellar parameters are comparable to those derived with EXOFASTv2. The data demonstrate that the primary star, Kepler-503, is not a solar analog, but instead a slightly evolved subgiant. When compared to stellar evolution models, the posterior distributions for the primary-star surface effective temperature and luminosity are located in the subgiant branch, which is in agreement with a slightly evolved system. Accordingly, these stellar parameters suggest that the purported exoplanet is actually an object near the hydrogen-burning mass limit of ∼0.075 M_⊙ (e.g., Chabrier et al. 2005).

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5.1. Constraint on the Companion Age

5.2. Constraints on the Companion Temperature

5.3. Constraints on Evolutionary Models

The study of objects similar to Kepler-503b is critical for the empirical calibration of the mass–radius relation near the hydrogen-burning mass limit (∼0.075 M_⊙). Figure 3 shows posterior distribution of Kepler-503b on a mass–radius diagram for brown dwarfs and low-mass stars. Its mass and radius are comparable to those of the brown dwarf KOI-189b (Díaz et al. 2014) and the metal-poor ([Fe/H] = −0.24 ± 0.16), low-mass star EBLM J0555-57Ab (von Boetticher et al. 2017), with values that span the boundary between L- and M-dwarfs. The mass of both KOI-189b and EBLM J0555-57Ab are within one standard deviation from Kepler-503b, but the estimated ages are very different. KOI-189b has an estimated age comparable to the age derived for the Kepler-503 system of ${6.9}_{-3.4}^{+6.4}$ Gyr, while EBLM J0555-57Ab is estimated to be much younger at 1.9 ± 1.2 Gyr. The evolutionary tracks in Figure 3 show that the change in metallicity cannot account for the change in radius of EBLM J0555-57Ab. We expect a population of objects spanning the hydrogen-burning mass limit at varying masses and ages, but this population is still poorly characterized, primarily due to the extreme paucity of well-measured objects.

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Kepler-503b is one of the few objects in the regime where evolutionary tracks converge with a well-constrained age, and can thus help refine said models. The properties of Kepler-503b appear consistent with evolutionary tracks for solar metallicity low-mass stars and brown dwarfs. From the L- and T-dwarf models by Saumon & Marley (2008), the 5 and 10 Gyr evolutionary tracks are the best matches for this object. One caveat is that, while the derived metallicity for the host star suggests that this is a slightly metal-rich system, the cloud-based models exist only for solar metallicities. Given the recent interest in very low-mass stars as targets for exoplanet searches (e.g., Gillon et al. 2017), it is essential that the super-solar metallicity regime be properly characterized. Future searches for planets around ultra-cool dwarfs will require precise masses and radii of the host star to properly characterize any detected exoplanets.

This Letter reveals a low-mass-ratio eclipsing binary system in a nearly circular orbit that was erroneously classified as a transiting exoplanet. Analysis of the photometric and spectroscopic data shows that Kepler-503 is an old system with a companion at the hydrogen-burning mass limit. This misclassification is largely due to the stellar parameters previously adopted (i.e., a solar-like host). The stellar classification from DR25 used a prior which is known to underestimate the number of sub-giants due to Malmquist bias (e.g., Bastien et al. 2014). Mathur et al. (2017) acknowledged that some systematic biases persist in the DR25 stellar properties catalog, resulting in misclassified systems such as Kepler-503.

This study is one example of the systems observed in the ongoing APOGEE KOI program, with the ultimate goal of (i) refining the false-positive rate of Kepler exoplanet candidates, (ii) revealing any dependencies with stellar or candidate parameters, and (iii) understanding binarity and its effect in the planet-host population. The recent second data release from the Gaia survey will be helpful for future validation of KOIs by providing a parallax that help to constrain the properties of the host star.

We thank the anonymous referee for comments that improved the quality of this publication. C.I.C., C.F.B., and S.M. acknowledge support from NSF award AST 1517592. N.D., S.R.M., and R.F.W. would like to acknowledge support from NSF grant Nos. 1616684 and 1616636. D.A.G.H. acknowledges support provided by the Spanish Ministry of Economy and Competitiveness (MINECO) under grant AYA-2017-88254-P. Some of the data presented in this Letter were obtained from MAST. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. 2MASS is a joint project of the University of Massachusetts and IPAC at Caltech, funded by NASA and the NSF. Funding for the Kepler mission is provided by the NASA Science Mission directorate. The NASA Exoplanet Archive is operated by Caltech, under contract with NASA under the Exoplanet Exploration Program.

Funding for SDSS-IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is http://www.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.