Modeling and Orbital Parameters of Kepler Heartbeat Stars

Heartbeat stars (HBSs) are astrophysical laboratories for studying binaries with eccentric orbits. A catalog of 173 Kepler HBSs was reported by Kirk et al., and we have modeled 153 of them by using a corrected version of Kumar et al.'s model based on the Markov Chain Monte Carlo method. The orbital parameters, including orbital period, eccentricity, orbital inclination, the argument of periastron, and epoch of the periastron passage of these HBSs, have been determined and are presented. Orbital parameters of more than 100 systems are obtained for the first time. After comparing the parameters of 38 overlapping systems with previous works, it is shown that the orbital parameters of HBSs can be reliably derived using this method. These samples can also be valuable targets for future studies of the structures and evolution of HBSs. The eccentricity–period (e–P) relation also reveals the existence of orbital circularization in HBSs. We then propose an empirical equation for the relationship between the upper limit of eccentricity and the orbital period in systems with orbital periods less than 10 days based on the e–P relation. In addition, it is possible that seven systems in the catalog with eccentricity less than 0.02 should be excluded from the HBS candidates.