The Mass and Radius of the Unseen M-dwarf Companion in the Single-lined Eclipsing Binary Hat-tr-205-013

We derive masses and radii for both components in the single-lined eclipsing binary HAT-TR-205-013, which consists of a F7V primary and a late M-dwarf secondary. The system’s period is short, P = 2.230736 ± 0.000010 days, with an orbit indistinguishable from circular, e = 0.012 ± 0.021. We demonstrate generally that the surface gravity of the secondary star in a single-lined binary undergoing total eclipses can be derived from characteristics of the light curve and spectroscopic orbit. This constrains the secondary to a unique line in the mass-radius diagram with M/R = constant. For HAT-TR-205-013, we assume the orbit has been tidally circularized, and that the primary’s rotation has been synchronized and aligned with the orbital axis. Our observed line broadening, Vrot sin irot = 28.9± 1.0 km s, gives a primary radius of RA = 1.28± 0.04 R⊙. Our light curve analysis leads to the radius of the secondary, RB = 0.167± 0.006 R⊙, and the semimajor axis of the orbit, a = 7.54± 0.30 R⊙ = 0.0351± 0.0014 AU. Our single-lined spectroscopic orbit and the semimajor axis then yield the individual masses, MB = 0.124 ± 0.010 M⊙ and MA = 1.04 ± 0.13 M⊙. Our result for HAT-TR-205-013 B lies above the theoretical mass-radius models from Department of Astronomy, Harvard University, 60 Garden Street, Cambridge, MA 02138 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 Department of Astronomy, Pontificia Universidad Católica, Casilla 306, Santiago 22, Chile Hubble Fellow Konkoly Observatory, Budapest, P.O. Box 67, H-1125, Hungary Planetary Science Institute, 1700 East Fort Lowell Road, Suite 106, Tucson, AZ 85719 Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85719