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 an F7V primary and a late M dwarf secondary. The system's period is short, P = 2230736 +/- 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-2 = 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, V-rot sin i(rot) 28.9 +/- 1.0 km s(-1), gives a primary radius of R-A 1.28 +/- 0.04 R-circle dot. Our light-curve analysis leads to the radius of the secondary, R-B = 0.167 +/- 0.006 R-circle dot, and the semimajor axis of the orbit, a = 7.54 +/- 0.30 R-circle dot = 0.0351 +/- 0. 0014 AU. Our single-lined spectroscopic orbit and the semimajor axis then yield the individual masses M-B = 0.124 +/- 0.010 M-circle dot and M-A = 1.04 +/- 0.13 M-circle dot. Our result for HAT-TR-205-013 B lies above the theoretical mass-radius models from the Lyon group, consistent with results from double-lined eclipsing binaries. The method we describe offers the opportunity to study the very low end of the stellar mass- radius relation.