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 F7 V 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/R² = 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_⊙. Our light-curve analysis leads to the radius of the secondary, R_B = 0.167 ± 0.006 R _⊙, and the semimajor axis of the orbit, a = 7.54 ± 0.30 M_⊙ = 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_⊙ and M_A = 1.04 ± 0.13 M_⊙. 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.