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We derive masses and radii for both components in the single-lined eclipsingbinary HAT-TR-205-013, which consists of a F7V primary and a late M-dwarfsecondary. The system's period is short, $P=2.230736 \pm 0.000010$ days, withan orbit indistinguishable from circular, $e=0.012 \pm 0.021$. We demonstrategenerally that the surface gravity of the secondary star in a single-linedbinary undergoing total eclipses can be derived from characteristics of thelight curve and spectroscopic orbit. This constrains the secondary to a uniqueline in the mass-radius diagram with $M/R^2$ = constant. For HAT-TR-205-013, weassume the orbit has been tidally circularized, and that the primary's rotationhas been synchronized and aligned with the orbital axis. Our observed linebroadening, $V_{\rm rot} \sin i_{\rm rot} = 28.9 \pm 1.0$ \kms, gives a primaryradius of $R_{\rm A} = 1.28 \pm 0.04$ \rsun. Our light curve analysis leads tothe radius of the secondary, $R_{\rm B} = 0.167 \pm 0.006$ \rsun, and thesemimajor axis of the orbit, $a = 7.54 \pm 0.30 \rsun = 0.0351 \pm 0.0014$ AU.Our single-lined spectroscopic orbit and the semimajor axis then yield theindividual masses, $M_{\rm B} = 0.124 \pm 0.010$ \msun and $M_{\rm A} = 1.04\pm 0.13$ \msun. Our result for HAT-TR-205-013 B lies above the theoreticalmass-radius models from the Lyon group, consistent with results fromdouble-lined eclipsing binaries. The method we describe offers the opportunityto study the very low end of the stellar mass-radius relation.

The Mass and Radius of the Unseen M-Dwarf Companion in the Single-Lined Eclipsing Binary HAT-TR-205-013