Measuring Model-independent Masses and Radii of Single-Lined Eclipsing Binaries: Analytic Precision Estimates

We derive analytic estimates for the ability with which one can obtain precise, empirical stellar masses and radii via single-lined eclipsing binaries (EBs) in the era of {\it Gaia\/} and {\it TESS}. Including stars that host transiting substellar companions, such single-lined EBs already number in the hundreds from ground-based transit surveys and will comprise a major component of the science yield from the upcoming {\it TESS\/} mission. We explore the requirements for obtaining a given fractional precision on the masses and radii of single-lined EBs using primarily empirical means: radial velocity and eclipse measurements along with either: estimates of the primary's (1) surface gravity from high-resolution spectroscopy; (2) radius inferred from parallax, effective temperature, and bolometric flux; or (3) surface gravity and density from asteroseismology. We then compare these requirements to the precision obtained from invoking stellar models or empirical relations. We show that, for a fiducial transiting hot Jupiter system, precise, accurate, and essentially model-independent mass and radius measurements for such single-lined EBs will be possible in the era of \emph{Gaia}. These will be comparable in precision to those obtained with double-lined EBs. Moreover, the systems for which these methods can be applied will vastly outnumber double-lined EBs, thereby possessing the potential to sample a more complete range of stellar types (such as M dwarfs); these systems will also, in many cases, be more amenable to precision etallicity and abundance determinations than are double-lined EBs.