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

Abstract

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 Gaia and 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 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 highresolution 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 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 metallicity and abundance determinations than are double-lined EBs.

HATS-34b and HATS-46b: re-characterization using TESS and Gaia

“…As we demonstrate in this paper, it is necessary to re-fit all of the data for each system, including the parallax constraints, to take full advantage of the available information, and achieve higher precision. Significant improvements in stellar and planetary parameters when incorporating parallax measurements have also been reported for the system KELT-11 (Beatty et al 2017) and for several M dwarfs with planets observed by Kepler (Stevens et al 2018). These works differ from the approach presented here in that they focused on measuring empirical stellar masses and radii, without relying on stellar evolution models.…”

“…Using Gaia Stevens et al (2018) derived analytical estimates of uncertainties for stellar mass and radii in the current era where TESS and Gaia data are available. We compare our uncertainties in the PARSEC Empirical results (e=0) in this work to the analytic estimates based upon Equations 50-53 in their paper.…”

“…As we show, the stellar evolution models still provide more precise parameter estimates than can be obtained from the purely empirical techniques. Finally, we note that Stevens et al (2018) presented analytical formulae for estimating the expected uncertainties when analysing a transiting planet system with a precise parallax measurement. We compare our results to these analytic expectations in Section 5.4.…”

KELT-9 as an eclipsing double-lined spectroscopic binary: a unique and self-consistent solution to the system

“…Instead it serves more as an effective surface gravity assuming a spherical star. Under this assumption, Section 2.3.1 of Stevens et al 2018 presents a derivation of system parameters from spectroscopic stellar RV semi-amplitude and spectroscopic stellar surface gravity. This constraint is the weakest because it does not account for the oblate geometry of the star.…”

“…Newton's fundamental law of gravitation can be combined with knowledge of the system's orbital motion to recover the dynamical masses of both stars purely empirically. These measurements calibrate the stellar evolution models that are typically used to determine the masses of stars and indirectly the planets they host (Popper 1980;Harmanec 1988;Andersen 1991;Torres et al 2010;Stevens et al 2018).…”