Mass ratio from Doppler beaming and R{\o}mer delay versus ellipsoidal modulation in the Kepler data of KOI-74

TL;DR

This study combines Kepler photometry and spectroscopy to analyze the KOI-74 binary system, revealing discrepancies in mass ratio estimates and measuring the Rømer delay, confirming the white dwarf companion.

Contribution

First complete light curve modeling of KOI-74 including Doppler beaming and Rømer delay, highlighting issues in mass ratio determination methods.

Findings

Radial velocity from Doppler beaming matches spectroscopic data.

Discrepancy between mass ratios from ellipsoidal modulation and radial velocity.

First measurement of Rømer delay in a compact binary light curve.

Abstract

We present a light curve analysis and radial velocity study of KOI-74, an eclipsing A star + white dwarf binary with a 5.2 day orbit. Aside from new spectroscopy covering the orbit of the system, we used 212 days of publicly available Kepler observations and present the first complete light curve fitting to these data, modelling the eclipses and transits, ellipsoidal modulation, reflection, and Doppler beaming. Markov Chain Monte Carlo simulations are used to determine the system parameters and uncertainty estimates. Our results are in agreement with earlier studies, except that we find an inclination of 87.0 \pm 0.4\degree, which is significantly lower than the previously published value. We find that the mass ratio derived from the radial velocity amplitude (q=0.104 \pm 0.004) disagrees with that derived from the ellipsoidal modulation (q=0.052 \pm 0.004} assuming corotation). This was found before, but with our smaller inclination, the discrepancy is even larger than previously reported. Accounting for the rapid rotation of the A-star is found to increase the discrepancy even further by lowering the mass ratio to q=0.047 \pm 0.004. These results indicate that one has to be extremely careful in using the amplitude of an ellipsoidal modulation signal in a close binary to determine the mass ratio, when a proof of corotation is not firmly established. The radial velocities that can be inferred from the detected Doppler beaming in the light curve are found to be in agreement with our spectroscopic radial velocity determination. We also report the first measurement of R{\o}mer delay in a light curve of a compact binary. This delay amounts to -56 \pm 17 s and is consistent with the mass ratio derived from the radial velocity amplitude. The firm establishment of this mass ratio at q=0.104 \pm 0.004 leaves little doubt that the companion of KOI-74 is a low mass white dwarf.