Mass ratio from Doppler beaming and Romer delay versus ellipsoidal modulation in the Kepler data of KOI-74

摘要

We present a light-curve analysis and radial velocity study of KOI-74, an eclipsing A star + white dwarf binary with a 5.2-d orbit. Aside from new spectroscopy covering the orbit of the system, we used 212 d 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 degrees.0 +/- 0 degrees.4, which is significantly lower than the previously published value. The altered inclination leads to different values for the relative radii of the two stars and therefore also the mass ratio deduced from the ellipsoidal modulations seen in this system. We find that the mass ratio derived from the radial velocity amplitude (q= 0.104 +/- 0.004) disagrees with that derived from the ellipsoidal modulation (q= 0.052 +/- 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, instead of assuming corotation with the binary orbit, is found to increase the discrepancy even further by lowering the mass ratio to q= 0.047 +/- 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 same problem could arise whenever an ellipsoidal modulation amplitude is used to derive the mass of a planet orbiting a host star that is not in corotation with the planets orbit. 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 Romer delay in a light curve of a compact binary. This delay amounts to -56 +/- 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 +/- 0.004 leaves little doubt that the companion of KOI-74 is a low-mass white dwarf.