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 \(87.0\pm 0.4^\circ \), 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 (\(q=0.104\pm 0.004\)) disagrees with that derived from the ellipsoidal modulation (\(q=0.052\pm 0.004\) assuming corotation). This mismatch 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 \(q=0.047\pm 0.004\). 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 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 planet’s 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 Rømer 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.
This chapter is based on
S. Bloemen, T. R. Marsh, P. Degroote, R. H. Østensen, P. I. Pápics, C. Aerts, D. Koester, B. T. Gänsicke, E. Breedt, R. Lombaert, S. Pyrzas, C. M. Copperwheat, K. Exter, G. Raskin, H. Van Winckel, S. Prins, W. Pessemier, Y. Frémat, H. Hensberge, A. Jorissen, S. Van Eck
Monthly Notices of the Royal Astronomical Society, 2012, vol. 422, pp. 2600–2608.
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Notes
- 1.
We use the terms ‘transit’ and ‘eclipse’ to indicate, respectively, the occultation of the A-star by the compact object and the occultation of the compact object by the A-star half an orbit later.
- 2.
Publicly released Kepler data can be downloaded from http://archive.stsci.edu/kepler/.
- 3.
Van Kerkwijk et al. (2010) use a similar equation but with a \(\sin ^3 i\) term, which should be \(\sin ^2 i\).
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Bloemen, S. (2015). Mass Ratio from Doppler Beaming and Rømer Delay Versus Ellipsoidal Modulation in the Kepler Data of KOI-74. In: High-Precision Studies of Compact Variable Stars. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-10283-2_5
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