Kepler Observations of the Beaming Binary KPD 1946+4340

Abstract

The Kepler Mission has acquired 33.5 d of continuous one-minute photometry of KPD 1946+4340, a short-period binary system that consists of a subdwarf B star (sdB) and a white dwarf. In the light curve, eclipses are clearly seen, with the deepest occurring when the compact white dwarf crosses the disc of the sdB (0.4 %) and the more shallow ones (0.1 %) when the sdB eclipses the white dwarf. As expected, the sdB is deformed by the gravitational field of the white dwarf, which produces an ellipsoidal modulation of the light curve. Spectacularly, a very strong Doppler beaming (also known as Doppler boosting) effect is also clearly evident at the 0.1 % level. This originates from the sdB’s orbital velocity, which we measure to be $164.0\pm 1.9\,\text {km}\,\text {s}^{-1}$ from supporting spectroscopy. We present light curve models that account for all these effects, as well as gravitational lensing, which decreases the apparent radius of the white dwarf by about 6 % when it eclipses the sdB. We derive system parameters and uncertainties from the light curve using Markov Chain Monte Carlo simulations. Adopting a theoretical white dwarf mass-radius relation, the mass of the subdwarf is found to be 0.47 $\pm \,0.03\,$M$_\odot$ and the mass of the white dwarf $0.59\pm 0.02\,$M$_\odot$. The effective temperature of the white dwarf is 15,900 $\pm \,300\,$K. With a spectroscopic effective temperature of $T_\mathrm{{eff}}$ = 34,730 $\pm \,250\,$K and a surface gravity of $\log g=5.43 \pm 0.04$, the subdwarf has most likely exhausted its core helium, and is in a shell He burning stage. The detection of Doppler beaming in Kepler light curves potentially allows one to measure radial velocities without the need of spectroscopic data. For the first time, a photometrically observed Doppler beaming amplitude is compared to a spectroscopically established value. The sdB’s radial velocity amplitude derived from the photometry ($168\, \pm \, 4\,\text {km}\,\text {s}^{-1}$) is in perfect agreement with the spectroscopic value. After subtracting our best model for the orbital effects, we searched the residuals for stellar pulsations but did not find any significant pulsation frequencies.

This chapter is based on

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