Ellipsoidal oscillations induced by substellar companions:: A prospect for the Kepler mission

Hundreds of substellar companions to solar-type stars will be discovered with the Kepler satellite. Kepler's extreme photometric precision gives access to low-amplitude stellar variability contributed by a variety of physical processes. We discuss in detail the periodic flux modulations arising from the tidal force on the star due to a substellar companion. An analytic expression for the variability is derived in the equilibrium-tide approximation. We demonstrate analytically and through numerical solutions of the linear, nonadiabatic stellar oscillation equations that the equilibrium-tide formula works extremely well for stars of mass < 1.4 M-circle dot with thick surface convection zones. More massive stars with largely radiative envelopes do not conform to the equilibrium-tide approximation and can exhibit flux variations greater than or similar to 10 times larger than naive estimates. Over the full range of stellar masses considered, we treat the oscillatory response of the convection zone by adapting a prescription that A. J. Brickhill developed for pulsating white dwarfs. Compared to other sources of periodic variability, the ellipsoidal light curve has a distinct dependence on time and system parameters. We suggest that ellipsoidal oscillations induced by giant planets may be detectable from as many as similar to 100 of the 10(5) Kepler target stars. For the subset of these stars that show transits and have radial-velocity measurements, all system parameters are well constrained, and measurement of ellipsoidal variation provides a consistency check, as well as a test of the theory of forced stellar oscillations in a challenging regime.