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Hundreds of substellar companions to solar-type stars will be discovered withthe Kepler satellite. Kepler's extreme photometric precision gives access tolow-amplitude stellar variability contributed by a variety of physicalprocesses. We discuss in detail the periodic flux modulations arising from thetidal force on the star due to a substellar companion. An analytic expressionfor the variability is derived in the equilibrium-tide approximation. Wedemonstrate analytically and through numerical solutions of the linear,nonadiabatic stellar oscillation equations that the equilibrium-tide formulaworks extremely well for stars of mass <1.4 Msun with thick surface convectionzones. More massive stars with largely radiative envelopes do not conform tothe equilibrium-tide approximation and can exhibit flux variations $\ga$10times larger than naive estimates. Over the full range of stellar massesconsidered, we treat the oscillatory response of the convection zone byadapting a prescription that A. J. Brickhill developed for pulsating whitedwarfs. Compared to other sources of periodic variability, the ellipsoidallightcurve has a distinct dependence on time and system parameters. We suggestthat ellipsoidal oscillations induced by giant planets may be detectable fromas many as ~100 of the 10^5 Kepler target stars. (Abridged)

Ellipsoidal Oscillations Induced by Substellar Companions: A Prospect for the Kepler Mission