  We develop a general framework for interpreting and analyzing high-precision
lightcurves from eccentric stellar binaries. Although our methods are general,
we focus on the recently discovered Kepler system KOI-54, a face-on binary of
two A stars with $e=0.83$ and an orbital period of 42 days. KOI-54 exhibits
strong ellipsoidal variability during its periastron passage; its lightcurve
also contains ~20 pulsations at perfect harmonics of the orbital frequency, and
another ~10 nonharmonic pulsations. Analysis of such data is a new form of
asteroseismology in which oscillation amplitudes and phases rather than
frequencies contain information that can be mined to constrain stellar
properties. We qualitatively explain the physics of mode excitation and the
range of harmonics expected to be observed. To quantitatively model observed
pulsation spectra, we develop and apply a linear, tidally forced, nonadiabatic
stellar oscillation formalism including the Coriolis force. We produce temporal
power spectra for KOI-54 that are semi-quantitatively consistent with the
observations. Both stars in the KOI-54 system are expected to be rotating
pseudosynchronously, with resonant nonaxisymmetric modes providing a key
contribution to the total torque; such resonances provide a possible
explanation for the two largest-amplitude harmonic pulsations observed in
KOI-54, although we find quantitative problems with this interpretation. We
show in detail that the nonharmonic pulsations observed in KOI-54 can be
produced by nonlinear three-mode coupling. The methods developed in this paper
can be generalized in the future to determine the best-fit stellar parameters
given pulsation data. We also derive an analytic model of KOI-54's ellipsoidal
variability, including both tidal distortion and stellar irradiation, which can
be used to model other similar systems.
