  Kepler observations of the star HD 187091 (KID 8112039, hereafter KOI-54)
revealed a remarkable light curve exhibiting sharp periodic brightening events
every 41.8 days with a superimposed set of oscillations forming a beating
pattern in phase with the brightenings. Spectroscopic observations revealed
that this is a binary star with a highly eccentric orbit, e=0.83. We are able
to match the Kepler light curve and radial velocities with a nearly face-on
(i=5.5 degree) binary star model in which the brightening events are caused by
tidal distortion and irradiation of nearly identical A stars during their close
periastron passage. The two dominant oscillations in the light curve,
responsible for the beating pattern, have frequencies that are the 91st and
90th harmonic of the orbital frequency. The power spectrum of the light curve,
after removing the binary star brightening component, reveals a large number of
pulsations, 30 of which have a signal-to-noise ratio > 7. Nearly all of these
pulsations have frequencies that are either integer multiples of the orbital
frequency or are tidally-split multiples of the orbital frequency. This pattern
of frequencies unambiguously establishes the pulsations as resonances between
the dynamic tides at periastron and the free oscillation modes of one of the
stars. KOI-54 is only the 4th star to show such a phenomenon, and is by far the
richest in terms of excited modes.
