  A new class of pulsating binary stars was recently discovered, whose
pulsation amplitudes are strongly modulated with orbital phase. Stars in close
binaries are tidally distorted, so we examine how a star's tidally induced
asphericity affects its oscillation mode frequencies and eigenfunctions. We
explain the pulsation amplitude modulation via tidal mode coupling such that
the pulsations are effectively confined to certain regions of the star, e.g.,
the tidal pole or the tidal equator. In addition to a rigorous mathematical
formalism to compute this coupling, we provide a more intuitive semi-analytic
description of the process. We discuss three resulting effects: 1. Tidal
alignment, i.e., the alignment of oscillation modes about the tidal axis rather
than the rotation axis; 2. Tidal trapping, e.g., the confinement of
oscillations near the tidal poles or the tidal equator; 3. Tidal amplification,
i.e., increased flux perturbations near the tidal poles where acoustic modes
can propagate closer to the surface of the star. Together, these phenomena can
account for the pulsation amplitude and phase modulation of the recently
discovered class of "tidally tilted pulsators." We compare our theory to the
three tidally tilted pulsators HD 74423, CO Cam, and TIC 63328020, finding that
tidally trapped modes that are axisymmetric about the tidal axis can largely
explain the first two, while a non-axisymmetric tidally aligned mode is present
in the latter. Finally, we discuss implications and limitations of the theory,
and we make predictions for the many new tidally tilted pulsators likely to be
discovered in the near future.
