  The prevalence of binary stars at close separations implies that many of
these systems will interact or merge during the binary's lifetime. This paper
presents hydrodynamic simulations of the scenario of binary coalescence through
unstable mass transfer, which drives the pair to closer separations. When the
donor star does not rotate synchronously with respect to the orbit, dynamical
tidal waves are excited in its envelope. We show that resonance crossings with
high azimuthal-order $(m\sim3$ to $6$) fundamental modes induce a visible
"polygram" distortion to the star. As the binary orbit tightens, the system
sweeps through resonance with modes of decreasing azimuthal order, which are
selectively excited. We compare our hydrodynamic simulations to predictions
from linear theory of resonant mode excitation. The linear theory provides an
estimate of mode amplitudes to within a factor of two, even as the oscillations
become quite non-linear as the stars coalesce. We estimate that a wave with 10%
radial amplitude generates approximately 1% photometric variability; this may
be detectible if such a binary coalescence is caught in action by future
photometric all-sky surveys.

Solar and Stellar Astrophysics