Quasi-Resonant Theory of Tidal Interactions
  When a spinning system experiences a transient gravitational encounter with
an external perturber, a quasi-resonance occurs if the spin frequency of the
victim matches the peak orbital frequency of the perturber. Such encounters are
responsible for the formation of long tails and bridges of stars during galaxy
collisions. For high-speed encounters, the resulting velocity perturbations can
be described within the impulse approximation. The traditional impulse
approximation, however, does not distinguish between prograde and retrograde
encounters, and therefore completely misses the resonant response. Here, using
perturbation theory, we compute the effects of quasi-resonant phenomena on
stars orbiting within a disk. Explicit expressions are derived for the velocity
and energy change to the stars induced by tidal forces from an external
gravitational perturber passing either on a straight line or parabolic orbit.
Comparisons with numerical restricted three-body calculations illustrate the
applicability of our analysis.
