Quasi-Resonant Theory of Tidal Interactions

TL;DR

This paper develops a perturbation theory to analyze quasi-resonant tidal interactions during galaxy encounters, revealing effects missed by traditional impulse approximation, with explicit formulas and numerical validation.

Contribution

It introduces a novel perturbation approach to quantify quasi-resonant effects in tidal interactions, improving upon the impulse approximation by distinguishing prograde and retrograde encounters.

Findings

Derived explicit formulas for velocity and energy changes in stars due to tidal forces.

Validated theoretical predictions with numerical restricted three-body simulations.

Highlighted the importance of quasi-resonance in galaxy collision dynamics.

Abstract

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.