Quasi Resonant Theory of Tidal Interactions


In order to deeply understand  the nature of the resonant stripping and to apply it in a more general context than dwarf spheroidal galaxies, I have subsequently  developed an analytic formalism that accurately describes the changes in velocities to the stars which results  from close gravitational encounters between spinning galaxies.  In fact,  the impulse approximation usually applied  to describe the changes in velocities during high-speed galactic  encounters does not account for resonances because the stars in the perturbed system (the victim) are assumed to remain roughly stationary and do not move over the course of the encounter.  Thus, I have explored the consequences of brief but violent tidal forces when a rotating system experiences  a time-dependent resonance, or quasi-resonance. Our theory accurately describes coplanar prograde or retrograde encounters involving spinning systems passing on straight line paths and on parabolic orbits. The formalism is also generalized to no-coplanar cases and a comparison to full N-body experiments to show the accuracy of the approximation is also being developed (see Figure below).

Our theory may be relevant to other  applications then galaxy interactions, such as to warped disks, studies of the stability of binary stars perturbed by a third body or to investigations of protoplanetary disks perturbed by close passages of stars.

Figure 1. Time evolution of the victim galaxy under the tidal effect of a slow perturber passing on a parabolic prograde orbit. The upper left panel illustrates the initial set up where test particles in the annuli are kicked by velocity increments according to the quasi-resonant approximation.  Time evolves from left to right. Bottom panels show the evolution in time of the victim (from the initial set up on the left to the final appearance of tails to the right) when an external perturber is passing on a parabolic orbit, in a restricted three-body simulation.

“Quasi-Resonant Theory of Tidal Interactions”.

D’Onghia, E., Vogelsberger, M., Figuere-Ciguere, C.-A., Hernquist, L. 2010,

Astrophysic. Journal, in press.