Quasi-resonant theory of tidal interactions

Elena D'Onghia*, Mark Vogelsberger, Claude Andre Faucher-Giguere, Lars Hernquist

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

76 Scopus citations


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

Original languageEnglish (US)
Pages (from-to)353-368
Number of pages16
JournalAstrophysical Journal
Issue number1
StatePublished - Dec 10 2010


  • Galaxies:interactions
  • Galaxies:kinematics and dynamics
  • Methods:analytical

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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