Oscillating solutions of the Vlasov-Poisson system -- A numerical investigation

Abstract

Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov-Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in time or damped. Along one-parameter families of polytropic steady states we establish an Eddington-Ritter type relation which relates the period of the oscillation to the central density of the steady state. The numerically obtained periods are used to estimate possible periods for typical elliptical galaxies.

20 pages

References in corpus (2)

• A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system
• A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

Cited by in corpus (7)

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• A numerical stability analysis for the Einstein-Vlasov system
• Stability and instability results for equilibria of a (relativistic) self-gravitating collisionless gas -- A review
• Collisionless equilibria in general relativity: stable configurations beyond the first binding energy maximum
• Damping versus oscillations for a gravitational Vlasov-Poisson system
• A Birman-Schwinger principle in galactic dynamics
• Numerical experiments on stationary, oscillating, and damped spherical galaxy models