Title: A stability criterion for any collisionless stellar equilibrium and some concrete applications thereof
Abstract: view Abstract Citations (31) References (10) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Stability Criterion for Any Collisionless Stellar Equilibrium and Some Concrete Applications Thereof Kandrup, Henry E. Abstract By viewing the Vlasov, or collisionless Boltzmann, equation of galactic dynamics as a Hamiltonian system with respect to an appropriate Lie bracket, an exact expression is derived for the energy associated with a phase-preserving, or symplectic, perturbation of an arbitrary equilibrium configuration, not assumed to possess any particular symmetries. Stability of the equilibrium hinges on the sign of the energy: positive energy for all perturbations implies linear and spectral stability. The existence of both negative and positive energy perturbations implies the existence of phase-preserving perturbations of zero linearized energy with arbitrarily large amplitudes. It is shown that a generic equilibrium depending on more than one constant of the motion will typically admit phase-preserving perturbations of negative energy that correspond to a local rearrangement of the velocity profile. It is also shown that, in analogy with spherical equilibria, a broad class of configurations with slab or cylindrical symmetries are stable with respect to 'centrally symmetric' perturbations. Publication: The Astrophysical Journal Pub Date: March 1991 DOI: 10.1086/169816 Bibcode: 1991ApJ...370..312K Keywords: Computational Astrophysics; Equilibrium Equations; Hamiltonian Functions; Stellar Motions; Boltzmann-Vlasov Equation; Perturbation Theory; Poisson Equation; Astrophysics; STARS: STELLAR DYNAMICS full text sources ADS |