Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method

Abstract

We complete classical investigations concerning the dynamical stability of an infinite homogeneous gaseous medium described by the Euler-Poisson system or an infinite homogeneous stellar system described by the Vlasov-Poisson system (Jeans problem). To determine the stability of an infinite homogeneous stellar system with respect to a perturbation of wavenumber k, we apply the Nyquist method. We first consider the case of single-humped distributions and show that, for infinite homogeneous systems, the onset of instability is the same in a stellar system and in the corresponding barotropic gas, contrary to the case of inhomogeneous systems. We show that this result is true for any symmetric single-humped velocity distribution, not only for the Maxwellian. If we specialize on isothermal and polytropic distributions, analytical expressions for the growth rate, damping rate and pulsation period of the perturbation can be given. Then, we consider the Vlasov stability of symmetric and asymmetric double-humped distributions (two-stream stellar systems) and determine the stability diagrams depending on the degree of asymmetry. We compare these results with the Euler stability of two self-gravitating gaseous streams. Finally, we determine the corresponding stability diagrams in the case of plasmas and compare the results with self-gravitating systems.

References in corpus (7)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Dynamical stability of collisionless stellar systems and barotropic stars: the nonlinear Antonov first law
• Dynamical stability of systems with long-range interactions: application of the Nyquist method to the HMF model
• Jeans type analysis of chemotactic collapse
• Jeans type instability for a chemotactic model of cellular aggregation
• Dynamics of finite and infinite self-gravitating systems with cold quasi-uniform initial conditions
• Infinite self-gravitating systems and cosmological structure formation

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