Stability of a self-gravitating homogeneous resistive plasma

Details Stability of a self-gravitating homogeneous resistive plasma Stability of a self-gravitating homogeneous resistive plasma

2011-11-17

arxiv.org/abs/1111.4051v1

Physica D: Nonlinear Phenomena Volume 241, Issue 6, 15 March 2012, Pages 721-728

Astronomy and Astrophysics

Astrophysics

High Energy Astrophysical Phenomena

12 pages, 3 figures, submitted to Physica D

Scientific paper

10.1016/j.physd.2011.12.011

In this paper, we analyze the stability of a homogeneous self-gravitating plasma, having a non-zero resistivity. This study provides a generalization of the Jeans paradigm for determining the critical scale above which gravitational collapse is allowed. We start by discussing the stability of an ideal self-gravitating plasma embedded in a constant magnetic field. We outline the existence of an anisotropic feature of the gravitational collapse. In fact, while in the plane orthogonal to the magnetic field the Jeans length is enhanced by the contribution of the magnetic pressure, outside this plane perturbations are governed by the usual Jeans criterium. The anisotropic collapse of a density contrast is sketched in details, suggesting that the linear evolution provides anisotropic initial conditions for the non-linear stage, where this effect could be strongly enforced. The same problem is then faced in the presence of non-zero resistivity and the conditions for the gravitational collapse are correspondingly extended. The relevant feature emerging in this resistive scenario is the cancellation of the collapse anisotropy in weakly conducting plasmas. In this case, the instability of a self-gravitating resistive plasma is characterized by the standard isotropic Jeans length in any directions. The limit of very small resistivity coefficient is finally addressed, elucidating how reminiscence of the collapse anisotropy can be found in the different value of the perturbation frequency inside and outside the plane orthogonal to the magnetic field.

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