Abstract
The Jeans stability criterion for gravitational collapse is examined for the case of an inert binary mixture in local equilibrium, neglecting dissipative effects. The corresponding transport equations are established using kinetic theory within the Euler regime approximation. It is shown that the corresponding dispersion relation is modified; yielding corrections to the Jeans wave number that can be generalized for several interesting cases involving positive entropy production such as matter- antimatter systems and ordinary matter-dark matter dynamics.
Highlights
Structure formation through gravitational collapse is one of the most important processes present in astrophysics
First identified by James Jeans in 1902 [1], gravity acts through very long scales allowing density fluctuations to grow exponentially when the mass present at certain scales surpasses a given mass thresehold
A very simple argument that leads to a fairly accurate approximation of this threshold consists in the consideration of the wave equation for the density fluctuations δρ, valid for an isothermal one-component system with equilibrium density ρ0 [2, 3]:
Summary
Structure formation through gravitational collapse is one of the most important processes present in astrophysics. Heat fluxes associated to density gradients (Dufour effect) have been addressed for the case of a dilute two component plasma [7]. The purpose of the present paper is to fill this gap giving the kinetic foundations of the derivation of the dispersion relation for an inert dilute binary gas in the presence of Newtonian gravity. In order to accomplish this task, the paper has been divided as follows: section two corresponds to the establishment of the evolution equations of the averages of the conserved microscopic quantities (mass, linear momentum and energy), special emphasis is made in the structure of the mass fluxes for each type of particle. Section four is devoted to a discussion of the results here obtained
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