The effect of dark matter on the Jeans instability with the q-nonextensive velocity distribution

Based on the framework of nonextensive statistics and its related kinetic theory, the Jeans instability in a self-gravitational system composed of dark and bright matters is restudied. The results show that the nonextensivity, the presence of dark matter, has significant effects on the dynamics of Jeans modes. With the increase in the q parameter and the ratio of dispersion velocities, as well as the decreased ratio of densities of dark to bright matters, both critical wave-numbers and growth rates of the instabilities are increased. In addition, as expected, when q → 1, the corresponding results for Maxwellian velocity distribution are recovered. The present results may shed new light on the comprehension of the intrinsic physical mechanism responsible for the collapse of interstellar gas clouds.