Jeans Instability of Dissipative Self-Gravitating Bose–Einstein Condensates with Repulsive or Attractive Self-Interaction: Application to Dark Matter

We study the Jeans instability of an infinite homogeneous dissipative self-gravitating Bose–Einstein condensate described by generalized Gross–Pitaevskii–Poisson equations Chavanis, P.H. Eur. Phys. J. Plus2017, 132, 248. This problem has applications in relation to the formation of dark matter halos in cosmology. We consider the case of a static and an expanding universe. We take into account an arbitrary form of repulsive or attractive self-interaction between the bosons (an attractive self-interaction being particularly relevant for the axion). We consider both gravitational and hydrodynamical (tachyonic) instabilities and determine the maximum growth rate of the instability and the corresponding wave number. We study how they depend on the scattering length of the bosons (or more generally on the squared speed of sound) and on the friction coefficient. Previously obtained results (notably in the dissipationless case) are recovered in particular limits of our study.