Abstract
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.
Highlights
Cosmological observations have revealed that baryonic matter represents only 5% of the content of the Universe
This core–halo structure is in agreement with the phenomenology of BECDM halos
We have made an exhaustive study of the Jeans instability of an infinite homogeneous dissipative self-gravitating Bose–Einstein condensates (BECs) based on the generalized GPP equations introduced in [61]
Summary
Cosmological observations have revealed that baryonic (visible) matter represents only 5% of the content of the Universe. By the GPP equations, and by Suárez and Chavanis [52] for general relativistic self-interacting BECs described by the Gross–Pitaevskii–Einstein (GPE) equations These authors showed that the formation of structures is suppressed at small scales even at T = 0 (unlike in the CDM model) because of the quantum pressure (Heisenberg) or the self-interaction of the bosons (in the repulsive case). They determined the quantum Jeans length λJ and the quantum Jeans mass MJ which provide an estimate of the minimum size and mass of BECDM halos (ground state).. The Appendices bring additional results or present alternative manners to derive the basic equations of the problem
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