The maximum mass of dilute axion stars
Résumé
We consider the possibility that dark matter is made of bosons in the form of Bose-Einstein condensates. We establish the mass-radius relation M (R) of nonrelativistic selfgravitating Bose-Einstein condensates with repulsive or attractive self-interaction. If the self-interaction is repulsive there exists an equilibrium state for any value of the mass but if the self-interaction is attractive, as in the case of axions, equilibrium states exist only below a maximum mass MmaxNR=5.073MP/|λ|[P.H. Chavanis, Phys. Rev. D 84, 043531 (2011)]. This is the maximum mass of dilute axion stars. Above that mass, the star collapses leading to a bosenova, a black hole, a dense axion star or axion drops. We consider how the maximum mass changes with the dimension of space, the presence of a central black hole, a cosmological constant, and relativistic effects. We apply these results to dark matter halos. We establish the general expression of the core mass – halo mass relation Mc(Mh). For a repulsive self-interaction, we show that the core mass Mc is always much below the maximum massMmaxGRset by general relativity so the core cannot collapse towards a black hole. For an attractive self-interaction, we show that the core mass Mc can reach in principle the maximum mass MmaxNR in sufficiently large dark matter halos, leading to core collapse, and we discuss if this situation can happen in practice.