Core mass -- halo mass relation of bosonic and fermionic dark matter halos harbouring a supermassive black hole

Pierre-Henri Chavanis

doi:10.1103/PhysRevD.101.063532

paper

Core mass -- halo mass relation of bosonic and fermionic dark matter halos harbouring a supermassive black hole

arXiv:1911.01937 · doi:10.1103/PhysRevD.101.063532

Abstract

We study the core mass -- halo mass relation of bosonic dark matter halos, in the form of self-gravitating Bose-Einstein condensates, harbouring a supermassive black hole. We use the ``velocity dispersion tracing'' relation according to which the velocity dispersion in the core $v_{c}^{2} \sim G M_{c} / R_{c}$ is of the same order as the velocity dispersion in the halo $v_{h}^{2} \sim G M_{h} / r_{h}$ (this relation can be justified from thermodynamical arguments) and the approximate analytical mass-radius relation of the quantum core in the presence of a central black hole obtained in our previous paper [P.H. Chavanis, Eur. Phys. J. Plus 134, 352 (2019)]. For a given minimum halo mass $(M_{h})_{min} \sim 1 0^{8} M_{⊙}$ determined by the observations, the only free parameter of our model is the scattering length $a_{s}$ of the bosons (their mass $m$ is then determined by the characteristics of the minimum halo). For noninteracting bosons and for bosons with a repulsive self-interaction, we find that the core mass $M_{c}$ increases with the halo mass $M_{h}$ and achieves a maximum value $(M_{c})_{max}$ at some halo mass $(M_{h})_{*}$ before decreasing. The whole series of equilibria is stable. For bosons with an attractive self-interaction, we find that the core mass achieves a maximum value $(M_{c})_{max}$ at some halo mass $(M_{h})_{*}$ before decreasing. The series of equilibria becomes unstable above a maximum halo mass $(M_{h})_{max} \geq (M_{h})_{*}$ . In the absence of black hole $(M_{h})_{max} = (M_{h})_{*}$ . At that point, the quantum core (similar to a dilute axion star) collapses. We perform a similar study for fermionic dark matter halos. We find that they behave similarly to bosonic dark matter halos with a repulsive self-interaction, the Pauli principle for fermions playing the role of the repulsive self-interaction for bosons.

Core mass -- halo mass relation of bosonic and fermionic dark matter halos harbouring a supermassive black hole

Abstract

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