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

Understand

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 $v_c^2\sim GM_c/R_c$ is of the same order as the velocity dispersion in the halo $v_h^2\sim GM_h/r_h$ (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.