On the possibility that ultra-light boson haloes host and form supermassive black holes

Several observations suggest the existence of supermassive black holes (SMBH) at the centres of galaxies. However, the mechanism under which these objects form remains non-completely understood. In this work, we review an alternative mechanism of formation of galactic SMBHs from the collapse of a fraction of a dark matter (DM) halo made of an ultra-light scalar field (SF) whose critical mass of collapse is ∼1013 M⊙. Once the BH is formed, a long-living quasi-resonant SF configuration survives and plays the role of a central fraction of the galactic DM halo. In this work, we construct a model with an ultra-light SF configuration laying in a Schwarzschild space–time to describe the centre of the DM halo hosting an SMBH in equilibrium, in the limit where self-gravitating effects can be neglected. We compute the induced stellar velocity dispersion in order to investigate the influence of the BH on to the velocity field of visible matter at the central galactic regions. We fit the empirical correlation between stellar velocity dispersions and masses of SMBHs considering two instances: the idealized case of DM-dominated (DMD) systems, where the gravitational influence of baryons is neglected, and cases of real luminous galaxies (LGAL). In the DMD case, we found it is possible to reproduce the observed stellar velocity dispersions at the effective radius of systems hosting SMBHs of at most 108 M⊙. In the LGAL case, we found that the baryons are crucial to reproduce the observed velocity dispersion.