The M-sigma Relation of Super Massive Black Holes from the Scalar Field Dark Matter

TL;DR

This paper models the M-sigma relation between supermassive black hole mass and galaxy velocity dispersion using scalar field dark matter, showing how black holes influence halo profiles and reproducing the observed relation with specific dark matter particle mass.

Contribution

It introduces a scalar field dark matter model that explains the M-sigma relation through black hole effects on galactic halo profiles, a novel approach compared to previous models.

Findings

The M-sigma relation is reproduced with a dark matter particle mass of approximately 5×10^{-22} eV.

Black holes significantly alter galactic halo profiles due to their gravitational influence on the scalar field.

Numerical simulations confirm the correlation between black hole mass and velocity dispersion in this model.

Abstract

We explain the M-sigma relation between the mass of super massive black holes in galaxies and the velocity dispersions of their bulges in the scalar field or the Bose-Einstein condensate dark matter model. The gravity of the central black holes changes boundary conditions of the scalar field at the galactic centers. Owing to the wave nature of the dark matter this significantly changes the galactic halo profiles even though the black holes are much lighter than the bulges. As a result the heavier the black holes are, the more compact the bulges are, and hence the larger the velocity dispersions are. This tendency is verified by a numerical study. The M-sigma relation is well reproduced with the dark matter particle mass $m\simeq 5\times 10^{-22} eV$.