The M-sigma Relation of Super Massive Black Holes from the Scalar Field
  Dark Matter
  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 $m\simeq 5\times 10^{-22} eV$.
