Axion core - halo mass and the black hole - halo mass relation:
  constraints on a few parsec scales
  If the dark matter is made of ultra-light axions, stable solitonic cores form
at the centers of virialized halos. In some range for the mass $m$ of the axion
particle, these cores are sufficiently compact and can mimic supermassive black
holes (SMBH) residing at galactic nuclei. We use the solitonic core--halo mass
relation, validated in numerical simulations, to constrain a new range of
allowed axion mass from measurements of the SMBH mass in (pseudo)bulge and
bulgeless galaxies. These limits are based on observations of galactic nuclei
on scales smaller than 10 pc. Our analysis suggests that $m < 10^{-18}$ eV is
ruled out by the data. We briefly discuss whether an attractive
self-interaction among axions could alleviate this constraint.
