Optical spectroscopic observations of intermediate-mass black holes and
  their host galaxies: the $M_{BH}-\sigma_*$ relation
  Intermediate-mass black holes (IMBHs; $M_{BH} <2*10^{5} M_{\odot}$) in galaxy
centers are cruciel for painting a coherent picture of the formation and growth
of supermassive black holes (SMBHs). Using Big Data analysis, we identified 305
IMBH candidates for IMBH and 1623 candidates of `light-weight' SMBHs ($2 *
10^{5} M_{odot} < M_{BH} <10^{6} M_{\odot}$). For 35 host galaxies from this
combined sample with the X-ray-confirmed active galactic nuclei (AGN) we
collected and analyzed optical spectroscopic observations. These data show that
bulge stellar velocity dispersions ($\sigma_*$) lie in the range of
24$\dots$118~km/s and do not follow the correlation with $M_{BH}$ established
by larger SMBHs indicating that in the $10^{5}-10^{6} M_{\odot}$ range the
accretion is the prevailing BH growth channel.
