A local baseline of the black hole mass scaling relations for active
  galaxies. IV. Correlations between $M_{\rm BH}$ and host galaxy $\sigma$,
  stellar mass, and luminosity
  The tight correlations between the mass of supermassive black holes ($M_{\rm
BH}$) and their host-galaxy properties have been of great interest to the
astrophysical community, but a clear understanding of their origin and
fundamental drivers still eludes us. The local relations for active galaxies
are interesting in their own right and form the foundation for any evolutionary
study over cosmic time. We present Hubble Space Telescope optical imaging of a
sample of 66 local active galactic nuclei (AGNs); for 14 objects, we also
obtained Gemini near-infrared images. We use state of the art methods to
perform surface photometry of the AGN host galaxies, decomposing them in
spheroid, disk and bar (when present) and inferring the luminosity and stellar
mass of the components. We combine this information with spatially-resolved
kinematics obtained at the Keck Telescopes to study the correlations between
$M_{\rm BH}$ (determined from single-epoch virial estimators) and host galaxy
properties. The correlations are uniformly tight for our AGN sample, with
intrinsic scatter 0.2-0.4 dex, smaller than or equal to that of quiescent
galaxies. We find no difference between pseudo and classical bulges or barred
and non-barred galaxies. We show that all the tight correlations can be
simultaneously satisfied by AGN hosts in the 10$^7$-10$^9$ $M_{\odot}$ regime,
with data of sufficient quality. The MBH-$\sigma$ relation is also in agreement
with that of AGNs with $M_{\rm BH}$ obtained from reverberation mapping,
providing an indirect validation of single-epoch virial estimators of $M_{\rm
BH}$.
