On the Correlations between Galaxy Properties and Supermassive Black
  Hole Mass
  We use a large sample of upper limits and accurate estimates of supermassive
black holes masses coupled with libraries of host galaxy velocity dispersions,
rotational velocities and photometric parameters extracted from Sloan Digital
Sky Survey i-band images to establish correlations between the SMBH and host
galaxy parameters. We test whether the mass of the black hole, MBH, is
fundamentally driven by either local or global galaxy properties. We explore
correlations between MBH and stellar velocity dispersion sigma, bulge
luminosity, bulge mass Sersic index, bulge mean effective surface brightness,
luminosity of the galaxy, galaxy stellar mass, maximum circular velocity Vc,
galaxy dynamical and effective masses. We verify the tightness of the MBH-sigma
relation and find that correlations with other galaxy parameters do not yield
tighter trends. We do not find differences in the MBH-sigma relation of barred
and unbarred galaxies. The MBH-sigma relation of pseudo-bulges is also coarser
and has a different slope than that involving classical bulges. The MBH-bulge
mass is not as tight as the MBH-sigma relation, despite the bulge mass proving
to be a better proxy of MBH than bulge luminosity. We find a rather poor
correlation between MBH and Sersic index suggesting that MBH is not related to
the bulge light concentration. The correlations between MBH and galaxy
luminosity or mass are not a marked improvement over the MBH sigma relation. If
Vc is a proxy for the dark matter halo mass, the large scatter of the MBH-Vc
relation then suggests that MBH is more coupled to the baryonic rather than the
dark matter. We have tested the need for a third parameter in the MBH scaling
relations, through various linear correlations with bulge and galaxy
parameters, only to confirm that the fundamental plane of the SMBH is mainly
driven by sigma, with a small tilt due to the effective radius. (Abridged)
