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 hole (SMBH) 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, M_bh, is fundamentally driven by either local or global galaxy properties. We explore correlations between M_bh and stellar velocity dispersion sigma_e, i-band bulge luminosity L_i,bulge, bulge mass M_bulge, bulge S\ue9rsic index n, bulge mean effective surface brightness , i-band luminosity of the galaxy L_i,gal, galaxy stellar mass M_star,gal, maximum circular velocity V_c, and galaxy dynamical and effective masses M_dyn,gal and M_e,gal. We verify the tightness of the M_bh-sigma_e relation and find that correlations with other galaxy parameters do not yield tighter trends. We do not find differences in the M_bh-sigma_e relation of barred and unbarred galaxies. The M_bh-sigma_e relation of pseudo-bulges is also coarser and has a different slope than that involving classical bulges. The M_bh-M_bulge is not as tight as the M_bh-sigma_e relation, despite the bulge mass proving to be a better proxy of M_bh than bulge luminosity, and despite adding the bulge effective radius as an additional fitting parameter. Contrary to various published reports, we find a rather poor correlation between M_bh and n (or ), suggesting that M_bh is not related to the bulge light concentration. The correlations between M_bh and galaxy luminosity or mass are not a marked improvement over the M_bh-sigma_e relation. These scaling relations depend sensitively on the host galaxy morphology: early-type galaxies follow a tighter relation than late-type galaxies. If V_c is a proxy for the dark matter halo mass, the large scatter of the M_bh-V_c relation then suggests that M_bh is more coupled to the baryonic rather than the dark matter. We have tested the need for a third parameter in the M_bh 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 \u3c3e with a small tilt due to the effective radius. We provide a compendium of galaxy structural properties for most of the SMBH hosts known to date