The SINFONI Black Hole Survey: The Black Hole Fundamental Plane revisited and the paths of (co-) evolution of supermassive black holes and bulges

Understand

We investigate the correlations between the black hole mass $M_{BH}$, the velocity dispersion $\sigma$, the bulge mass $M_{Bu}$, the bulge average spherical density $\rho_h$ and its spherical half mass radius $r_h$, constructing a database of 97 galaxies (31 core ellipticals, 17 power-law ellipticals, 30 classical bulges, 19 pseudo bulges) by joining 72 galaxies from the literature to 25 galaxies observed during our recent SINFONI black hole survey.

• For the first time we discuss the full error covariance matrix.
• We analyse the well known $M_{BH}-\sigma$ and $M_{BH}-M_{Bu}$ relations and establish the existence of statistically significant correlations between $M_{Bu}$ and $r_h$ and anti-correlations between $M_{Bu}$ and $\rho_h$.
• We establish five significant bivariate correlations ($M_{BH}-\sigma-\rho_h$, $M_{BH}-\sigma-r_h$, $M_{BH}-M_{Bu}-\sigma$, $M_{BH}-M_{Bu}-\rho_h$, $M_{BH}-M_{Bu}-r_h$) that predict $M_{BH}$ of 77 core and power-law ellipticals and classical bulges with measured and intrinsic scatter as small as $\approx 0.36$ dex and $\approx 0.33$ dex respectively, or 0.26 dex when the subsample of 45 galaxies defined by Kormendy and Ho (2013) is considered.