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

TL;DR

This study analyzes the relationships between supermassive black holes and galaxy bulges, revealing new correlations and insights into their co-evolution, with implications for different galaxy types and formation scenarios.

Contribution

It introduces a comprehensive analysis of black hole and bulge correlations, including the full error covariance matrix, and identifies new significant multivariate relations.

Findings

Established five significant bivariate correlations predicting black hole mass

Pseudo bulges have systematically lower black hole masses but align with relations at high densities

Findings support co-evolution scenarios and highlight differences among galaxy types

Abstract

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. In contrast, pseudo bulges have systematically lower $M_{BH}$, but approach the predictions of all the above relations at spherical densities $\rho_h\ge 10^{10} M_\odot/kpc^3$ or scale lengths $r_h\le 1$ kpc. These findings fit in a scenario of co-evolution of BH and classical-bulge masses, where core ellipticals are the product of dry mergers of power-law bulges and power-law Es and bulges the result of (early) gas-rich mergers and of disk galaxies. In contrast, the (secular) growth of BHs is decoupled from the growth of their pseudo bulge hosts, except when (gas) densities are high enough to trigger the feedback mechanism responsible for the existence of the correlations between $M_{BH}$ and galaxy structural parameters.