The fundamental relation between supermassive black holes and their host galaxies

Abstract

We study the correlations between supermassive black holes (BHs) and their host galaxies, using a sample of 83 BH masses collected from the most recent and reliable spatially resolved estimates available from the literature. We confirm the mono- and bivariate correlations between SMBHs and the bulges of their host galaxies, confirming that the correlation with the effective velocity dispersion is not significantly improved by higher dimensionality. Instead, pseudo-bulges do not seem to correlate with their SMBHs, probably because their secular evolution is often unable to trigger accretion onto the central BH. We then present a novel approach aimed at finding the fundamental relation between SMBHs and their host galaxies. For the first time, we analytically combine BH masses with the Fundamental Plane (FP), showing that MBH–σe appears to be the fundamental relation rather than a putative ‘BH Fundamental Plane’ of the kind MBH–σe–Re. These results can be explained by a picture which sees the MBH–σe relation as a natural outcome of the change in AGN feedback from momentum-driven to energy-driven. The other scaling relations are then established through the FP.

The Case for the Fundamental MBH-σ Relation

“…Our results are shown in Figures 1, 2, which show the residuals extracted from the recent homogeneous sample calibrated by de Nicola et al [54]. Figure 1 shows that black hole mass strongly correlates with velocity dispersion at fixed galaxy luminosity with a Pearson coefficient r ∼ 0.7 (top left panel), and even more so at fixed effective radius with r ∼ 0.8 (bottom left panel), while the corresponding correlations with stellar luminosity or effective radius are significantly less strong with r ∼ 0.4 at fixed velocity dispersion (right panels).…”

“…In this paper we have reviewed previous evidence for the M BH -σ e being the most fundamental of all black hole-host galaxy scaling relations (among those discovered so far) and we have presented new evidence based on the statistical analysis of the sample recently compiled by de Nicola et al [54]. Both residuals [(e.g., [44]) and PCA analyses point to σ e being more fundamental than both stellar luminosity/mass or effective radius in their correlation to central black hole mass.…”

“…de Nicola et al [54] presented a systematic study of black hole scaling relations on an improved sample of local black holes, confirming that "the correlation with the effective velocity dispersion is not significantly improved by higher dimensionality." The authors concluded that the M BH -σ e is fundamental over multidimensional alternatives, independent of bulge decompositions.…”

“…In the PCA analysis we continue to use the dataset from de Nicola et al [54]. To ensure that quantities with a higher dispersion are not over-weighted, we normalize our variables to their mean values, dividing by the standard deviation of their distributions.…”

“…Correlations between residuals from the observed scaling relations, as indicated. The residuals are extracted from the recent homogeneous sample calibrated by de Nicola et al[54]. It can be clearly seen that black hole mass is strongly correlated with velocity dispersion at fixed galaxy luminosity with a Pearson coefficient r ∼ 0.7 (top left panel), and even more so at fixed effective radius with r ∼ 0.8 (bottom left panel).…”