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.
We investigate the accuracy and precision of triaxial dynamical orbit models by fitting two dimensional mock observations of a realistic N-body merger simulation resembling a massive early-type galaxy with a supermassive black hole (SMBH). We show that we can reproduce the triaxial N-body merger remnant’s correct black hole mass, stellar mass-to-light ratio and total enclosed mass (inside the half-light radius) for several different tested orientations with an unprecedented accuracy of 5-10 per cent. Our dynamical models use the entire non-parametric line-of-sight velocity distribution (LOSVD) rather than parametric LOSVDs or velocity moments as constraints. Our results strongly suggest that state-of-the-art integral-field projected kinematic data contain only minor degeneracies with respect to the mass and anisotropy recovery. Moroever, this also demonstrates the strength of the Schwarzschild method in general. We achieve the proven high recovery accuracy and precision with our newly developed modeling machinery by combining several advancements: (i) our new semi-parametric deprojection code probes degeneracies and allows to constrain the viewing angles of a triaxial galaxy; (ii) our new orbit modeling code SMART uses a 5-dim orbital starting space to representatively sample in particular near-Keplerian orbits in galaxy centers; (iii) we use a generalised information criterion AICp to optimise the smoothing and to compare different mass models to avoid biases that occur in χ2-based models with varying model flexibilities.
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