The (Black Hole Mass)-(Spheroid Stellar Density) Relations: $M_{\rm BH}$--$\mu$ (and $M_{\rm BH}$--$\Sigma$) and $M_{\rm BH}$--$\rho$

TL;DR

This study explores the relationships between black hole mass and various stellar density measures in galaxy spheroids, revealing different trends for galaxy types and how scatter decreases with larger measurement apertures.

Contribution

It presents new correlations between black hole mass and stellar density metrics, including the first diagrams for $M_{BH}$--$ ho$ and $M_{BH}$--$ ext{}\mu$, highlighting differences across galaxy types.

Findings

Discovered the $M_{BH}$--$ ext{ }\mu_{0, ext{sph}}$ relation.

Identified different $M_{BH}$--$ ext{ }\mu_{e, ext{sph}}$ and $M_{BH}$--$ ho_{e, ext{int}, ext{sph}}$ trends for galaxy types.

Showed scatter decreases with larger aperture sizes, from 0.69 to 0.59 dex.

Abstract

This paper is the fourth in a series presenting (galaxy morphology, and thus galaxy formation)-dependent black hole mass, $M_{\rm BH}$, scaling relations. We have used a sample of 119 galaxies with directly-measured $M_{\rm BH}$ and host spheroid parameters obtained from multi-component decomposition of, primarily, $3.6\,\mu$m Spitzer images. Here, we investigate the correlations between $M_{\rm BH}$ and the projected luminosity density $\mu$, the projected stellar mass density $\Sigma$, and the deprojected (internal) stellar mass density $\rho$, for various spheroid radii. We discover the predicted $M_{\rm BH}$--$\mu_{\rm 0,sph}$ relation and present the first $M_{\rm BH}$--$\mu_{\rm e, sph}$ and $M_{\rm BH}$--$\rho_{\rm e,int, sph}$ diagrams displaying slightly different (possibly curved) trends for early- and late-type galaxies (ETGs and LTGs) and an offset between ETGs with (fast-rotators, ES/S0) and without (slow-rotators, E) a disk. The scatter about various $M_{\rm BH}$--$\langle\Sigma\rangle_{\rm R,sph}$ (and $\langle\rho\rangle_{\rm r,sph}$) relations is shown to systematically decrease as the enclosing aperture (and volume) increases, dropping from 0.69~dex when using the spheroid \enquote{compactness}, $\langle\Sigma\rangle_{\rm 1kpc,sph}$, to 0.59~dex when using $\langle\Sigma\rangle_{\rm 5kpc,sph}$. We also reveal that $M_{\rm BH}$ correlates with the internal density, $\rho_{\rm soi,sph}$, at the BH's sphere-of-influence radius, such that core-S\'ersic (high S\'ersic index, $n$) and (low-$n$) S\'ersic galaxies define different relations with total rms scatters 0.21~dex and 0.77~dex, respectively.(Abridged)