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

Abstract

This paper is the fourth in a series presenting (galaxy morphology, and thus galaxy formation)-dependent black hole mass, $M_{\mathrm{BH}}$, scaling relations. We have used a sample of 119 galaxies with directly-measured $M_{\mathrm{BH}}$ and host spheroid parameters obtained from multi-component decomposition of, primarily, $3.6\mu$m Spitzer images. Here, we investigate the correlations between $M_{\mathrm{BH}}$ 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 $M_{\mathrm{BH}}$--${\mu }_{0,\mathrm{sph}}$ relation and present the first $M_{\mathrm{BH}}$--${\mu }_{\mathrm{e},\mathrm{sph}}$ and $M_{\mathrm{BH}}$--${\rho }_{\mathrm{e},\mathrm{int},\mathrm{sph}}$ 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 $M_{\mathrm{BH}}$--$⟨\Sigma {⟩}_{\mathrm{R},\mathrm{sph}}$ (and $⟨\rho {⟩}_{\mathrm{r},\mathrm{sph}}$) relations is shown to systematically decrease as the enclosing aperture (and volume) increases, dropping from 0.69~dex when using the spheroid \enquote{compactness}, $⟨\Sigma {⟩}_{1kpc,\mathrm{sph}}$, to 0.59~dex when using $⟨\Sigma {⟩}_{5kpc,\mathrm{sph}}$. We also reveal that $M_{\mathrm{BH}}$ correlates with the internal density, ${\rho }_{\mathrm{soi},\mathrm{sph}}$, at the BH's sphere-of-influence radius, such that core-Sérsic (high Sérsic index, $n$) and (low-$n$) Sérsic galaxies define different relations with total rms scatters 0.21~dex and 0.77~dex, respectively.(Abridged)

27 pages, 12 figures, 2 tables, submitted to ApJ

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