The (Black Hole Mass)-(Spheroid Stellar Density) Relations: $M_{\rm BH}$--$μ$ (and $M_{\rm BH}$--$Σ$) and $M_{\rm BH}$--$ρ$

Abstract

This paper is the fourth in a series presenting (galaxy morphology, and thus galaxy formation)dependent black hole mass, M BH , scaling relations. We have used a sample of 119 galaxies with directly-measured M BH and host spheroid parameters obtained from multi-component decomposition of, primarily, 3.6 µm Spitzer images. Here, we investigate the correlations between M BH and the projected luminosity density µ, the projected stellar mass density Σ, and the deprojected (internal) stellar mass density ρ, for various spheroid radii. We discover the predicted M BH -µ 0,sph relation and present the first M BH -µ e,sph and M BH -ρ 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 (fastrotators, ES/S0) and without (slow-rotators, E) a disk. The scatter about various M BH -Σ R,sph (and ρ r,sph ) relations is shown to systematically decrease as the enclosing aperture (and volume) increases, dropping from 0.69 dex when using the spheroid "compactness", Σ 1kpc,sph , to 0.59 dex when using Σ 5kpc,sph . We also reveal that M BH correlates with the internal density, ρ soi,sph , at the BH's sphere-ofinfluence 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. The M BH -ρ soi,sph relations shall help with direct estimation of tidal disruption event rates, binary BH lifetimes, and together with other BH scaling relations, improve the characteristic strain estimates for long-wavelength gravitational waves pursued with pulsar timing arrays and space-based interferometers.