The (Black Hole Mass)-(Spheroid Stellar Density) Relations: M _BH- μ (and M _BH-ς) and M _BH- ρ

This paper is the fourth in a series presenting (galaxy morphology, and thus galaxy formation)-dependent black hole (BH) mass, M BH, scaling relations. We have used a sample of 119 galaxies with directly measured M BH and host spheroid parameters obtained from multicomponent decomposition of, primarily, 3.6 μm Spitzer images. Here, we investigate the correlations between M BH and the projected (apparent) luminosity density μ, the projected stellar mass density ς, and the de-projected (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, respectively) and an offset between ETGs with (fast-rotators, 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-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. The M BH-«ρ»soi,sph relations will 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.