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.