The (Black Hole Mass)–(Spheroid Stellar Density) Relations: M BH –μ (and M BH –Σ) and M BH –ρ

Abstract

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 μ m 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.