2016ApJ...821...88S

The Sersic {R}^{1/n} model is the best approximation known to date for describing the light distribution of stellar spheroidal and disk components, with the Sersic index n providing a direct measure of the central radial concentration of stars. The Sersic index of a galaxy's spheroidal component, nsph, has been shown to tightly correlate with the mass of the central supermassive black hole, MBH. The {M}_BH–{n}sph correlation is also expected from other two well known scaling relations involving the spheroid luminosity, Lsph: the L_sph–{n}sph and the {M}_BH–Lsph. Obtaining an accurate estimate of the spheroid Sersic index requires a careful modeling of a galaxy's light distribution and some studies have failed to recover a statistically significant {M}_BH–{n}sph correlation. With the aim of re-investigating the {M}_BH–{n}sph and other black hole mass scaling relations, we performed a detailed (i.e., bulge, disks, bars, spiral arms, rings, halo, nucleus, etc.) decomposition of 66 galaxies, with directly measured black hole masses, that had been imaged at 3.6 µm with Spitzer. In this paper, the third of this series, we present an analysis of the L_sph–{n}sph and {M}_BH–{n}sph diagrams. While early-type (elliptical+lenticular) and late-type (spiral) galaxies split into two separate relations in the L_sph–{n}sph and {M}_BH–Lsph diagrams, they reunite into a single {M}_BH∝{n}_sph^{3.39±0.15} sequence with relatively small intrinsic scatter (ε≃0.25 dex). The black hole mass appears to be closely related to the spheroid central concentration of stars, which mirrors the inner gradient of the spheroid gravitational potential.