THE LOCAL BLACK HOLE MASS FUNCTION DERIVED from the M _BH-P and the M _BH-n RELATIONS

We present a determination of the supermassive black hole (SMBH) mass function for early- and late-type galaxies in the nearby universe (z < 0.0057), established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the southern hemisphere. The sample is defined by limiting luminosity (redshift-independent) distance, D _L = 25.4 Mpc, and a limiting absolute B-band magnitude, . These limits define a sample of 140 spiral, 30 elliptical (E), and 38 lenticular (S0) galaxies. We established the Sérsic index distribution for early-type (E/S0) galaxies in our sample. Davis et al. established the pitch angle distribution for their sample, which is identical to our late-type (spiral) galaxy sample. We then used the pitch angle and the Sérsic index distributions in order to estimate the SMBH mass function for our volume-limited sample. The observational simplicity of our approach relies on the empirical relation between the mass of the central SMBH and the Sérsic index for an early-type galaxy or the logarithmic spiral-arm pitch angle for a spiral galaxy. Our SMBH mass function agrees well at the high-mass end with previous values in the literature. At the low-mass end, although inconsistencies exist in previous works that still need to be resolved, our work is more in line with expectations based on modeling of black hole evolution.