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, M_B=-19.12. These
limits define a sample of 140 spiral, 30 elliptical (E), and 38 lenticular (S0)
galaxies. We established the Sersic index distribution for early-type (E/S0)
galaxies in our sample. Davis et al. (2014) 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 Sersic 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 Sersic index (Graham et al.
2007) for an early-type galaxy or the logarithmic spiral arm pitch angle
(Berrier et al. 2013) 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, while 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.
