The Millennium Galaxy Catalogue: The $M_{bh}$--$L_{spheroid}$ derived
  supermassive black hole mass function
  Supermassive black hole mass estimates are derived for 1743 galaxies from the
Millennium Galaxy Catalogue using the recently revised empirical relation
between supermassive black hole mass and the luminosity of the host spheroid.
The MGC spheroid luminosities are based on $R^{1/n}$-bulge plus
exponential-disc decompositions. The majority of black hole masses reside
between $10^6 M_{\odot}$ and an upper limit of $2\times10^9 M_{\odot}$. Using
previously determined space density weights, we derive the SMBH mass function
which we fit with a Schechter-like function. Integrating the black hole mass
function over $10^6< M_{bh}/ M_{\odot} < 10^{10}$ gives a supermassive black
hole mass density of ($3.8 \pm 0.6) \times 10^5 h^{3}_{70} M_{\odot}$
Mpc$^{-3}$ for early-type galaxies and ($0.96 \pm 0.2) \times10^5 h^{3}_{70}
M_{\odot}$ Mpc$^{-3}$ for late-type galaxies. The errors are estimated from
Monte Carlo simulations which include the uncertainties in the $M_{bh}$--$L$
relation, the luminosity of the host spheroid and the intrinsic scatter of the
$M_{bh}$--$L$ relation. Assuming supermassive black holes form via baryonic
accretion we find that ($0.008\pm0.002) h_{70}^{3}$ per cent of the Universe's
baryons are currently locked up in supermassive black holes. This result is
consistent with our previous estimate based on the $M_{bh}$--$n$ (S{\'e}rsic
index) relation.
