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.