We provide a new estimate of the local supermassive black hole mass function using ( i ) the empirical relation between supermassive black hole mass and the Sérsic index of the host spheroidal stellar system and ( ii ) the measured ( spheroid ) Sérsic indices drawn from 10k galaxies in the Millennium Galaxy Catalogue .
The observational simplicity of our approach , and the direct measurements of the black hole predictor quantity , i.e .
the Sérsic index , for both elliptical galaxies and the bulges of disc galaxies makes it straightforward to estimate accurate black hole masses in early- and late-type galaxies alike .
We have parameterised the supermassive black hole mass function with a Schechter function and find , at the low-mass end , a logarithmic slope ( 1 + \alpha ) of \sim 0.7 for the full galaxy sample and \sim 1.0 for the early-type galaxy sample .
Considering spheroidal stellar systems brighter than M _ { B } = -18 mag , and integrating down to black hole masses of 10 ^ { 6 } M _ { \odot } , we find that the local mass density of supermassive black holes in early-type galaxies \rho _ { bh,early - type } = ( 3.5 \pm 1.2 ) \times 10 ^ { 5 } h ^ { 3 } _ { 70 } M _ { \odot } Mpc ^ { -3 } , and in late-type galaxies \rho _ { bh,late - type } = ( 1.0 \pm 0.5 ) \times 10 ^ { 5 } h ^ { 3 } _ { 70 } M _ { \odot } Mpc ^ { -3 } .
The uncertainties are derived from Monte Carlo simulations which include uncertainties in the M _ { bh } – n relation , the catalogue of Sérsic indices , the galaxy weights and Malmquist bias .
The combined , cosmological , supermassive black hole mass density is thus \Omega _ { bh,total } = ( 3.2 \pm 1.2 ) \times 10 ^ { -6 } h _ { 70 } .
That is , using a new and independent method , we conclude that ( 0.007 \pm 0.003 ) h _ { 70 } ^ { 3 } per cent of the universe ’ s baryons are presently locked up in supermassive black holes at the centres of galaxies .