A theoretical model for the M-bh-sigma relation for supermassive black holes in galaxies

We construct a model for black hole formation in galactic bulges. The initi al state is a slowly rotating isothermal sphere, with an effective transpor t speed a(eff) and rotation rate Omega. The black hole mass is determined w hen the centrifugal radius of the collapse flow exceeds the capture radius of the central black hole. This model reproduces the observed correlation b etween black hole masses and galactic velocity dispersions, M-bh approximat e to 10(8) M. x (sigma /200 km s(-1))(4), where sigma = root 2a(eff). This model also predicts the ratio muB of black hole mass to host mass: mu (B) a pproximate to 0.004(sigma /200 km s(-1)).