A theoretical model for the Mbh-σ relation for supermassive black holes in galaxies

We construct a model for black hole formation in galactic bulges. The initial state is a slowly rotating isothermal sphere, with an effective transport speed a(eff) and rotation rate Omega. The black hole mass is determined when the centrifugal radius of the collapse flow exceeds the capture radius of the central black hole. This model reproduces the observed correlation between black hole masses and galactic velocity dispersions, M-bh approximate 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) approximate to 0.004(sigma /200 km s(-1)).