The massive black hole-velocity dispersion relation and the halo baryon fraction: a case for positive AGN feedback

Force balance considerations put a limit on the rate of AGN radiation momentum output, $L/c$, capable of driving galactic superwinds and reproducing the observed $\mbh -\sigma $ relation between black hole mass and spheroid velocity dispersion. We show that black holes cannot supply enough momentum in radiation to drive the gas out by pressure alone. Energy-driven winds give a $\mbh -\sigma $ scaling favoured by a recent analysis but also fall short energetically once cooling is incorporated. We propose that outflow-triggering of star formation by enhancing the intercloud medium turbulent pressure and squeezing clouds can supply the necessary boost, and suggest possible tests of this hypothesis. Our hypothesis simultaneously can account for the observed halo baryon fraction.