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

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