Momentum-driven feedback and the M-\sigma relation in non-isothermal galaxies

TL;DR

This paper models the velocity fields of momentum-driven shells from black hole or star cluster feedback in non-isothermal galaxies, revealing how the critical black hole mass for feedback-driven escape scales with halo properties.

Contribution

It introduces the first model of momentum-driven feedback in non-isothermal halos with peaked circular-speed profiles, deriving the critical CMO mass for shell escape.

Findings

Critical CMO mass scales as the fourth power of peak circular speed.

The model applies to real galaxies with large halo masses.

Feedback can drive shells to escape in massive, non-isothermal halos.

Abstract

We solve for the velocity fields of momentum-conserving supershells driven by feedback from supermassive black holes or nuclear star clusters (central massive objects: CMOs). We treat, for the first time, the case of CMOs embedded in gaseous protogalaxies with non-isothermal dark matter haloes having peaked circular-speed profiles. We find the CMO mass that is sufficient to drive any shell to escape any such halo. In the limit of large halo mass, relevant to real galaxies, this critical CMO mass depends only on the peak circular speed in the halo, scaling as M_crit \propto V_c,pk^4.