Simulations of momentum feedback by black hole winds

The observed super-massive black hole (SMBH) mass -- galaxy velocity dispersion ($M_{\rm bh} - σ$) correlation may be established when winds/outflows from the SMBH drive gas out of the potential wells of classical bulges. Here we present numerical simulations of this process in a static isothermal potential. Simple spherically symmetric models of SMBH feedback at the Eddington luminosity can successfully explain the $M_{\rm bh} - σ$ and nuclear cluster mass $M_{\rm NC}-σ$ correlations, as well as why larger bulges host SMBHs while smaller ones host nuclear star clusters. However these models do not specify how SMBHs feed on infalling gas whilst simultaneously producing feedback that drives gas out of the galaxy. More complex models with rotation and/or anisotropic feedback allow SMBHs to feed via a disc or regions not exposed to SMBH winds, but in these more realistic cases it is not clear why a robust $M_{\rm bh} - σ$ relation should be established. In fact, some of the model predictions contradict observations. For example, an isotropic SMBH wind impacting on a disc (rather than a shell) of aspect ratio $H/R \ll 1$ requires the SMBH mass to be larger by a factor $\sim R/H$, which is opposite to what is observed. We conclude that understanding how a SMBH feeds is as important a piece of the puzzle as understanding how its feedback affects its host galaxy. Finally, we note that in aspherical cases the SMBH outflows induce differential motions in the bulge. This may pump turbulence that is known to hinder star formation in star forming regions. SMBH feedback thus may not only drive gas out of the bulge but also reduce the fraction of gas turned into stars.

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