Past exam of the relativistic Astrophysics and Cosmology course of the University of Cambridge / 2013 / Paper 1 / 3 / d / Solution

accretion onto a massive black hole releases luminosity $L\simeq \eta \dot{M}{c}^2$. Even a small coupling of this energy to surrounding gas can matter because a galactic binding energy is only of order $M_{\mathrm{gas}}{\sigma }^2$, with stellar velocity dispersion $\sigma \ll c$. active-galactic-nucleus feedback means that the energy or momentum changes the gas supply, cooling or star formation, potentially regulating further accretion. Large energy availability alone does not establish efficient coupling.

In a radiatively efficient bright nucleus, radiation pressure and winds can push on dusty or ionized gas. Outflows can remove fuel or shock-heat it; the outcome depends on cooling, covering factor, clumping and whether the flow escapes. In a mechanically dominated state, relativistic jets inflate radio cavities in a hot halo or galaxy cluster. Their expansion, shocks, sound waves and subsequent motions can distribute energy and suppress a cooling flow. The two descriptions identify useful channels rather than a universal sharp division between all nuclei.

An approximately pressure-balanced cavity containing a relativistic fluid has enthalpyX-ray pressure estimates, cavity volume and buoyant or sound-crossing ages permit comparison with radiative cooling losses. Radio images check the jet association; X-ray fronts and ripples help locate transferred energy. Deep Chandra observations of Perseus reveal such structures and motivate mechanical heating of the cooling atmosphere.^[ref]

Projection, nonrelativistic cavity contents, pressure gradients, uncertain ages and intermittent duty cycles affect the power estimate. Injected cavity energy need not all dissipate where cooling occurs. A successful negative feedback loop requires that falling gas increases accretion, heating then reduces cooling or inflow, and the delay does not destroy regulation. This can explain reduced cooling and the shortage of excessively massive star-forming galaxies; correlations between black-hole mass and bulge properties are supporting context rather than standalone proof of causation. The key comparison is coupled heating versus local cooling and binding, including where and when energy is deposited.