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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.

Without feedback, efficiently cooling gas would turn into stars too readily. Young stars return radiation, winds and supernova energy and momentum to their surroundings. This can heat gas, disrupt dense clouds and drive outflows, with the strongest fractional effect in shallow potential wells. The outflow mass-loading factor ${\eta }_w={\dot{M}}_{\mathrm{out}}/{\dot{M}}_{\ast }$ is useful, but its dependence on escape speed differs between energy-limited and momentum-limited models. Some expelled gas later recycles; feedback also transports metals and changes subsequent cooling.

active-galactic-nucleus feedback is important in massive galaxies and hot haloes. Radiative or mechanical power from black-hole accretion can suppress the supply of cold gas. Collimated jets inflate radio/X-ray cavities, while broader winds can carry significant momentum and kinetic energy. For a relativistic cavity fluid with adiabatic index $4/3$, its enthalpy is approximately $4pV$, so $4pV/t_{\mathrm{age}}$ estimates mechanical power. Comparing it with the gas cooling luminosity tests whether that energy budget is sufficient, rather than merely showing that a radio source is present.

Deep Chandra observations of Perseus resolved bubbles, a density jump and weak surface-brightness ripples consistent with repeated mechanical disturbance of the intracluster gas. Their interpretation as heating requires a dissipation mechanism and a coupling history, not just a large instantaneous power.^[ref]

Observed outflow geometry, filling factors, cavity ages and cooling corrections create substantial uncertainties. Feedback can also compress gas and locally promote star formation. Simulations must track radiative losses and the scale on which energy or momentum couples: depositing unresolved thermal energy is not automatically equivalent to driving a resolved wind. A successful model should explain stellar masses, gas fractions, metallicity and circumgalactic or intracluster thermodynamics together.