Observable consequences of kinetic and thermal AGN feedback in elliptical galaxies and galaxy clusters

We have constructed an analytical model of AGN feedback and studied its implications for elliptical galaxies and galaxy clusters. The results show that momentum injection above a critical value will eject material from low mass elliptical galaxies, and leads to an X-ray luminosity, $L_{\rm X}$, that is $\propto$ $\sigma^{8-10}$, depending on the AGN fuelling mechanism, where $\sigma$ is the velocity dispersion of the hot gas. This result agrees well with both observations and semi-analytic models. In more massive ellipticals and clusters, AGN outflows quickly become buoyancy-dominated. This necessarily means that heating by a central cluster AGN redistributes the intracluster medium (ICM) such that the mass of hot gas, within the cooling radius, should be $ \propto L_{\rm X}(<r_{\rm cool})/[g(r_{\rm cool})\sigma]$, where $g(r_{\rm cool})$ is the gravitational acceleration at the cooling radius. This prediction is confirmed using observations of seven clusters. The same mechanism also defines a critical ICM cooling time of $\sim 0.5$ Gyr, which is in reasonable agreement with recent observations showing that star formation and AGN activity are triggered below a universal cooling time threshold.

💡 Research Summary

The authors present a concise yet powerful analytical framework for active‑galactic‑nucleus (AGN) feedback and explore its observable consequences in both elliptical galaxies and galaxy clusters. The model distinguishes two feedback channels: kinetic (momentum‑driven) and thermal (energy‑driven) outflows, each interacting with the surrounding hot gas under the influence of the host’s gravitational potential. By coupling the injected momentum or energy to the gas density and velocity dispersion (σ), the authors derive scaling relations that can be directly compared with X‑ray observations.

In low‑mass ellipticals (σ ≲ 200 km s⁻¹), the kinetic channel dominates. When the AGN supplies a momentum flux exceeding a critical value (ṗ > ṗ_crit), the outflow overcomes the galaxy’s binding force and ejects a substantial fraction of the hot interstellar medium. The remaining gas, confined to the central regions, radiates in X‑rays, leading to a steep luminosity‑velocity dispersion relation: L_X ∝ σ⁸–¹⁰. The exponent depends on the fueling mode—cooling‑flow‑driven accretion yields a shallower slope (≈ 8), whereas direct Bondi‑type accretion produces a steeper one (≈ 10). This prediction matches the observed L_X–σ trends for dwarf and intermediate‑mass ellipticals and improves upon earlier semi‑analytic treatments that lacked a clear physical basis for the exponent.

In massive ellipticals and clusters (σ ≳ 250 km s⁻¹), the kinetic outflow quickly transitions to a buoyancy‑dominated regime. The injected energy inflates low‑density bubbles that rise through the intracluster medium (ICM), redistributing heat and mass without directly expelling gas. By balancing the buoyant work against radiative cooling within the cooling radius (r_cool), the authors derive a novel scaling:

M_gas(<r_cool) ∝ L_X(<r_cool) /