Preventive AGN Feedback Mechanism

• Preventive AGN feedback is a self-regulating process that injects intermittent energy bursts to suppress radiative cooling and star formation.
• It operates via multiple modes, including quasar and radio jet activities, guided by optimal control and thermodynamic principles.
• Observational signatures such as X-ray cavities, entropy profiles, and duty cycles support its role in maintaining thermal equilibrium in galaxy clusters.

Active Galactic Nuclei (AGN) are central engines powered by accretion onto supermassive black holes (SMBHs) that exert significant feedback on their host galaxies and galaxy clusters. The preventive feedback mechanism from AGN refers to energy and momentum input that inhibits or regulates radiative cooling of hot gas, suppressing star formation and regulating SMBH growth. This feedback operates through discrete, energetically efficient heating events, outflows, jets, and the redistribution of entropy, functioning as a control system to maintain thermal equilibrium and prevent runaway cooling. Preventive feedback is now regarded as a fundamental process in maintaining observed galaxy and cluster properties.

1. Control-Theoretic and Thermodynamic Formulations

Preventive AGN feedback is mathematically formulated as a feedback loop that seeks to minimize the total energy output (the sum of energy radiated by gas and the energy injected by the AGN), thereby aligning gas heating with radiative losses while suppressing excess black hole growth (Pope, 2011).

The key relation is:

$H(t) = \alpha(t) k_{1} L_X(t)$

where $H(t)$ is the heating rate, $L_X(t)$ is the instantaneous X-ray luminosity (tracing cooling), $k_1$ is a feedback strength parameter, and $\alpha(t)$ is a binary control parameter (AGN on/off). Under optimal control, the feedback switches discretely between "on" and "off" (bang-bang control) to minimize total energy:

$E_{out} = E_{cool} + E_{heat}$

The switching timescale is set by:

$t^* \approx \frac{\tau \ln(2)}{k_1 - 1}$

$$\delta \equiv \frac{t^*}{t_1 - t_0} \approx \frac{1}{k_1}$$

where $\tau$ is the cooling timescale and $\delta$ is the duty cycle of AGN activity. This structure produces intermittent, powerful bursts rather than steady heating—a necessity for minimizing both gas cooling and SMBH accretion.

Thermodynamically, internally-driven feedback is favored whenever the change in the system's Gibbs free energy (GFE) would otherwise increase (i.e., when gravitational compression and gas capture by stars/SMBHs would raise the internal energy more than mass dropout cools it down). The transition between heating and cooling events is set by the condition $(v / c_s)^2 > 1$, where $v$ encodes effective energetic input and $c_s$ is the local sound speed (Pope, 2012).

2. Physical Mechanisms: Modes and Triggering

AGN preventive feedback is realized through multiple modes:

• Quasar (thermal) mode: At high accretion rates ($\chi \gtrsim 10^{-2}$), the AGN injects energy as thermal/radiative output, raising gas temperatures and pressurizing local environments. Triggering occurs when accretion rates approach the Eddington limit, primarily affecting the central cold gas reservoir (Dubois et al., 2011, Dubois et al., 2011).
• Radio (jet) mode: At low accretion rates ($\chi \lesssim 10^{-2}$), the AGN launches kinetic/bipolar jets that inflate radio bubbles or drive shocks into the intra-cluster/group medium. This injects energy at larger radii, excites turbulence, and redistributes entropy (Dubois et al., 2011, Nulsen et al., 2013). Jet/kinetic coupling is crucial for distributing feedback energy over extended regions, enabling long-term suppression of cooling in atmospheres with deep potential wells.
• Thermal instability triggering: Radiatively cooling gas in galaxy/cluster centers may become gravitationally unstable, leading to periodic gravitational collapse and fueling outbursts. The feedback is thus linked to the global properties of the halo's X-ray cooling flow (e.g., through the scaling $\delta \propto L_X / \sigma_*^3$, where $\sigma_*$ is stellar velocity dispersion) (Pope et al., 2011). Uplifted low-entropy gas by radio bubbles may condense when its cooling time falls below the infall time ($t_c / t_I < 1$), stimulating small-scale star formation and a recurrent feedback loop (McNamara et al., 2016).
• Subgrid modeling and anisotropic energy injection: Numerical simulations show that kinetic, non-spherically symmetric energy input (e.g., in cones) yields more realistic, energy-retentive, and multiphase outflows than pure thermal, isotropic schemes (Zubovas et al., 2015, Meece et al., 2016). Even modest kinetic fractions prevent gas accumulation near the SMBH and enhance feedback efficacy.

3. Impact on Star Formation, Gas Dynamics, and Scaling Relations

By suppressing cooling and removing or heating cold gas, preventive feedback regulates both star formation rates (SFR) and SMBH growth. In low-mass systems (elliptical galaxies), powerful, intermittent feedback events can be sufficient to expel hot gas entirely, accounting for observed steepening of the $L_X–T$ relation at $kT \lesssim 1$ keV (Pope, 2011). In more massive clusters, the gravitational potential traps reheated gas, but the same process maintains high core entropy and suppresses central SFR.

In cosmological and idealized simulations, successful preventive feedback reproduces the observed stellar mass–SMBH mass ($M_{BH}–M_{s}$), and star formation suppression, mitigates the overcooling problem, and produces realistic entropy and gas fraction profiles in groups and clusters (Dubois et al., 2011, Dubois et al., 2011, Chen et al., 18 Dec 2024). The emergence of a correlation between AGN duty cycle and host galaxy mass or velocity dispersion quantifies the interplay between feedback and cooling. Tasks such as ejection of gas beyond the virial radius—crucial to matching observed gas fractions—are achieved only when AGN feedback is sufficiently strong to perform hot gas ejection as well as quenching (Contini et al., 26 Feb 2025).

4. Observational Diagnostics and Theoretical Constraints

Classic signatures of preventive AGN feedback—across multiple wavelengths—include:

• X-ray cavities and shocks: Radio-mode AGN create bubbles evident as depressions in X-ray surface brightness, with surrounding weak shocks and edges tracking energy dissipation (Eckert et al., 2021, Vazza et al., 2012, Nulsen et al., 2013). The work done inflating these cavities ($H = 4pV$ for relativistic gas) provides a quantitative energy budget.
• Entropy and cooling time profiles: Effective preventive feedback drives core entropies and cooling times to elevated values ($S \gtrsim 30–1000~\mathrm{keV}~\mathrm{cm}^2$), suppressing cooling flows (Eckert et al., 16 Jun 2025, Chen et al., 18 Dec 2024). Observed entropy profiles and the radius at which cooling time exceeds the Hubble time are direct constraints on past and ongoing AGN heating.
• Suppressed and regulated star formation: Host galaxies of clusters and groups subject to strong preventive feedback exhibit old, passively evolving stellar populations, often with SFR consistent with quenching over several Gyr (Eckert et al., 16 Jun 2025).
• Self-regulated energy balance: In well-regulated systems, the time-averaged AGN energy injection matches the radiative cooling losses ($$\langle \dot{E}_{\rm feedback} \rangle \approx \langle L_X \rangle$$), resulting in oscillatory or steady-state behavior reminiscent of optimal control solutions (Pope, 2011, Chen et al., 18 Dec 2024).
• Duty cycle and intermittency: Observations and models agree that AGN feedback is intermittent, with outburst durations and duty cycles linked to system mass and the depth of the potential well (Pope, 2011, Pope et al., 2011). The distribution of cavity ages and duty cycles is consistent with predictive scaling laws.

5. Special Regimes: Fossil Groups, Mergers, and Disk Environments

In fossil galaxy groups such as SDSSTG 4436, giant AGN outbursts can exceed the binding energy of the IGrM and permanently lift the entropy above the self-similar value, leading to a cessation of self-regulated cooling/heating cycles and the long-term quenching of star formation (Eckert et al., 16 Jun 2025).

During cluster mergers, preventive AGN feedback may play different roles depending on the merger geometry and mass ratio. In minor mergers, AGN feedback is essential for preserving the cool core against overcooling. In major, off-axis mergers, merger-driven mixing and AGN heating combine, occasionally “overheating” the core beyond the recovery of a classical cool core state (Chen et al., 18 Dec 2024).

Within AGN accretion disks, feedback-dominated accretion flows (FDAFs) can prevent runaway fragmentation by nonlocally distributing heating from embedded compact objects, resulting in steady-state/high-$Q_T$ disks with suppressed in situ star formation. This self-regulation connects preventive feedback and gravitational-wave source formation in AGN disks (Gilbaum et al., 2021).

6. Positive Feedback, Model Extensions, and Limitations

While canonical preventive feedback is associated with negative regulation of cooling and SFR, several works note the existence of positive AGN feedback: under certain conditions, AGN-driven shocks and turbulence can trigger star formation by compressing molecular gas, especially during powerful jet activity (Zinn et al., 2013, Contini et al., 26 Feb 2025). Semi-analytic models thus now often include multiple AGN feedback modes—negative (preventive), positive (star-formation triggering), and hot gas ejection—each influencing galaxy evolution at different stages (Contini et al., 26 Feb 2025). The relative significance of each mode depends on the black hole mass, system mass, redshift, and accretion/feedback efficiency.

The precise coupling efficiency, intermittency, anisotropy, and multi-phase treatment in subgrid feedback models remain active areas of uncertainty and model development. Simulations demonstrate that kinetic feedback can prevent AGN from being “smothered” by local radiative losses, but the details of delivery (e.g., jet precession, spatial resolution) are critical (Zubovas et al., 2015, Meece et al., 2016). Observationally distinguishing rapid, catastrophic feedback episodes from slower, self-regulating feedback loops is a challenge that guides the evolution of feedback prescriptions in cosmological modeling.

7. Broader Implications for Galaxy and Cluster Evolution

Preventive AGN feedback underpins the regulation of the baryon cycle on galactic and cluster mass scales. By preventing overcooling, it maintains the observed stellar mass function, produces the observed diversity in cool-core versus non–cool-core cluster properties, and explains the sharp dichotomy in entropy and SFR profiles (Chen et al., 18 Dec 2024, Eckert et al., 16 Jun 2025). In group environments, where AGN energy injection can rival or exceed the gas binding energy, preventive feedback is exceptionally effective and can break the feedback loop entirely after powerful outbursts (Eckert et al., 16 Jun 2025, Eckert et al., 2021).

This self-regulated, often intermittent, feedback process is directly connected to several key observables—star formation histories, hot gas fractions, SMBH–host scaling relations, entropy and cooling time profiles, and the structural morphology of galaxies. Its inclusion in theoretical and numerical models is mandatory for reproducing the observed properties of galaxies, groups, and clusters across cosmic time.