AGN Feedback Models

Updated 6 December 2025

AGN feedback models are theoretical and numerical frameworks that describe the energy and momentum output from supermassive black holes, essential for regulating star formation and gas cooling.
These models combine radiative (quasar) and mechanical (radio) modes, employing methods like Bondi accretion and energy injection thresholds to reproduce key scaling relations.
Implemented in cosmological simulations, AGN feedback models successfully match observed baryon fractions, gas distributions, and cooling flows while highlighting challenges in energy coupling and resolution.

Active Galactic Nucleus (AGN) feedback models provide a comprehensive theoretical and numerical framework to describe the impact of energy and momentum released by accreting supermassive black holes (SMBHs) on their galactic and cluster-scale environments. The AGN feedback paradigm is now a central component in models of galaxy formation and evolution, addressing longstanding problems such as the cooling flow in clusters, suppression of star formation in massive galaxies, and the regulation of baryonic mass fractions relative to dark matter. The field encompasses a wide range of physical ingredients—accretion theory, multi-phase outflow and jet physics, hydrodynamics, cosmic-ray transport, and star formation—and is tested using both cosmological simulations and multi-wavelength observations.

1. Theoretical Foundations and Physical Prescriptions

AGN feedback is typically classified into two canonical operational modes: the "quasar (radiative) mode" and the "radio (mechanical/kinetic) mode" (Combes, 2014). The quasar mode dominates at high accretion rates ( $L/L_{\rm Edd}\gtrsim0.01$ ), driving winds and outflows that can unbind interstellar gas primarily via radiation pressure and energy-conserving shocks, with fundamental scaling relations (e.g., $M_{\rm BH}\propto\sigma^4$ ) emerging from an interplay of radiative momentum and gravity. The radio mode, operative at low specific accretion rates, involves the production of powerful relativistic jets and mechanical outflows, where energy is deposited into the hot, diffuse medium via inflation of bubbles, shocks, turbulence, and non-thermal particles (Hlavacek-Larrondo et al., 2022, Combes, 2014).

Key physical ingredients in modern AGN feedback models include:

Black-hole accretion rates calculated using resolved (or subgrid) Bondi–Hoyle–Lyttleton (BHL), torque-limited, or viscous disk prescriptions, sometimes decomposed into cold and hot-phase contributions (Steinborn et al., 2014, Teyssier et al., 2010).
Accretion rate capping at the Eddington limit,

$\dot M_{\rm Edd} = \frac{4\pi G M_{\rm BH} m_p}{\epsilon_r \sigma_T c},$

with radiative efficiency $\epsilon_r\sim0.1$ (but possibly mass- or spin-dependent).

Dual feedback power channels: radiative luminosity (quasar mode) and mechanical (kinetic/outflow) power (radio mode), assigned in a continuous or switchable fashion depending on the Eddington ratio or accretion regime (Steinborn et al., 2014, Yao et al., 2020).
Subgrid energy and momentum injection into simulation elements, often as stochastic thermal dumps or resolved kinetic kicks, with the coupling efficiency tuned to empirical scaling relations (e.g., $M_{\rm BH}$ – $\sigma$ , AGN-driven mass outflows $>10\,L_{\rm AGN}/c$ ) (Teyssier et al., 2010, Kondapally et al., 2023).

Table: Representative AGN Feedback Model Features

Model/Framework	Accretion Law(s)	Feedback Channel(s)	Transition Criteria
Booth & Schaye (2009)	Boosted Bondi (cold hot)	Thermal (energy dump)	None (continuous)
Steinborn et al. (2015)	Cold/hot Bondi	Mech. & Rad., continuous	$f_{\rm Edd} \sim 0.05$
FEGA25 (Contini et al.)	Croton et al. analytic	Neg., pos., ejection	Energy and hot gas reviews
TNG/SIMBA/EAGLE	Torque-limited/Bondi	Kinetic, thermal, X-ray	Mass/acc. ratio dependent

2. Numerical Implementation in Cosmological Simulations

Cosmological and zoom-in hydrodynamic codes (e.g., RAMSES, AREPO, GADGET, SIMBA, MACER3D) employ AGN feedback subgrid modules that connect the unresolved physics of SMBH accretion and energy deposition with the resolved gas and star formation on kiloparsec to megaparsec scales (Teyssier et al., 2010, Zhang et al., 8 Apr 2025). Implementations differ in resolution, feedback coupling methodology, and the treatment of multiphase gas.

In AMR codes (e.g., RAMSES), the Booth & Schaye (2009) model calculates accretion using resolved gas density, sound speed, and velocity within a fixed "sink" radius around the SMBH, injecting accumulated AGN energy thermally once a critical threshold is met (e.g., energy to heat sink gas to $T_{\min}=10^7$ K) (Teyssier et al., 2010).
In SPH/moving-mesh codes, models may inject mechanical energy as momentum kicks, thermalize energy stochastically, or combine modes based on local gas properties and accretion rates (Steinborn et al., 2014, Khaire et al., 2023).
More sophisticated treatments (e.g., MACER3D) explicitly resolve the Bondi radius, incorporate multi-mode (hot/cold/super-Eddington) accretion solutions, and inject winds and radiation with angular dependence, linking accretion flow physics directly to the simulated ISM and CGM (Zhang et al., 8 Apr 2025, Yao et al., 2020).
Semi-analytic models (SAMs), such as FEGA25, encode analytic prescriptions for black hole growth, radio-mode heating, positive feedback, and ejection of hot gas based on halo and BH properties, with parameters calibrated to observed scaling relations and baryon cycle measurements (Contini et al., 26 Feb 2025, Contini et al., 14 Jul 2025).

Crucially, the methodology—mass and energy injection thresholds, coupling efficiencies, feedback region size, and transition between feedback modes—strongly influences the simulation’s ability to reproduce observed mass functions, star-formation rates, and gas fractions.

3. Observational Constraints and Empirical Calibration

Observational validation of AGN feedback models is multidimensional. Key diagnostics include:

Stellar Mass and Gas Fractions: Models with AGN feedback can suppress the stellar mass fraction in the central galaxies of clusters from $f_*\sim8$ \% (supernovae only) to $f_*\sim1$ –2\%, matching the $2$–$3$\% observed in M87 and similar systems (Teyssier et al., 2010).
Baryon Displacement and Missing Baryons: AGN-driven shocks and winds can expel hot gas beyond the virial radius, reproducing $\sim$ 10% baryon deficits seen in clusters (observed $f_{\rm bar}\sim0.13$ inside $R_{200c}$ ), compared to a cosmic mean of $0.15$ (Teyssier et al., 2010).
Total Mass Profiles: AGN feedback can turn the expected adiabatic contraction of dark matter (expected without feedback) into mild expansion, better matching real cluster potentials (Teyssier et al., 2010).
Sunyaev-Zel'dovich Effect: The integrated thermal pressure signal around galaxies and clusters (measured by ACT, SPT) provides direct evidence for or against strong AGN-induced heating. Some simulations with strong feedback overpredict the observed tSZ signal; others reproduce it at high redshift but overshoot at low $z$ (Spacek et al., 2017, Grayson et al., 2023).
Radio AGN Demographics: The fraction of radio-loud AGN as a function of stellar mass and sSFR provides strong constraints; current simulations tuned to match the stellar mass function often fail to reproduce the sharp mass and weak sSFR dependence in the observed radio AGN fraction, implying missing or miscalibrated feedback triggers (Suresh et al., 6 Aug 2025).
X-ray Cavities and Shock Power: Bubble/cavity energetics and scaling with cooling luminosity are directly compared to model predictions, yielding energetic consistency only if AGN mechanical power is sufficient and appropriately coupled (Hlavacek-Larrondo et al., 2022).

4. Advances: Multi-mode and Non-Thermal Feedback Prescriptions

Recent models have introduced multi-channel feedback to address observational and theoretical challenges.

Positive Feedback: The possibility of AGN-driven triggering of star formation via outflow-induced compression has been incorporated in some SAMs and hydro codes (FEGA25, FEGA), with contributions to stellar mass fractions $\lesssim$ 10\%, preferentially active at high redshift or low-mass galaxies (Contini et al., 26 Feb 2025, Contini et al., 17 May 2024). Phenomenological forms for positive feedback are activated when the negative mode leaves residual cooling.
Hot Gas Ejection: To resolve the persistent overprediction of hot gas in massive halos, models now include channels that directly eject hot gas beyond the virial radius (e.g., AGNeject1, AGNeject2 in FEGA25). AGNeject2, which activates only upon surplus energy beyond cooling balance, can produce the observed "U-shaped" cavity in baryon fraction versus halo mass at $z=0$ (Contini et al., 14 Jul 2025).
Cosmic-ray Feedback: Some cluster models and analytic treatments recognize cosmic-ray-driven heating, wherein CRs propagate away from jets, couple via Alfvénic streaming to the ICM, and deliver volumetric heating rates

$\mathcal{H}_{\rm CR}(r) = - v_A \cdot \nabla P_{\rm CR}(r),$

balancing radiative cooling nearly radius-by-radius (Pfrommer, 2013). This mechanism naturally establishes temperature floors and multiphase core structures.

Optimized/Bang–Bang Feedback: Control-theory-inspired prescriptions minimize total energy by balancing heating and cooling with intermittent AGN bursts rather than continuous feedback. The predicted duty cycles and event energies scale with system potential, explaining stronger, more violent feedback in low-mass galaxies and more continuous heating in clusters (Pope, 2011).

5. Impact on Galaxy, Halo, and Cluster Evolution

The principal effect of AGN feedback models is the self-regulated regulation of baryon cooling, star formation, and black hole growth:

Suppression of Overcooling and Star Formation: Feedback halts runaway cooling flows in massive galaxies and clusters, maintaining the central galaxy as a low–star-formation, massive elliptical, and preventing excessive BCG masses (Hlavacek-Larrondo et al., 2022, Teyssier et al., 2010).
Redistribution of Baryons: Models incorporating both negative and ejection modes reproduce observed baryon and hot gas fractions over cosmic time, with SN-driven ejection dominating in halos $\log M_{200}\lesssim12$ , and AGN-driven ejection taking over at higher masses (Contini et al., 26 Feb 2025, Contini et al., 14 Jul 2025).
Consistency with Observed Scaling Relations: Refined feedback models are able to recover the $M_{\rm BH}$ – $M_*$ , $M_{\rm BH}$ – $\sigma$ , and stellar-to-halo mass relations, and address discrepancies in the high-mass end of the galaxy stellar mass function (Steinborn et al., 2014, Contini et al., 26 Feb 2025).

6. Challenges, Controversies, and Future Directions

Despite empirical success, AGN feedback modeling faces persistent uncertainties:

Degeneracy and Calibration: Many observables (e.g., Ly $\alpha$ forest statistics, tSZ signals) are degenerate with respect to multiple physical parameters (e.g., cool baryon fraction and photoionization rates), limiting their ability to uniquely constrain feedback models without independent measurements (Khaire et al., 2023).
Model Disparities: Different simulation suites (EAGLE, SIMBA, TNG100) deploy distinct feedback triggers and energy-coupling schemes (thermal vs kinetic, continuous vs bursty), leading to qualitatively divergent predictions for AGN demographic statistics. None simultaneously reproduces the sharply rising radio-AGN fraction with $M_*$ and its weak dependence on sSFR (Suresh et al., 6 Aug 2025).
Energy and Momentum Coupling: The physical mechanism(s) by which AGN energy couples to multiphase ISM and CGM, and the interplay of jets, cosmic rays, turbulence, and thermal instabilities, remain incompletely understood. The transition between accretion and feedback modes, and the true duty cycle of radio-AGN episodes, are unresolved.
Numerical Limitations: Resolution dependence (e.g., BCG stellar mass converges slowly with cell size in AMR; strong feedback may push gas out too efficiently or at too small a scale) remains intrinsic to all current implementations (Teyssier et al., 2010, Yao et al., 2020).

The field is rapidly advancing with the introduction of physically motivated ejection, positive feedback, and multi-phase coupling, but precise, quantitative comparison to spatially resolved, multi-wavelength observations remains critical for further progress.

7. Representative Equations and Model Components

The core of most AGN feedback models can be summarized as follows:

Bondi-Hoyle Accretion:

$\dot M_{\rm BH} = \alpha_{\rm boost}\frac{4\pi G^2 M_{\rm BH}^2\,\rho}{(c_s^2+u^2)^{3/2}}$

Eddington Cap:

$\dot M_{\rm acc} = \min(\dot M_{\rm BH}, \dot M_{\rm Edd})$

AGN Energy Injection:

$\Delta E = \epsilon_c\,\epsilon_r\,\dot M_{\rm acc}c^2\,\Delta t$

Thermal/Mechanical Feedback Threshold:

$E_{\rm AGN} > \tfrac{3}{2} m_{\rm gas} k_B T_{\min} \quad\Longrightarrow\quad \mathrm{inject}\ E_{\rm AGN}$

Radio-Mode AGN Ejection in SAMs:

$M_{\rm ejected} = \frac{\delta M_{\rm BH}}{M_{\rm BH}} \frac{M_{\rm hot}}{10^8\,M_\odot/h} \left[1-\frac{V_{200}}{V_{\rm scale}}\right]_+$

CR Feedback Heating:

$\mathcal{H}_{\rm CR}(r) = - v_A \cdot \nabla P_{\rm CR}(r)$

Optimized Feedback Control:

$\mathrm{Duty~cycle~}\delta = \frac{1}{k_1},\quad k_1 = \frac{2\phi\eta\mu m_pc^2}{5k_B T}$

Each term above is calibrated and interpreted in light of empirical scaling relations, ensuring that AGN feedback models produce physically plausible mass assembly and gas/entropy/temperature profiles for galaxies and clusters.

References: