AGN-Driven Wind Feedback Model

• AGN-driven wind feedback models are theoretical frameworks that describe how energy and momentum from supermassive black holes regulate galaxy evolution.
• They employ energy-driven and momentum-driven regimes, using parameters like εf, v_w, and εr to simulate kinetic and thermal feedback in the interstellar medium.
• These models impact black hole growth, star formation quenching, and chemical enrichment, supported by X-ray, molecular, and radio observational diagnostics.

Active galactic nucleus (AGN)–driven wind feedback models are foundational to understanding the co-evolution of supermassive black holes and their host galaxies. These models describe the processes by which winds and outflows—launched from the vicinity of an accreting black hole—couple AGN energy and momentum to the surrounding interstellar medium (ISM), regulating star formation, black hole growth, and the structural and chemical evolution of galaxies.

1. Physical Foundations and Core Mechanisms

The core premise of AGN-driven wind feedback models is that the accretion of gas onto a supermassive black hole liberates substantial energy, a fraction of which is imparted to the host galaxy’s gas reservoir in the form of winds. The feedback mechanisms are categorized based on:

• The carrier of energy and momentum (thermal energy, kinetic energy/momentum, radiation),
• The mode of coupling (isotropic heating, directional velocity kicks, radiation pressure), and
• The scale and dynamical regime (Bondi/r_B, parsec scales, galactic scales).

Two archetypal regimes are established:

• Thermal feedback: Radiative energy is deposited as heat within neighboring gas, raising its temperature.
• Kinetic feedback: Energy is injected by imparting velocity kicks or momentum boosts to gas, simulating AGN-driven winds.

Subdividing kinetic feedback yields:

• Energy-driven winds (EDW): The injected wind’s kinetic energy matches the available AGN feedback (post-shock gas energy is retained, driving adiabatic expansion).
• Momentum-driven winds (MDW): The wind momentum matches the AGN radiation momentum (initial fast wind loses energy efficiently to cooling—typically via inverse Compton scattering—while preserving momentum).

The interplay between these regimes is governed by physical parameters such as the feedback efficiency ($\epsilon_f$), wind velocity ($v_w$), and the radiative efficiency of the black hole ($\epsilon_r$). The energy/momentum budget and the properties of the ISM (density, multi-phase structure, disk geometry) are critical in determining the feedback’s impact (Barai et al., 2013, Tombesi et al., 2015, King et al., 2015).

2. Parameterization and Implementation in Simulations

AGN wind feedback is implemented in simulations using physically based sub-grid models. The key parameterizations include:

Wind Mode	Mass Outflow Rate $\dot{M}_w$	Physical Basis
Thermal feedback	Not well defined; energy added to local gas as heat	Isotropic, energy
EDW	$$\dot{M}_w = \dfrac{2\epsilon_f\epsilon_r \dot{M}_{\rm BH} c^2}{v_w^2}$$	Energy conservation
MDW	$$\dot{M}_w = \dfrac{\epsilon_f\epsilon_r \dot{M}_{\rm BH} c}{v_w}$$	Momentum conservation

Here, $\dot{M}_{\rm BH}$ is the black hole accretion rate, typically prescribed by a modified Bondi–Hoyle formula (sometimes scaled to account for unresolved ISM structure). For power- and momentum-driven outflows, $\epsilon_f$ tunes the strength of the feedback and must be set to reproduce observed scaling relations, such as the $M_{\rm BH} - \sigma_*$ relation.

For kinetic feedback, the wind is generally imparted to stochastic subsets of gas particles within a kernel around the black hole, with choices of $v_w$ and $\epsilon_f$ dictating the mass loading and energetics. Wind velocities are explored in the range $v_w = 5,000$–$10,000$ km/s for sub-relativistic models, consistent with observed ultra-fast outflows (UFOs). For MDW, higher $\epsilon_f$ is often required to match observations, but this can lead to runaway black hole growth during mergers (Barai et al., 2013).

Numerical artifacts can affect feedback behavior. A notable advancement is the introduction of algorithms to prevent unphysical expansion of a gas "hole" around the black hole by monitoring and limiting the growth of the accretion kernel based on neighboring smoothing lengths, preserving physical removal of gas rather than numerical evacuation (Barai et al., 2013).

3. Impact on Galaxy Evolution and Scaling Relations

The consequences of AGN wind feedback manifest in multiple facets of galaxy evolution:

• Black hole growth regulation: By removing gas from the nucleus, kinetic winds self-limit accretion rates, enabling simulated black holes to obey the empirical $M_{\rm BH} - \sigma_*$ relation. The strongest effect is seen in kinetic/EDW models with tuned parameters, whereas pure thermal or MDW models may under- or over-regulate growth depending on context.
• Gas expulsion and quenching: Kinetic feedback efficiently ejects central gas, whose removal suppresses star formation (particularly in the nucleus), often by orders of magnitude in SFR. Morphological signatures include bipolar, intermittent jet-like outflows, central density depressions, and enhanced temperature at large radii, especially in isolated disk galaxies and galaxy mergers.
• Chemical enrichment: Kinetic models transport metals into the circumgalactic medium (CGM), flattening or inverting metallicity radial profiles (e.g. carbon abundance $Z_C$ at $20$–$100/h$ kpc), while thermal feedback has little effect. The CGM metallicity thus provides a robust diagnostic for distinguishing feedback prescriptions (Barai et al., 2013).

The transition between momentum- and energy-driven regimes, as theorized by King and collaborators (Pounds, 2013, King et al., 2015), is pivotal. Initially, inner wind shocks cool efficiently via inverse Compton, maintaining a momentum-driven phase with nearly constant gas velocity. Beyond a critical radius—typically $\sim$1 kpc—Compton cooling becomes inefficient, and the shocked wind becomes energy-conserving, leading to a rapid acceleration of the outflowing shell. This two-phase dynamic has been directly confirmed through spatially-resolved kinematical mapping (Marconcini et al., 31 Mar 2025).

4. Diagnostics and Observational Signatures

AGN wind feedback models are constrained and tested against multiwavelength diagnostics:

• X-ray spectra: Detection of highly ionized blue-shifted iron (FeXXV/FeXXVI) lines in luminous AGN with velocities $v \sim 0.1-0.2c$ are evidence of ultra-fast outflows, supporting wind models with significant kinetic energy (Pounds, 2013, Tombesi et al., 2015, King et al., 2015, Tombesi, 2016).
• Molecular outflows: Connection between fast (X-ray) winds and kpc-scale molecular outflows (e.g. detected in OH lines via Herschel) establishes the link between nuclear AGN power and galaxy-scale quenching. Observed momentum boosts often exceed $(L_{\rm AGN}/c)$, characteristic of energy-conserving outflows (Tombesi et al., 2015).
• CGM metallicity: Outflows populate the halo with metal-rich gas, yielding distinct metallicity gradients in kinetic feedback models—up to $10$–$1000$ times more carbon in the CGM than in thermal/no-AGN cases (Barai et al., 2013).
• Radio emission: Shocks induced by AGN-driven winds accelerate nonthermal electrons, producing synchrotron emission detectable in the radio band. Model predictions for radio luminosity ($\sim 10^{29}$ erg s$^{-1}$ Hz$^{-1}$) and evolving spectral indices match observations in both massive and dwarf ellipticals, including M32 (Xia et al., 25 Jul 2025).

Modern feedback models invoke spatially resolved, multi-phase kinematic modeling tools (e.g., MOKA3D) to recover the intrinsic velocity and acceleration structure of outflows and to separate disk rotation from wind-driven components (Marconcini et al., 31 Mar 2025).

5. Regimes of Feedback Efficiency and Limitations

The efficiency and character of AGN wind feedback are controlled by a combination of physical and numerical factors:

• Feedback efficiency scaling: For kinetic models, required $\epsilon_f$ increases as $v_w^2$ (EDW), so faster winds move less mass but deliver more energy per particle; they can more efficiently evacuate the nucleus and impact the CGM. In MDW, higher $\epsilon_f$ is needed to maintain a given outflow rate at lower $v_w$, but this can lead to excessive black hole growth during mergers (Barai et al., 2013).
• Merger and geometry dependence: Mergers boost central gas density, making AGN feedback more effective and altering the success of different wind models. The geometry of the gas reservoir—disk versus spheroidal—strongly affects outflow escape fractions and the directionality of the feedback (Hartwig et al., 2017). Outflows preferentially escape perpendicular to the disk where densities are lower, as confirmed in 2D/3D hydrodynamic simulations.
• Numerical artifacts: Artificial evacuation of the nucleus by kernel expansion can masquerade as physical feedback and must be mitigated by algorithmic checks (Barai et al., 2013).

Limitations include the rapid radiative cooling of thermally injected energy in dense, star-forming gas (which makes purely thermal feedback largely ineffective in multiphase ISM models), the dependence of subgrid prescriptions on resolution and kernel size, and the sensitivity of results to unresolved ISM physics.

6. Theoretical and Future Directions

AGN wind feedback remains a subject of active research, with key theoretical and computational needs including:

• Greater fidelity in modeling the transition from momentum- to energy-driven regimes, including the microphysics of shock cooling, Compton and free-free processes, and two-fluid (electron-ion) equilibration.
• Improved treatment of the ISM’s multiphase structure and the inclusion of realistic clumping, turbulence, magnetic fields, and radiative transfer.
• Enhanced spatial and spectral resolution in both simulations and observations to track the episodicity and duty cycle of AGN outflows, especially on sub-kiloparsec scales.
• Multi-probe approaches integrating X-ray, infrared, radio, and UV diagnostics to fully characterize the multi-phase, multi-scale impact of AGN winds on galaxy evolution.

As future observational facilities provide more sensitive mapping of outflows across the electromagnetic spectrum, and as simulation sophistication increases, the AGN-driven wind feedback model will continue to be refined, providing a physically motivated framework underlying the tight empirical correlations observed between supermassive black holes and their hosts.