Kinetic AGN Feedback

• Kinetic AGN feedback is the process by which active galactic nuclei transfer mechanical energy via jets and outflows to regulate the gas cooling and star formation in galaxies.
• It relies on empirical relations linking radio luminosity and kinetic power, with notable effects including shock heating, cavity inflation, and turbulence in the ISM/ICM.
• Simulations incorporating kinetic feedback validate that energy injection from AGN jets sustains thermal equilibrium and modulates galaxy evolution over cosmic time.

Kinetic AGN feedback refers to the transfer of mechanical energy and momentum from active galactic nuclei (AGN) to their galactic and extragalactic environments, predominantly via collimated jets and outflows. This process regulates the thermodynamic state, baryon cycling, and star formation history of galaxies and clusters over cosmic time. Unlike radiative (quasar-mode) feedback—which involves photon-pressure or fast radiatively driven winds at high Eddington ratios—kinetic feedback is typically associated with lower accretion rates and is characterized by the injection of mechanical energy into the surrounding medium, resulting in large-scale outflows, shock heating, turbulence, and suppression (or, under some circumstances, triggering) of gas condensation and star formation.

1. Theoretical Formalism and Empirical Characterization

Kinetic feedback is quantitatively described through statistical and physical parameters that link accretion phenomena to observable outflow and jet properties. A fundamental aspect is the relationship between accretion rate, radiative output, radio emission, and kinetic jet power. The mechanical (kinetic) output of an AGN is often parameterized as

$$L_{\mathrm{K}} = \epsilon_{\mathrm{kin}} \dot{M}_{\mathrm{acc}} c^2$$

where $L_{\mathrm{K}}$ is the kinetic luminosity, $\epsilon_{\mathrm{kin}}$ is the kinetic efficiency, $\dot{M}_{\mathrm{acc}}$ is the accretion rate, and $c$ is the speed of light. Empirical mapping of radio luminosity to jet kinetic power is implemented via scaling relations, calibrated using observations of X-ray cavity power and radio lobes:

Regime	Relation	Source
High-luminosity	$$L_K = 1.4 \times 10^{37} [L_{1.4}/(10^{25})]^{0.85} ~\mathrm{W}$$	Willott et al. (1999)
Low-luminosity	$$L_K = 1.2 \times 10^{37} [L_{1.4}/(10^{25})]^{0.40} ~\mathrm{W}$$	Best et al. (2006)

A critical contribution is the measurement of the full probability distribution $P(R_x | L_X, z)$ of the radio-to-X-ray luminosity ratio $$R_x = \log[ (\nu L_\nu (1.4\,\mathrm{GHz})) / L_X(2-10\,\mathrm{keV}) ]$$, parameterized as a skewed, asymmetric function of X-ray luminosity and redshift. High values of $R_x$ are more probable at lower $L_X$ and (possibly) higher $z$. This distribution, integrated with the X-ray luminosity function, yields a self-consistent radio luminosity function and, by further conversion, a kinetic luminosity function and integrated energy density (Franca et al., 2010).

2. Physical Mechanisms of Energy Injection

Mechanical (kinetic) feedback operates primarily via AGN jets and winds, with their energy transfer mediated through:

• Jets and Cavities: Radio jets inject energy into the ISM/ICM, inflating bubbles and cavities observed as X-ray deficits coincident with radio lobes. The enthalpy of these cavities is given by $E_{\mathrm{cav}} \sim 4PV$, where $P$ is the ambient pressure and $V$ the cavity volume (Fabian, 2012, Morganti, 2017).
• Outflows (Winds): AGNs drive multiphase outflows spanning ionized, atomic, and molecular gas. Kinetic luminosity is quantified as $\dot{E}_k = (1/2) \dot{M} v^2$, with $\dot{M}$ the mass outflow rate and $v$ the velocity. Outflows at $R \gtrsim 100$ pc with sufficient kinetic luminosities ($\gtrsim 0.5\%~L_{\mathrm{Edd}}$) have been robustly measured to impact galactic-scale evolution (Miller et al., 2020, Laha et al., 2020).

Kinetic feedback is further characterized by the fraction of accreted mass energy channeled to the jets (the “kinetic efficiency”), empirically found to be $\epsilon_{\mathrm{kin}} \approx 5 \times 10^{-3}$, with evidence for higher values at low redshift (Franca et al., 2010).

3. Impact on Multiphasic Gas and Thermodynamic Regulation

The effect of kinetic feedback is direct and multi-scale:

• Suppression of Cooling and Star Formation: In cluster cool cores, kinetic energy input from jets/bubbles offsets radiative cooling, preventing runaway cooling flows and maintaining thermal balance. The duty cycle of AGN bubbling is high ($>70–95\%$), and the cumulative mechanical energy ($\sim 4PV$ per bubble) closely matches the core cooling luminosity (Fabian, 2012, Morganti, 2017, Qiu et al., 2018).
• Gas Dispersal and Metal Enrichment: In massive elliptical and early-type galaxies, kinetic mode feedback expels central dense gas, limits black hole growth, enriches the CGM with metals, and regulates the spatial distribution of X-ray emission and metallicity profiles, but quiescence is fully maintained only when kinetic and radiative modes are both active (Eisenreich et al., 2017).
• Regulation in Massive Galaxies: Simulations show that pure kinetic feedback (with or without inclusion of thermal or magnetic components) effectively prevents catastrophic cooling in high-pressure, multiphase CGM environments, maintaining observed entropy profiles and modulating the cold gas extent. Partitioning AGN energy into both kinetic and thermal components can lead to “entropy bumps” in the central region and extended cold gas structures (Prasad et al., 24 Aug 2025).
• Generation of Turbulence and Multi-Phase Outflows: At high redshift and in specific environments (e.g., Fornax A), the simultaneous presence of compact turbulence-driven condensation inflowing toward the AGN and fast multi-phase outflows (ionized, atomic, and molecular) at velocities up to 2000 km/s demonstrates the dual role of kinetic feedback in both feeding and regulating AGN activity (Maccagni et al., 2021).

4. Observational Diagnostics and Empirical Constraints

Multi-wavelength observations reveal the signatures of kinetic AGN feedback, providing powerful constraints on feedback models:

• Cavities/Bubbles: X-ray imaging reveals cavities in the ICM that correlate spatially with radio jets, directly probing mechanical energy injection (cavity enthalpy, buoyancy ages) (Fabian, 2012, Morganti, 2017).
• Kinematic Outflows: Integral field spectroscopy measures high-velocity (FWHM $\sim 400–1000$ km/s), non-gravitational broadening, and bulk outflow velocities ($\Delta v \sim 200–400$ km/s) in the ionized gas of radio galaxies at $z \sim 2$, confirming that AGN are energetically capable of driving significant galaxy-scale outflows (Collet et al., 2015).
• Energy and Momentum Coupling: Observations indicate that kinetic outflows can reach momentum boosts (relative to pure photon momentum) of $\sim 20$ or higher, indicating energy-conserving outflow propagation. The observed kinetic energy imparted to the ionized gas is typically a few percent of the available jet power, supporting efficient but non-total energy transfer to the multiphase ISM (Morganti, 2017).

A major result is that both "radio quiet" (low radio-loudness) and "radio loud" AGN contribute substantially to the total kinetic energy density, with radio quiet systems accounting for about half of the total budget (Franca et al., 2010).

5. Implementation in Numerical Simulations and Model Calibration

Contemporary hydrodynamical simulations implement kinetic AGN feedback using various subgrid prescriptions:

• Kinetic vs. Thermal Feedback: Models distinguish between pure thermal (quasar mode) and kinetic/momentum-driven (radio mode) feedback—often triggering kinetic events at low accretion rates. Kinetic feedback is implemented via stochastic “kicks” to gas cells/particles or via explicit mass-loaded jet models, with parameters such as feedback efficiency ($\epsilon_f$) and wind velocity ($v_w$) tuned to reproduce observed BH–host relations (Barai et al., 2013, Weinberger et al., 2016, Barai et al., 2016, Prasad et al., 24 Aug 2025).
• Energy Partitioning: Simulations test various partitions of AGN power, such as 75% kinetic + 25% thermal, or pure kinetic, showing that the former can drive sufficient heating for the observed entropy profiles, whereas the latter prevents central overheating but leads to less extended cold gas (dependent on the host CGM structure) (Prasad et al., 24 Aug 2025).
• Intermittency and Duty Cycles: Incorporating cold gas accretion results in highly variable AGN power output, naturally generating a feedback duty cycle (periodicity $\sim 100$ Myr), leading to self-regulated cycles of gas condensation, AGN triggering, and feedback (Barai et al., 2016).
• Multi-scale Impact: AGN jet feedback models capable of long-range energy transport (e.g., collimated jets, hydrodynamic decoupling before thermalization) have strong impacts on the thermodynamic state of the circumgalactic and intergalactic medium, modifying observables like the HI Lyman-α forest and aligning simulated absorber statistics with measurements (Tillman et al., 2022).

Simulations constrained by empirical radio luminosity functions, kinetic energy density estimates, and stellar mass/halo mass scaling produce results in near agreement with observed global energetics and cosmic evolution of kinetic feedback (Franca et al., 2010, Kondapally et al., 2023, Igo et al., 31 Mar 2025).

6. Cosmic Evolution, Energetic Budget, and Global Relevance

Empirical studies tracing radio-loud AGN populations reveal key trends in the evolution, energetics, and population demographics of kinetic AGN feedback:

• Cosmic Energy Density: The integrated kinetic energy density from AGN jets is estimated as $$\Omega_{\mathrm{kin}} \sim 10^{50}\,\mathrm{J}\,\mathrm{Mpc}^{-3}$$, with the kinetic luminosity density $\Omega_{\mathrm{kin}}$ remaining nearly constant ($4–5 \times 10^{32}\,\text{W}\,\text{Mpc}^{-3}$) from $z \sim 2.5$ to $z \sim 0.5$. This is dominated by low-excitation radio galaxies (LERGs) (Kondapally et al., 2023).
• Dominance Over Radiative Feedback: For galaxies with $\log M_*/M_\odot > 10.6$, the kinetic (jet) mode dominates over all plausible levels of radiatively-driven feedback. In massive halos, the kinetic energy input is sufficient to strongly affect the entropy and cooling balance in group/cluster cores, though it generally does not unbind global halo gas (Igo et al., 31 Mar 2025).
• Redshift Dependence: The kinetic energy density declines by about a factor of five at $z < 0.5$, contrary to previous assumptions of constant or increasing radio-mode feedback toward the present (Franca et al., 2010).

The extraction of jet power, radio luminosity function decompositions, incidence distributions by stellar mass and morphology, and large-scale energetic comparisons provides an empirical anchor for calibrating and validating AGN feedback in cosmological models (Igo et al., 31 Mar 2025).

7. Synthesis and Implications for Galaxy and Cluster Evolution

Kinetic AGN feedback is now established as a key mechanism in regulating galaxy and cluster evolution. Its main observable and theoretical consequences include:

• Suppression of cooling flows and star formation in massive halos and maintenance of thermal equilibrium in group/cluster cores.
• Regulation of black hole growth rates and alignment with empirical scaling relations (e.g., $M_{\mathrm{BH}}-\sigma_*$) via energy- and momentum-driven outflows calibrated by feedback efficiency and wind velocity.
• Significant impact of both radio-loud and radio-quiet AGN on the total cosmic kinetic energy budget, with low-luminosity AGN radiative heating (via high Compton temperatures) playing a non-negligible role even in traditionally “kinetic-dominated” regimes.
• Anisotropic clearing of sightlines and expansion of gas reservoirs in high-redshift galaxies, with biconical outflow geometry favored by observations, but with the caveat of seeding and outflow statistical degeneracies (Vito et al., 2022).

Future efforts, enabled by new observational facilities (e.g., SKA, XRISM, ALMA), detailed multi-phase gas kinematic analyses, and high-resolution simulations, are poised to further illuminate the detailed coupling, efficiency, and downstream effects of kinetic AGN feedback across cosmic time.