Instantaneous AGN Feedback

• Instantaneous AGN feedback is the rapid coupling of energy and momentum from an active galactic nucleus to the surrounding gas on timescales comparable to the AGN duty cycle.
• It involves both radiative and mechanical processes that trigger shocks, turbulence, and swift changes in the thermal state of the interstellar and circumgalactic media.
• This feedback mechanism is essential for regulating star formation, controlling gas accretion, and balancing cooling flows across a wide range of cosmic environments.

Instantaneous AGN feedback refers to the rapid coupling of energy and/or momentum from an active galactic nucleus (AGN) to the interstellar medium (ISM), circumgalactic medium (CGM), or the larger-scale environment of its host galaxy. Unlike long-term cumulative effects, instantaneous AGN feedback is characterized by the ability of AGN-driven phenomena—such as radiation, winds, and jets—to induce marked changes in the physical state (ionization, temperature, turbulence, or kinematics) of surrounding gas on timescales comparable to, or shorter than, the duty cycle of the AGN itself. The observational and theoretical signatures of such feedback are manifest across a broad range of scales, from sub-parsec to hundreds of kiloparsecs, and have critical implications for star formation, gas accretion, and galaxy evolution.

1. Physical Mechanisms and Mathematical Formulation

The coupling of AGN output to ambient gas can proceed via radiative (e.g., photoionization, Compton heating), mechanical (e.g., outflows, jets), or hybrid modes:

• Radiative feedback: AGN radiation couples to the ISM/CGM and imparts energy to the gas via Compton scattering and photoionization. For example, energy injection at large radii (e.g., the Bondi radius) can elevate electron temperatures above the local virial value, suppressing accretion and inducing intermittent AGN activity (1105.4822).
• Mechanical feedback: AGN jets and winds transfer momentum and energy dynamically, driving shocks, turbulence, and gas removal. The feedback is often modeled by equating a fraction of the AGN's luminosity to the work required to unbind or heat the ambient gas reservoir.
• Mathematical description: The general form of AGN feedback energy coupling is encapsulated by

$$f_t \cdot L_B \cdot \delta t = \frac{G \cdot M \cdot \delta M_g}{R}$$

where $f_t$ is the time-dependent energy coupling efficiency, $L_B$ is the AGN bolometric luminosity, $M$ and $R$ are the galaxy mass and size, and $\delta M_g$ is the gas mass ejected (1008.1583).

The time-dependence of feedback can be modeled as a Gaussian in time, with peak efficiency $f_0$ occurring at $t_p$ (typically $\sim0.5$ Gyr after the starburst) and width $\tau$ (the feedback timescale), as

$$f_t = f_0 \cdot \exp\left[ -\frac{(t - t_p)^2}{2\tau^2} \right]$$

A critical threshold for “instantaneous” feedback in quenching phenomena is $\tau \lesssim 0.2$ Gyr, similar to AGN duty cycles (1008.1583).

2. Timescales, Intermittency, and Duty Cycles

Instantaneous AGN feedback is fundamentally episodic or burst-like. Optimal control theory applied to galaxy cooling–heating systems predicts feedback should occur in discrete “bang–bang” bursts that minimize total energy injection, as shown by models that relate the AGN “on” fraction (duty cycle, $\delta$) to the strength of feedback $k_1$ through $\delta \approx 1/k_1$ (1103.0548). Stronger feedback corresponds to rarer but more intense outbursts, while weaker feedback is more continuous.

Characteristic instantaneous timescales and duty cycles can be quantified:

• Feedback timescales: Viable models require $\tau \lesssim 0.2$ Gyr for rapid color transition in early-type galaxies (1008.1583).
• Oscillation timescales: In hot accretion flows, AGN can cycle between active and inactive phases on timescales $\sim 10^4$–$10^5$ yr, set by the thermal/viscous timescale at the Bondi radius and gas cooling timescale (1105.4822).
• Simulated cluster/galaxy timescales: Instantaneous jet feedback in cool-core clusters can produce AGN outbursts on timescales $\sim 10$ Myr, closely tied to the accretion and cooling dynamics (Li et al., 2015).

The bursty nature of instantaneous feedback is crucial for interpreting observed AGN variability, the prevalence of young radio sources, and the energy regulation in cluster and group environments.

3. Observational Diagnostics of Instantaneous Feedback

Key observables associated with instantaneous AGN feedback across different scales and physical contexts include:

• Circumgalactic Lyα emission: The MUSE-based QSO MUSEUM survey demonstrates that the Lyα surface brightness and linewidths in the CGM of $z\sim3$ quasars increase with instantaneous bolometric luminosity, after controlling for black hole mass. The Lyα velocity dispersion profile

$$\sigma(r) = \sigma_{50}(r/50\,\mathrm{ckpc})^{\beta}$$

with $\beta \approx -1$, steepens in luminous quasars in the central $R<40$ kpc, indicating that the present AGN output drives turbulence and illuminates a larger fraction of the CGM in real time (Lobos et al., 22 Jul 2025).

• Gas depletion and quenching: In nearby early-type galaxies, the inability of star formation alone to exhaust the cold gas reservoir on observed migration timescales ($\lesssim 1$ Gyr) requires the rapid removal of gas via AGN feedback. Observational constraints on young stellar fractions and cold gas mass ($\lesssim 0.6\%$) corroborate this model (1008.1583).
• Intermittent outbursts and mechanical feedback: VLBA monitoring of nuclear radio sources (e.g., NGC 3079) captures parsec-scale shocks and deceleration episodes, directly measuring bursts of mechanical energy deposition on monthly–yearly timescales. Jet-driven shocks inject $3\times10^{50}$–$10^{52}$ erg into the ISM over short intervals (Fernandez et al., 2023).
• Cluster and group environments: Detection of buoyant radio bubbles, cavities, and weak shocks in hot atmospheres provides evidence for AGN feedback events that offset cooling “instantaneously” on the timescale of each outburst (typically controlled by AGN duty cycles or dynamical times across $\sim$10–100 Myr) (Eckert et al., 2021, Brienza et al., 2021, Oosterloo et al., 2023).
• Ionization cones and photoionization signatures: Correlations between AGN luminosity, Lyα nebula surface brightness, and the inferred ionization cone opening angle indicate that an increasing fraction of the CGM is illuminated “instantly” as AGN luminosity increases, supporting models where SB$_\mathrm{Ly\alpha}$ traces the instantaneous photon output and geometry (Lobos et al., 22 Jul 2025).

These diagnostics establish that AGN feedback leaves rapid, luminosity-dependent imprints on gas emission, kinematics, and ionization structure.

4. Impact on Star Formation and Gas Regulation

The immediate effects of AGN feedback on star formation can be negative (quenching), positive (triggering), or neutral, with mechanisms and outcomes depending on gas phase, density structure, and the nature of energy coupling:

• Negative feedback: Rapid AGN-driven gas removal leads to accelerated quenching of star formation. Theoretical and simulation models demonstrate that the feedback-driven expulsion of more than half the cold gas reservoir within $\lesssim$0.2 Gyr is required to explain color–mass evolution and the small young stellar fractions in elliptical galaxies (1008.1583). In some contexts (e.g., radiative mode AGN), the local SFR may be suppressed by several percent, although the instantaneous effect can be much less than run-to-run SFR fluctuations in high-resolution simulations (Roos et al., 2014).
• Positive feedback: Enhanced star formation rates, especially in radio-loud AGN with strong jets, can result from jet-induced shocks and compression of molecular clouds, increasing SFR by factors of 3–5 compared to radio-quiet AGN at fixed X-ray luminosity (1306.6468). The spatial distribution of triggered star formation can extend to kiloparsec scales as the AGN spreads cooling gas or compresses the ISM via bipolarly-driven winds (Ciotti et al., 2015).
• Ineffectiveness of instantaneous quenching: High-resolution simulations of $z\sim2$ disk galaxies demonstrate that even in strong AGN phases (quasar regime), the instantaneous SFR reduction due to thermal and radiative feedback seldom exceeds a few percent, due to efficient shielding of star-forming gas in dense clumps (Roos et al., 2014).

Thus, the instantaneous impact of AGN feedback on star formation is complex, ranging from rapid global quenching to locally enhanced or largely unaffected SFRs, depending on the ISM structure and feedback coupling efficiency.

5. Theoretical Modeling, Subgrid Prescriptions, and Simulation Approaches

Correctly capturing instantaneous AGN feedback in simulations necessitates detailed subgrid modeling due to the enormous dynamical range between scales where energy is released and the scales resolved in galaxy formation simulations:

• Thermal vs. kinetic feedback: Classical thermal feedback injects AGN energy isotropically into nearby gas; however, this can suffer from excessive local cooling losses and isotropy assumptions that fail to reflect real AGN outflow morphologies. Improvements include conical energy injection matching the opening angles of observed jets or winds, which increases energy retention and allows realistic coexistence of inflows and outflows (Zubovas et al., 2015).
• Momentum-driven models: Directly imparting momentum “kicks” within bi-conical regions (with axis aligned to gas angular momentum or BH spin) efficiently captures observed kinetic wind properties and instantly couples feedback to surrounding gas, matching the biconical outflows seen in observations (Sala et al., 2020).
• Control theory and feedback duty cycles: Implementing optimal, “bang-bang” control in the equations governing galaxy cooling allows explicit modeling of discrete, intermittent feedback that optimally regulates black hole growth and thermal equilibrium (1103.0548).
• Feedback in dwarf galaxies: Analytical and numerical models show that fast AGN (wind-driven) outflows can eject gas in dwarf galaxies more efficiently than SNe for a wide parameter range, with critical halo masses and Eddington ratios setting the threshold for gas expulsion (Dashyan et al., 2017).
• Chaotic cold accretion cycles: Simulations and high-resolution ALMA observations (e.g., of 3C 84) demonstrate “feedback–feeding” cycles in which AGN jets induce cooling and promote cold filament infall, enabling nearly instantaneous gas inflow to the SMBH and closing the feedback loop (Oosterloo et al., 2023).

Accurate representation of instantaneous feedback is thus contingent on model choices for energy and momentum injection geometry, coupling to the multiphase ISM, and temporal resolution.

6. Cosmological and Extragalactic Implications

Instantaneous AGN feedback fundamentally shapes galaxy and large-scale structure evolution:

• Suppression of runaway cooling flows: In cool-core clusters and groups, episodic AGN outbursts (jets, shocks, and bubble inflation) can balance radiative cooling, preventing the formation of excessive cold gas and regulating star formation rates. This process keeps the minimum $t_\mathrm{cool}/t_\mathrm{ff}$ ratio within observed limits and restricts star formation in the brightest cluster galaxies (Li et al., 2015, Eckert et al., 2021).
• IGM heating and Lyα forest signatures: Jet-mode AGN feedback in models such as Simba can instantaneously heat the IGM, flattening the column density distribution function and broadening the Doppler ($b$) parameter distribution in the Lyα forest ($z\lesssim2$). The suppression of low $N_\mathrm{HI}$ absorbers and increase in $b$ are direct indicators of widespread, rapid AGN-driven IGM heating, which can be degenerate with UV background variations and modulated by stellar feedback (Tillman et al., 2023).
• Broad sSFR distributions in galaxy populations: AGN feedback imparts a broadening to the galaxy population’s sSFR distribution at fixed mass, even when instantaneous AGN luminosity does not correlate with suppressed SFR. This cumulative effect explains the observed scatter in sSFR in high-mass galaxies, as predicted and reproduced by models including AGN feedback (e.g., EAGLE) (Scholtz et al., 2017, Harrison et al., 2019).

These effects underscore that instantaneous AGN feedback is essential for regulating baryon cycling, shaping galaxy scaling relations, and determining the thermal state of the circumgalactic and intergalactic medium.

7. Future Prospects and Open Issues

Progress in understanding instantaneous AGN feedback hinges on the following:

• High-cadence, high-resolution observations: While signatures of instantaneous feedback are robust (e.g., parsec-scale shocks (Fernandez et al., 2023), low-frequency mapping of ancient bubbles (Brienza et al., 2021)), extending such diagnostics to larger samples and across the full range of AGN types remains an active endeavor.
• Direct coupling efficiency measurements: Quantifying the fraction of AGN bolometric output coupled into kinetic or thermal modes as a function of environment and gas phase is required for precision modeling.
• Improved subgrid models: Incorporation of anisotropic energy injection, multiphase ISM, and physically-motivated feedback duty cycles in cosmological and zoom-in simulations will refine predictions for both instantaneous and cumulative AGN impact.
• Disentangling feedback from environment: Interpreting velocity dispersions, emission strengths, and gas kinematics must account for the superposition of AGN-driven and gravitationally-driven motions, particularly when using Lyα or other resonant-line tracers as feedback proxies (Lobos et al., 22 Jul 2025).
• Multi-wavelength and time-domain studies: Observations leveraging ALMA, LOFAR, Chandra, MUSE, and future facilities (e.g., Athena, SKA, XRISM) will be critical in mapping the spatial and temporal footprints of instantaneous AGN feedback across cosmic history.

In summary, instantaneous AGN feedback represents the rapid, episodic transfer of energy and momentum from accreting supermassive black holes to the ambient gas on a range of spatial and temporal scales. Its signatures—whether manifested as sudden gas expulsion, turbulence generation, radiative heating, or immediate perturbations to the CGM—are central to regulating accretion, extinguishing or triggering star formation, and shaping the evolutionary pathways of galaxies and their environments. The convergence of high-cadence observations and sophisticated modeling continues to elucidate the crucial role of instantaneous AGN feedback in cosmic structure formation.