Positive AGN Feedback in Galaxy Evolution

• Positive AGN feedback is the process by which energy from active galactic nuclei compresses gas, triggering enhanced star formation in galaxies.
• Mechanisms like jet-induced shocks and overpressurized winds compress dense molecular clouds, leading to rapid and localized starburst episodes.
• The integration of numerical, theoretical, and observational models explains how positive feedback alters star formation rates and galactic evolution.

Positive AGN feedback refers to the process by which energy and momentum released from active galactic nuclei (AGN) act to enhance, rather than suppress, star formation in their host galaxies. Contrary to the classical paradigm that AGN outflows are primarily responsible for terminating star formation by heating or expelling gas (“negative feedback”), a wide body of theoretical, numerical, and observational work now demonstrates that AGN-driven pressure, shocks, or turbulence can, under certain physical conditions, compress dense interstellar gas or destabilize galactic discs, triggering localized or galaxy-wide bursts of star formation. This complex interplay of quenching and triggering underpins major uncertainties in models of galaxy evolution, and motivates the explicit modeling of positive AGN feedback in contemporary semi-analytic and hydrodynamical frameworks.

1. Physical Mechanisms of Positive AGN Feedback

The prevailing mechanisms underlying positive AGN feedback involve the injection of mechanical, radiative, or cosmic ray energy into the multiphase interstellar medium (ISM) or circumgalactic environment, resulting in conditions favorable to star formation enhancement.

Jet-Induced Compression and Shocks

Relativistic radio jets propagating through an inhomogeneous, clumpy ISM create expanding over-pressurized cocoons that generate strong shocks and turbulent motions (Gaibler, 2014, Wagner et al., 2015). When these shocks sweep through gas-rich regions, they induce rapid cooling, compressing molecular clouds, locally reducing Jeans masses, and shortening free-fall times. Under such circumstances, the effective pressure on gas clouds can exceed quiescent ISM values by factors of up to $\sim 10^3$, leading to fragmentation and collapse on timescales substantially shorter than in the absence of AGN activity (Bieri et al., 2015). The critical importance of cloud size and column density emerges: large ($\gtrsim$25–50 pc), high-column-density clouds experience compression rather than ablation, maximizing the triggering of star formation (Wagner et al., 2015).

Outflow-Driven Overpressurization and Disc Instability

Beyond jets, AGN-driven wide-angle winds or outflows can over-pressurize entire galactic discs. Hydrodynamical simulations demonstrate that when an external pressure enhancement—driven by an AGN-induced bow shock or energy-driven blastwave—is applied quasi-isotropically, even Toomre-stable discs ($Q > 1$) are forced into instability, rapidly fragmenting into dense star-forming clumps (Bieri et al., 2015, Bieri et al., 2015). The mean star formation rate (SFR) in such cases typically scales as $SFR \propto \sqrt{P_{ext}}$, where $P_{ext}$ is the external pressure, so that moderate pressure boosts drive order-of-magnitude enhancements in global SFR (Bieri et al., 2015).

Spatial Relocation and Temporal Episodicity

In complex morphologies, such as barred spiral galaxies, the expulsion of gas from the nucleus by AGN feedback and its subsequent collision with inflowing bar-driven gas redistributes star formation into low-radius rings, even as nuclear SFR is suppressed (Robichaud et al., 2017). The episodic (“flickering”) nature of AGN activity—natural in optimized control-theoretic models (Pope, 2011)—further implies that positive feedback occurs transiently, with enhanced star formation following the passage of outflows until mechanical or radiative feedback becomes dominant.

2. Quantitative Models and Theoretical Frameworks

Several classes of models describe the AGN positive feedback process, unifying control-theoretic, hydrodynamical, and semi-analytic approaches.

Control-Theoretic Formulation and Bang-Bang Solutions

The problem of regulating star formation and X-ray luminosity in massive galaxies is posed as a control system:

$H(t) = \alpha(t) k_1 L_x(t)$

where $H(t)$ is the AGN heating rate, $L_x(t)$ the X-ray luminosity (tracing gas cooling), $k_1$ feedback strength, and $\alpha(t)$ a binary control parameter (Pope, 2011). Minimizing the total energy output leads to “bang-bang” solutions—short, discrete AGN outbursts that, during the off-phases, favor conditions where local compressions and cooling instabilities (i.e., positive feedback) are more likely to arise.

Hydrodynamical and Subgrid Prescriptions

Numerical simulations (e.g., RAMSES-based AMR codes (Bieri et al., 2015)) implement star formation via a Schmidt-like law: $$\dot{\rho}_* = \epsilon_* \frac{\rho_{gas}}{t_{ff}}$$ with triggering thresholds set by local overpressure and density. In externally pressurized discs, the minimum perturbed free-fall time determines the rapid onset of star formation after outflow passage.

Semi-Analytic Modeling in Galaxy Formation

Recent semi-analytic models (SAMs), such as FEGA and FEGA25, formalize AGN positive feedback as an explicit burst mode: $$\dot{M}_*^{\mathrm{pAGN}} = \alpha_{\mathrm{pAGN}} \left(\frac{\delta M_{\mathrm{BH}}}{M_{\mathrm{BH}}}\right) \dot{M}_{\mathrm{cool,new}}$$ Here, $\dot{M}_*^{\mathrm{pAGN}}$ is the SFR triggered by positive AGN feedback, $\dot{M}_{\mathrm{cool,new}}$ is the residual cooling rate after AGN heating, and $\alpha_{\mathrm{pAGN}}$ a calibrated efficiency parameter. This formulation ensures that positive feedback is dynamically coupled to black hole accretion and the efficiency of negative feedback and gas ejection (Contini et al., 17 May 2024, Contini et al., 26 Feb 2025).

3. Observational Signatures and Empirical Constraints

Multiple lines of evidence from resolved imaging and statistical samples support the reality of AGN-driven star formation triggering.

Enhanced Star Formation and Starburst-Ring Morphologies

Spatially resolved mapping (e.g., with VLT/MUSE and ALMA) reveals that regions where AGN outflows intersect gas-rich rings, such as in NGC 5728, display enhanced SFRs ($\sim1.8~M_\odot~\mathrm{yr}^{-1}~\mathrm{kpc}^{-2}$) and elevated star formation efficiencies (up to $\sim3$–$5\times$ higher than adjacent regions), directly implicating outflow compression in star formation enhancement (Shin et al., 2019).

Star Formation and AGN Power Correlations

A robust, nearly linear scaling between AGN bolometric luminosity and starburst luminosity is quantified in star-forming discs: $L_{*} \propto L_{\mathrm{AGN}}^{5/6}$ with observed starburst luminosities in maximum cases up to $L_{*} \sim 50\,L_{\mathrm{AGN}}$ (Zubovas et al., 2013). This statistical correlation is modulated by AGN duty cycle, gas morphology, and temporal mismatch between AGN phase duration and star formation response.

Jet Power Thresholds and Mass-Dependent Switching

Samples at $z \approx 1$ demonstrate that the enhancement of SFR due to radio jets peaks for moderate jet powers; beyond a mass-dependent critical threshold, feedback switches to a dominantly negative (quenching) regime (Kalfountzou et al., 2017). Radio-loud quasars (RLQs) exhibit SFRs up to $2.5\times$ higher than mass- and luminosity-matched radio-quiet quasars (RQQs), whereas the most radio-luminous galaxies tend to have suppressed SFRs.

Ultraviolet and Molecular Gas Mapping

High-resolution UV imaging (e.g., UVIT observations of Centaurus A (Joseph et al., 2022)), reveals hundreds of young star-forming sources preferentially arrayed along the axis of AGN jets, with bifurcated morphologies and clear age gradients (median ages $~48$–64 Myr), implying recent jet-triggered star-forming episodes.

4. Scaling Relations, Model Calibration, and Evolutionary Impact

The explicit inclusion of positive AGN feedback alters key observables and improves theoretical predictions of galaxy evolution.

Effect on Star Formation Main Sequence and Stellar Mass Function

The introduction of a burst mode for AGN-triggered star formation in SAMs (FEGA, FEGA25) modifies the star formation rate–stellar mass relation (“main sequence”), increasing the SFRs at fixed mass particularly in low- and intermediate-mass halos. The positive feedback mode can account for up to 20–25% of the stellar mass buildup in some systems, without violating constraints on the stellar mass function or overproducing high-mass galaxies (Contini et al., 17 May 2024, Contini et al., 26 Feb 2025).

Morphology and Metallicity Distributions

Enhanced central star formation induced by AGN is predicted to impact bulge-to-total ratios, stellar metallicities, and morphological evolution, as sudden starbursts may foster bulge growth and rapid enrichment, shifting the distribution of morphological types in good agreement with observed trends, especially at high redshift.

Temporal and Mass-Dependent Dominance

Positive AGN feedback is predicted to be most pronounced at early cosmic times (high redshift) and in environments where the negative feedback mode is inherently less efficient. As halo mass increases, negative feedback and hot gas ejection become dominant, gradually suppressing the impact of positive bursts and yielding the observed decline in cosmic SFR density toward low redshift.

5. Key Limiting Factors and Necessary Physical Conditions

The effectiveness of positive AGN feedback is sensitive to a range of physical galactic and AGN properties:

• ISM Structure: Large, high-column-density molecular clouds embedded in a disc-like configuration maximize compressive triggering and minimize destructive ablation (Wagner et al., 2015).
• Gas Richness: A high cosmic gas fraction (characteristic of high-redshift galaxies) supplies raw material for star formation enhancement after AGN outflow passage (Gaibler, 2014).
• Geometry and Orientation: Alignment of jets or outflows with dense gas structures (e.g., intersection of outflows with star formation rings (Shin et al., 2019), or alignment of the jet axis with UV-bright filaments in Centaurus A (Joseph et al., 2022)) are key determinants.
• AGN Power and Duty Cycle: A critical threshold in jet power exists: below this, jets compress and enhance, above it, they heat or eject, swinging the balance from positive to negative feedback (Kalfountzou et al., 2017).
• Timescale Mismatch: The timescales for AGN episodes (tens to hundreds of Myr) are generally much shorter than the duration over which pressure-induced star formation persists, explaining the rarity of observing simultaneous AGN and SF bursts despite the widespread occurrence of triggered starbursts (Zubovas et al., 2013).

6. Integration in Galaxy Evolution Models and Future Prospects

The coordinated inclusion of positive AGN feedback in models such as FEGA25—where negative, positive, and hot gas ejection modes operate in parallel and are coupled through parameterizations of AGN accretion and energy injection—significantly improves the reproduction of observed galaxy scaling relations, including the evolution of the star-forming main sequence, the fraction of passive galaxies with mass and redshift, and the cosmic star formation rate history (Contini et al., 26 Feb 2025).

Looking forward, more precise constraints on the efficiency of energy coupling (and momentum loading) between AGN output and the ISM, direct mapping of induced starbursts with next-generation facilities (e.g., JWST, ALMA), and refined subgrid and analytic prescriptions in SAMs and hydrodynamical simulations will clarify the conditions and evolutionary stages at which positive AGN feedback critically shapes galaxy assembly, structure, and star formation histories.