The limits of feedback from active galactic nuclei

Technical Summary: The Limits of Feedback from Active Galactic Nuclei

Problem Statement
Observations of galaxy groups and clusters reveal a strong mass-dependent trend in gas fractions: low-mass groups ($M_{200m} \simeq 10^{13} M_\odot$) exhibit significant gas depletion (fractions as low as $\simeq 0.05$), while high-mass clusters ($M_{200m} > 10^{14} M_\odot$) retain gas fractions close to the cosmic baryon limit ($\simeq 0.15$). While Active Galactic Nuclei (AGN) feedback is widely accepted as the mechanism responsible for heating and removing gas, the physical reason why this feedback becomes ineffective in massive clusters remains unclear. Specifically, it is necessary to determine where the gas goes, why it stops being expelled in high-mass systems, and how the transition from effective to ineffective feedback occurs.

Methodology
The authors utilize the FLAMINGO suite of cosmological hydrodynamical simulations to investigate these dynamics. The analysis focuses primarily on the "Fiducial" m8 simulation (gas particle mass $1.34 \times 10^8 M_\odot$) and a set of m9 resolution variants (gas particle mass $1.07 \times 10^9 M_\odot$). These variants include systematic changes to AGN feedback strength (thermal models with varying temperature thresholds $\Delta T_{AGN}$ and kinetic "Jet" models) to test the robustness of the findings.

The post-processing pipeline involves:

1. Halo Identification: Using HBTHERONS to identify halos and subhalos, focusing on the central black hole and the main halo.
2. Flow Quantification: Calculating radial profiles of gas inflow and outflow rates, energy fluxes (enthalpy + kinetic), and entropy ($K \equiv p/\rho^{5/3}$) as a function of radius, normalized to the virial radius $r_{200m}$.
3. Stacking and Alignment: Stacking halos in mass bins and, for Jet variants, aligning halos based on flow eigenvalues to analyze anisotropic outflow structures.
4. Energetic and Entropic Analysis: Comparing inflow/outflow energy budgets and entropy generation against theoretical predictions based on Rankine-Hugoniot shock relations and buoyancy arguments.

Key Contributions and Results

• The Entropy Ceiling: The study identifies a "ceiling" for AGN-driven entropy production. In the Fiducial thermal model, outflowing gas reaches a plateau entropy of approximately $360\text{--}370 \, \text{keV cm}^2$ for halos with $M_{200m} < 10^{13.7} M_\odot$. This ceiling is nearly independent of halo mass.
• Mechanism of Self-Limitation: The entropy ceiling arises from shock heating. AGN feedback initially heats gas to high temperatures ($\sim 10^8$ K), creating overpressurized regions that expand and drive shocks. These shocks efficiently deposit entropy only if they are strong. Once the ambient gas is sufficiently heated, subsequent shocks become too weak (low Mach number) to inject further entropy. This self-limiting process is derived using Rankine-Hugoniot relations, predicting a ceiling value consistent with the simulation results.
• Three-Zone Model: The authors delineate three radial zones governing gas transport:
  1. Inner Zone ($r \lesssim 0.3 r_{200m}$): Strong shocks generate entropy up to the ceiling value.
  2. Intermediate Buoyancy Zone: Gas rises at constant entropy (the ceiling) driven by buoyancy.
  3. Outer Zone: Depending on halo mass, the outflow either escapes into the Hubble flow, stalls, or encounters a termination shock.
• Critical Mass and Feedback Ineffectiveness: The transition from effective to ineffective feedback is determined by comparing the entropy ceiling to the virial entropy of the inflowing gas. In low-mass halos, the ceiling entropy exceeds the virial entropy, allowing buoyant outflows to escape. In massive clusters ($M_{200m} > 10^{13.7} M_\odot$ for the Fiducial model), the virial entropy of the inflowing gas exceeds the entropy ceiling. Consequently, the outflow cannot overcome the gravitational potential, stalls, and potentially shocks at the "splashback" radius.
• Gas Fractions and "Lingering" Gas: The paper derives an expression for the time evolution of the virial gas fraction ($\dot{f}_{gas}$), showing it is governed by three terms: physical gas flows, total mass flow (dominated by dark matter), and the expansion of the virial radius.
  • Physical outflows persist up to $M_{200m} \simeq 10^{13.7} M_\odot$.
  • However, the measured gas fraction begins to rise at a lower mass ($M_{200m} \simeq 10^{13.0} M_\odot$). This is because in the intermediate mass range, outflows stall just outside the virial radius ("lingering" gas). As the halo grows and its virial radius expands, it incorporates this lingering gas, passively increasing the measured gas fraction even while net outflows are still occurring.
• Feedback Variants:
  • Thermal vs. Jet: Both thermal and kinetic (Jet) feedback models exhibit an entropy ceiling. However, the Jet model shows a weak mass dependence ($K \propto M_{200m}^{0.22}$) due to the collimated geometry of the outflows, whereas the thermal model is nearly mass-independent.
  • Strength Dependence: Variants with stronger feedback (higher $\Delta T_{AGN}$) exhibit higher entropy ceilings and correspondingly higher critical masses for the transition to ineffective feedback.

Significance
The paper provides a physical explanation for the observed mass dependence of gas fractions in galaxy groups and clusters. It argues that the "missing" baryons in groups are not lost to the universe but are displaced to the outskirts (within 2–3 virial radii) by buoyant outflows. In massive clusters, the feedback mechanism fails not because the energy budget is insufficient, but because the ambient gas is already too hot (high entropy) for the AGN-driven shocks to generate the additional entropy required for buoyancy.

The authors claim this picture is supported by the consistency between the simulated entropy ceiling, the Rankine-Hugoniot predictions, and observational constraints from X-ray, Sunyaev-Zel'dovich (tSZ/kSZ), and Fast Radio Burst (FRB) data. The work suggests that the limit of AGN effectiveness is a fundamental consequence of the thermodynamic state of the halo gas and the self-limiting nature of shock heating, rather than a failure of the feedback energy injection itself. The results imply that future X-ray missions with high spectral resolution and wide fields of view (e.g., NewAthena, LEM) are necessary to resolve the shocks and separate inflow/outflow phases to test these predictions observationally.