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arxiv: 2605.16483 · v1 · pith:D4Y3IEG3new · submitted 2026-05-15 · 🌌 astro-ph.GA · astro-ph.CO

The limits of feedback from active galactic nuclei

Andrew Pontzen , Hiranya V. Peiris , Joop Schaye , Matthieu Schaller This is my paper

Pith reviewed 2026-05-20 16:07 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords AGN feedbackgalaxy groupsgalaxy clustershalo gasentropyoutflowsbaryon fractionshock heating
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The pith

AGN feedback self-limits via weak shocks, creating an entropy ceiling that lets outflows escape only in halos below 10^13.7 solar masses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines why active galactic nuclei feedback removes gas from galaxy groups but leaves it largely intact in clusters. Heating occurs in an inner zone through shocks, but this process self-limits once the gas reaches a temperature where further entropy injection weakens. This establishes a nearly constant ceiling entropy of 360 keV cm² for the outflows, independent of halo mass and explained via Rankine-Hugoniot shock relations. The heated gas then rises buoyantly and escapes only if this ceiling exceeds the entropy of inflowing gas, a condition met solely below a halo mass of 10^13.7 solar masses because inflow entropy scales with the virial temperature. The result accounts for depleted gas in groups versus near-cosmic baryon fractions in clusters, with gas reincorporated as halos grow.

Core claim

Heating in the inner zone self-limits because, once the gas is sufficiently hot, shocks become too weak to deposit further entropy. Consequently, outflows have a ceiling entropy value (360 keV cm²) that is nearly independent of halo mass. These values (and trends with redshift and feedback variants) are explained using an argument based on the Rankine-Hugoniot relations. Outflows rise at fixed entropy through the buoyancy zone, escaping the halo if the ceiling value is sufficiently elevated over that of the inflowing gas. This condition is satisfied only for halo masses M_200m < 10^13.7 M_⊙, because inflow entropy tracks the virial relation. Variants with stronger feedback raise the critical

What carries the argument

Self-limited entropy ceiling for AGN outflows derived from Rankine-Hugoniot relations, which caps injected entropy at a fixed value independent of halo mass.

If this is right

  • Stronger feedback raises the entropy ceiling and shifts the critical mass to 10^14 solar masses while weaker feedback lowers it to 10^13.5 solar masses.
  • Above the critical mass outflows stall and may form a termination shock near the splashback radius.
  • Virial gas fractions rise with halo mass from 10^13 solar masses onward because reincorporation during halo expansion dominates over permanent outflows.
  • Groups below the threshold show depleted gas while clusters retain close to the cosmic baryon fraction.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The mass threshold could appear as a sharp transition in observed gas content between groups and clusters.
  • Gas reincorporation during halo growth may affect long-term star formation in central galaxies.
  • Analogous self-limitation could arise in other feedback processes if shock heating sets the entropy scale.

Load-bearing premise

Inflow entropy tracks the virial relation with halo mass so the fixed outflow ceiling exceeds it and permits escape only below the critical mass.

What would settle it

Entropy profiles or gas fraction measurements in halos spanning 10^13 to 10^14 solar masses that confirm whether outflows escape below 10^13.7 solar masses and stall above it.

Figures

Figures reproduced from arXiv: 2605.16483 by Andrew Pontzen, Hiranya V. Peiris, Joop Schaye, Matthieu Schaller.

Figure 1
Figure 1. Figure 1: FIG. 1. The gas-to-total ratio as a function of physical radius mea [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The non-gravitational energy flux (enthalpy + kinetic energy) [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The average outflow (solid) and inflow (dashed) rates as a [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The entropy in gas inflows and outflows at the virial radius [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Summary of FLAMINGO’s feedback variants in terms of [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Stacked flow and entropy plots for Fiducial (top panels) and Jet fgas [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
read the original abstract

We use FLAMINGO to investigate why feedback from active galactic nuclei (AGN) significantly depletes gas in galaxy groups but is ineffective in clusters. We delineate three radial zones: an inner zone where AGN feedback heats halo gas via shocks; an intermediate buoyancy zone where the heated halo gas rises; and an outer zone where the outflow may stall in a termination shock. Heating in the inner zone self-limits because, once the gas is sufficiently hot, shocks become too weak to deposit further entropy. Consequently, outflows have a ceiling entropy value ($360\, {\rm keV\, cm^2}$) that is nearly independent of halo mass. These values (and trends with redshift and feedback variants) are explained using an argument based on the Rankine-Hugoniot relations. Outflows rise at fixed entropy through the buoyancy zone, escaping the halo if the ceiling value is sufficiently elevated over that of the inflowing gas. This condition is satisfied only for halo masses $M_{\rm 200m}<10^{13.7}\,{\rm M_\odot}$, because inflow entropy tracks the virial relation. Variants with stronger (or weaker) feedback have a higher (or lower) entropy ceiling and a correspondingly modified critical mass of $M_{\rm 200m}=10^{14.0}\,{\rm M_\odot}$ (or $10^{13.5}\,{\rm M_\odot}$). In clusters above the critical mass, the increased inflow entropy causes the outflow to stall and potentially shock at the 'splashback' radius. We derive an expression for the time evolution of the virial gas fraction, which shows how lingering gas is reincorporated as the halo virial radius expands. This effect dominates over outflows unless they rejoin the Hubble flow; as a result, virial gas fractions rise as a function of mass starting at $M_{\rm 200m} = 10^{13.0}\,{\rm M_\odot}$. These effects explain why groups have depleted gas, while clusters have close to the cosmic baryon fraction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses the FLAMINGO simulations to explain the mass-dependent effectiveness of AGN feedback, arguing that shocks in an inner zone self-limit to produce a nearly mass-independent entropy ceiling of 360 keV cm² via Rankine-Hugoniot relations. Outflows then rise buoyantly and escape only below a critical halo mass of 10^13.7 M_⊙ (with variants shifting this to 10^13.5–10^14.0 M_⊙), because inflow entropy follows the virial scaling; above this mass the outflow stalls. The paper also derives an analytic expression for the time evolution of the virial gas fraction that incorporates reincorporation as the halo grows, accounting for the rise in baryon fraction with mass above ~10^13 M_⊙.

Significance. If the central claims hold, the work supplies a physically grounded mechanism for why AGN feedback depletes gas in groups but leaves clusters near the cosmic baryon fraction, with the Rankine-Hugoniot derivation and feedback-variant trends providing a clear, testable prediction. The analytic gas-fraction evolution further links the result to observable halo growth. The combination of simulation trends with a parameter-light analytic argument is a notable strength.

major comments (2)
  1. [§3] §3 (inner-zone analysis): the entropy ceiling of 360 keV cm² is stated to be nearly independent of halo mass and derived from Rankine-Hugoniot relations, but the manuscript must show the explicit steps that yield this numerical value and demonstrate its mass independence across the simulated halo range (e.g., by plotting the post-shock entropy versus M_200m).
  2. [§4.1] §4.1 (buoyancy and escape condition): the sharp critical mass at 10^13.7 M_⊙ rests on the assumption that inflow entropy tracks the virial relation K_in ∝ M^{2/3}. The paper should quantify the scatter and systematic deviations from this scaling in the simulations (including any contribution from filaments or prior feedback) to establish whether the threshold remains abrupt or becomes gradual.
minor comments (2)
  1. [Figure 3] Figure 3: the termination-shock radius is difficult to read against the background; increase line contrast or add a shaded band.
  2. [Eq. (7)] Eq. (7): the symbols for the time-dependent virial radius and gas fraction are introduced without a preceding definition list; add an explicit symbol table.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed report. The comments identify opportunities to strengthen the clarity of our derivations and the supporting analysis from the simulations. We respond to each major comment below and describe the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (inner-zone analysis): the entropy ceiling of 360 keV cm² is stated to be nearly independent of halo mass and derived from Rankine-Hugoniot relations, but the manuscript must show the explicit steps that yield this numerical value and demonstrate its mass independence across the simulated halo range (e.g., by plotting the post-shock entropy versus M_200m).

    Authors: We agree that the explicit derivation steps should be shown in full. The current manuscript summarizes the Rankine-Hugoniot argument for the self-limiting entropy ceiling, but we will expand §3 in the revised version to include the complete step-by-step calculation, including the relevant jump conditions, the assumptions about pre-shock conditions, and how the ceiling value of 360 keV cm² emerges independently of halo mass. We will also add a new figure displaying post-shock entropy versus M_200m across the simulated halo sample to demonstrate the near mass-independence directly. revision: yes

  2. Referee: [§4.1] §4.1 (buoyancy and escape condition): the sharp critical mass at 10^13.7 M_⊙ rests on the assumption that inflow entropy tracks the virial relation K_in ∝ M^{2/3}. The paper should quantify the scatter and systematic deviations from this scaling in the simulations (including any contribution from filaments or prior feedback) to establish whether the threshold remains abrupt or becomes gradual.

    Authors: We acknowledge that quantifying the scatter strengthens the justification for the critical mass. While the manuscript relies on the average virial scaling for inflow entropy, which is supported by the simulations, we will add an explicit analysis in the revised §4.1. This will report the measured scatter around K_in ∝ M^{2/3}, discuss systematic deviations, and address possible contributions from filamentary accretion and earlier feedback episodes. The additional material will allow readers to assess whether the escape threshold is best described as abrupt or somewhat gradual, while preserving the central conclusion that the transition occurs near 10^{13.7} M_⊙. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent Rankine-Hugoniot and virial relations

full rationale

The paper derives the mass-independent entropy ceiling of 360 keV cm² directly from Rankine-Hugoniot shock relations applied to the inner zone, as an explanatory argument for the self-limiting heating. The critical halo mass threshold is obtained by comparing this fixed ceiling against the inflow entropy, which is stated to track the standard virial scaling relation (an external, well-established result from gravitational collapse physics, not fitted or derived within the paper). No load-bearing step reduces by construction to a fit, self-definition, or self-citation chain; the central claim retains independent content from standard shock physics and virial theorem scalings. The derivation is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard hydrodynamic shock relations and a domain assumption about inflow entropy; no new particles or forces are introduced.

free parameters (1)
  • feedback strength variants
    Stronger or weaker AGN feedback is shown to shift the entropy ceiling and critical mass, but the baseline ceiling is derived rather than fitted.
axioms (2)
  • standard math Rankine-Hugoniot relations govern entropy deposition in AGN-driven shocks
    Invoked to derive the self-limiting ceiling entropy of 360 keV cm².
  • domain assumption Inflowing gas entropy follows the virial scaling with halo mass
    Used to determine the mass below which the ceiling entropy exceeds inflow entropy.

pith-pipeline@v0.9.0 · 5919 in / 1452 out tokens · 67427 ms · 2026-05-20T16:07:31.512887+00:00 · methodology

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Reference graph

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