AGNeject2: AGN Hot Gas Ejection Mode

• AGNeject2 is an AGN feedback mode that ejects the excess hot gas from galaxy halos, addressing the overprediction of baryon fractions in intermediate-mass systems.
• It employs an energy surplus criterion, activating only when AGN power exceeds cooling needs, thereby selectively removing hot gas while leaving cold gas and stellar components untouched.
• The model predicts late-time, mass-dependent ejection that produces a U-shaped baryon fraction trend in group-scale halos, aligning with observational constraints from X-ray and SZ studies.

Searching arXiv for AGNeject2 and FEGA25-related papers to ground the article in the current literature. AGNeject2 is a hot-gas ejection mode for active galactic nucleus feedback in the FEGA25 semi-analytic model of galaxy formation and evolution. It is introduced as one of two alternative implementations of an AGN-driven process that removes hot gas from the halo and ejects it beyond the virial radius, while leaving the cold gas and stellar components untouched. In FEGA25, AGNeject2 supplements the standard negative AGN feedback mode, which suppresses cooling, and a positive AGN mode, which triggers star formation. Its defining feature is that it uses only the excess AGN energy beyond that required to quench cooling to eject a portion of the hot halo gas, thereby addressing the overprediction of hot gas fractions in low- and intermediate-mass halos that has persisted in both semi-analytic models and hydrodynamical simulations (Contini et al., 14 Jul 2025).

1. Definition and motivation

AGNeject2 is formulated within FEGA25 as an AGN feedback implementation that transfers hot gas from the halo reservoir to an ejected reservoir located beyond the virial radius. The mode is explicitly designed to act on the hot gas component alone. This selective action is central to its role in the baryon cycle, because the stated objective is to reduce the hot gas fraction in Milky Way–to–group scale halos without directly modifying stellar masses or cold gas masses (Contini et al., 14 Jul 2025).

The motivation is both modeling-driven and physically motivated. The modeling issue is that semi-analytic models and hydrodynamical simulations have long tended to overpredict the hot gas fraction in halos with roughly $\log M_{\rm halo}\sim 12{-}13$, and supernova feedback alone cannot reduce the hot gas to the levels implied by observational baryon budgets. The physical intuition is that, in radio-mode AGN feedback, AGN heating is usually treated as a preventative process that offsets radiative cooling, but in many halos the AGN power can exceed what is required to balance cooling. AGNeject2 operationalizes the idea that this surplus energy can do additional work by lifting hot gas out of the halo potential well (Contini et al., 14 Jul 2025).

This makes AGNeject2 distinct from a purely phenomenological ejection prescription. The paper explicitly characterizes it as more physically motivated because the ejection channel is triggered by the AGN energy budget after the cooling requirement has already been met. A plausible implication is that AGNeject2 is intended not merely as a fit to baryon fractions, but as a minimal phenomenological encoding of mechanically driven AGN outflows and cavity work in halo gas.

2. Mathematical formulation within FEGA25

AGNeject2 is built on the same radio-mode AGN prescription used by AGNeject1. Hot gas accretes onto the central black hole at a rate

$$\dot{M}_{\rm BH} = \kappa_{\rm AGN} \left(\frac{f_{\rm hot}}{0.1}\right) \left(\frac{V_{200}}{200\,{\rm km\,s^{-1}}}\right)^3 \left(\frac{M_{\rm BH}}{10^8\,M_\odot/h}\right).$$

The associated radio or mechanical power is

$$\dot{E}_{\rm radio} = \eta_{\rm rad}\,\dot{M}_{\rm BH} c^2, \qquad \eta_{\rm rad} = 0.1.$$

This power reduces the effective cooling rate according to

$$\dot{M}_{\rm cool,new} = \dot{M}_{\rm cool} - 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$

If the AGN power is large enough, $\dot{M}_{\rm cool,new}$ reaches zero and cooling is fully quenched. AGNeject2 acts only when the AGN power exceeds this threshold, i.e. when

$$\dot{M}_{\rm cool} < 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$

The amount of gas associated with this surplus is denoted $M_{\rm excess}$. The paper does not provide an explicit closed-form expression for $M_{\rm excess}$ in terms of $\dot{E}_{\rm radio}$, but defines it conceptually as the amount of gas that could be heated or affected by the excess of AGN power over the cooling power (Contini et al., 14 Jul 2025).

The AGNeject2 ejection law is then

$$M_{\rm ejected} = M_{\rm excess}\left(1 - \frac{V_{200}}{V_{\rm scale}}\right),$$

with the understanding that $$\dot{M}_{\rm BH} = \kappa_{\rm AGN} \left(\frac{f_{\rm hot}}{0.1}\right) \left(\frac{V_{200}}{200\,{\rm km\,s^{-1}}}\right)^3 \left(\frac{M_{\rm BH}}{10^8\,M_\odot/h}\right).$$0 if $$\dot{M}_{\rm BH} = \kappa_{\rm AGN} \left(\frac{f_{\rm hot}}{0.1}\right) \left(\frac{V_{200}}{200\,{\rm km\,s^{-1}}}\right)^3 \left(\frac{M_{\rm BH}}{10^8\,M_\odot/h}\right).$$1 or if there is no surplus energy. The factor $$\dot{M}_{\rm BH} = \kappa_{\rm AGN} \left(\frac{f_{\rm hot}}{0.1}\right) \left(\frac{V_{200}}{200\,{\rm km\,s^{-1}}}\right)^3 \left(\frac{M_{\rm BH}}{10^8\,M_\odot/h}\right).$$2 imposes a halo-potential dependence: deeper potential wells eject a smaller fraction of the excess-affected gas. In the calibration adopted for AGNeject2, the parameters are

• $$\dot{M}_{\rm BH} = \kappa_{\rm AGN} \left(\frac{f_{\rm hot}}{0.1}\right) \left(\frac{V_{200}}{200\,{\rm km\,s^{-1}}}\right)^3 \left(\frac{M_{\rm BH}}{10^8\,M_\odot/h}\right).$$3
• $$\dot{M}_{\rm BH} = \kappa_{\rm AGN} \left(\frac{f_{\rm hot}}{0.1}\right) \left(\frac{V_{200}}{200\,{\rm km\,s^{-1}}}\right)^3 \left(\frac{M_{\rm BH}}{10^8\,M_\odot/h}\right).$$4
• $$\dot{M}_{\rm BH} = \kappa_{\rm AGN} \left(\frac{f_{\rm hot}}{0.1}\right) \left(\frac{V_{200}}{200\,{\rm km\,s^{-1}}}\right)^3 \left(\frac{M_{\rm BH}}{10^8\,M_\odot/h}\right).$$5

The ejected gas is not irreversibly lost. FEGA25 includes four baryonic reservoirs—stars, cold gas, hot gas within $$\dot{M}_{\rm BH} = \kappa_{\rm AGN} \left(\frac{f_{\rm hot}}{0.1}\right) \left(\frac{V_{200}}{200\,{\rm km\,s^{-1}}}\right)^3 \left(\frac{M_{\rm BH}}{10^8\,M_\odot/h}\right).$$6, and ejected gas beyond the virial radius—and the reincorporation law is

$$\dot{M}_{\rm BH} = \kappa_{\rm AGN} \left(\frac{f_{\rm hot}}{0.1}\right) \left(\frac{V_{200}}{200\,{\rm km\,s^{-1}}}\right)^3 \left(\frac{M_{\rm BH}}{10^8\,M_\odot/h}\right).$$7

Thus, “beyond the virial radius” denotes storage in a separate reservoir with finite reincorporation probability rather than permanent expulsion (Contini et al., 14 Jul 2025).

3. Distinction from AGNeject1

AGNeject2 is best understood in contrast to AGNeject1, the alternative hot-gas ejection mode implemented in the same framework. AGNeject1 ejects hot gas according to

$$\dot{M}_{\rm BH} = \kappa_{\rm AGN} \left(\frac{f_{\rm hot}}{0.1}\right) \left(\frac{V_{200}}{200\,{\rm km\,s^{-1}}}\right)^3 \left(\frac{M_{\rm BH}}{10^8\,M_\odot/h}\right).$$8

This ties ejection directly to black hole growth and hot gas mass, modulated by halo velocity, regardless of whether the AGN energy merely balances cooling or substantially exceeds it. The paper therefore characterizes AGNeject1 as essentially phenomenological (Contini et al., 14 Jul 2025).

By contrast, AGNeject2 ties ejection specifically to excess AGN energy beyond that needed to quench cooling. This difference in construction produces different timing and redshift dependence. AGNeject1 yields continuous, moderate ejection over an extended period, whereas AGNeject2 yields delayed but intense late-time ejection once AGN power overtakes the cooling requirement (Contini et al., 14 Jul 2025).

The calibrations also differ. AGNeject1 uses $$\dot{M}_{\rm BH} = \kappa_{\rm AGN} \left(\frac{f_{\rm hot}}{0.1}\right) \left(\frac{V_{200}}{200\,{\rm km\,s^{-1}}}\right)^3 \left(\frac{M_{\rm BH}}{10^8\,M_\odot/h}\right).$$9, $$\dot{E}_{\rm radio} = \eta_{\rm rad}\,\dot{M}_{\rm BH} c^2, \qquad \eta_{\rm rad} = 0.1.$$0, and $$\dot{E}_{\rm radio} = \eta_{\rm rad}\,\dot{M}_{\rm BH} c^2, \qquad \eta_{\rm rad} = 0.1.$$1, whereas AGNeject2 uses $$\dot{E}_{\rm radio} = \eta_{\rm rad}\,\dot{M}_{\rm BH} c^2, \qquad \eta_{\rm rad} = 0.1.$$2, $$\dot{E}_{\rm radio} = \eta_{\rm rad}\,\dot{M}_{\rm BH} c^2, \qquad \eta_{\rm rad} = 0.1.$$3, and $$\dot{E}_{\rm radio} = \eta_{\rm rad}\,\dot{M}_{\rm BH} c^2, \qquad \eta_{\rm rad} = 0.1.$$4 (Contini et al., 14 Jul 2025).

The paper reports the following qualitative contrast in outcomes.

Aspect	AGNeject1	AGNeject2
Ejection basis	BH-growth scaling	Excess-energy scaling
Redshift behavior	Little redshift evolution	Strong late-time evolution
Baryon-fraction trend	Smooth, monotonic increase	U-shaped cavity at $$\dot{E}_{\rm radio} = \eta_{\rm rad}\,\dot{M}_{\rm BH} c^2, \qquad \eta_{\rm rad} = 0.1.$$5

The central distinction is therefore not only algorithmic but phenomenological: AGNeject1 distributes ejective feedback in a broadly continuous way, whereas AGNeject2 concentrates it in the regime where AGN power overshoots cooling.

4. Halo-mass and redshift dependence

AGNeject2 contains no explicit redshift term in its ejection law. Its redshift dependence emerges dynamically from the evolution of black hole mass, halo mass, and the frequency with which radio-mode AGN power exceeds the cooling requirement. The reported outcome is that AGN ejection efficiency is essentially zero across all halo masses at $$\dot{E}_{\rm radio} = \eta_{\rm rad}\,\dot{M}_{\rm BH} c^2, \qquad \eta_{\rm rad} = 0.1.$$6, becomes noticeable but still small around $$\dot{E}_{\rm radio} = \eta_{\rm rad}\,\dot{M}_{\rm BH} c^2, \qquad \eta_{\rm rad} = 0.1.$$7, and rises rapidly from $$\dot{E}_{\rm radio} = \eta_{\rm rad}\,\dot{M}_{\rm BH} c^2, \qquad \eta_{\rm rad} = 0.1.$$8 to $$\dot{E}_{\rm radio} = \eta_{\rm rad}\,\dot{M}_{\rm BH} c^2, \qquad \eta_{\rm rad} = 0.1.$$9, especially for $$\dot{M}_{\rm cool,new} = \dot{M}_{\rm cool} - 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$0 (Contini et al., 14 Jul 2025).

The model therefore activates primarily at late times, $$\dot{M}_{\rm cool,new} = \dot{M}_{\rm cool} - 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$1. In the paper’s interpretation, this is the epoch when black holes in intermediate-mass halos are sufficiently massive, cooling flows are moderate, and AGN power can exceed cooling dramatically. This late activation is a defining empirical behavior of AGNeject2 and differentiates it from AGNeject1’s comparatively redshift-independent action (Contini et al., 14 Jul 2025).

Its halo-mass dependence is likewise sharply structured. At $$\dot{M}_{\rm cool,new} = \dot{M}_{\rm cool} - 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$2, AGN ejection efficiency in AGNeject2 peaks around $$\dot{M}_{\rm cool,new} = \dot{M}_{\rm cool} - 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$3 at approximately $$\dot{M}_{\rm cool,new} = \dot{M}_{\rm cool} - 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$4 of the halo mass in gas ever ejected by AGN. The range in which AGN ejection dominates over supernova ejection is roughly $$\dot{M}_{\rm cool,new} = \dot{M}_{\rm cool} - 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$5 at $$\dot{M}_{\rm cool,new} = \dot{M}_{\rm cool} - 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$6. Below $$\dot{M}_{\rm cool,new} = \dot{M}_{\rm cool} - 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$7, supernova feedback dominates baryon removal, while at very high masses, $$\dot{M}_{\rm cool,new} = \dot{M}_{\rm cool} - 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$8, supernovae and AGN contribute comparably, at the level of a few percent each, to total ejected mass (Contini et al., 14 Jul 2025).

This produces a tripartite feedback regime within FEGA25. Low-mass halos are supernova-dominated; intermediate-mass group-scale halos at late times are AGNeject2-dominated; and massive groups and clusters exhibit mixed SN and AGN contributions. A plausible implication is that AGNeject2 is specifically tuned to the group regime where preventative feedback alone is insufficient to reproduce the observed baryon budget.

5. Effects on baryon fractions and galaxy properties

The principal observable consequence of AGNeject2 is a cavity in the baryon fraction–halo mass relation at $$\dot{M}_{\rm cool,new} = \dot{M}_{\rm cool} - 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$9. In the model, the total baryon fraction inside $\dot{M}_{\rm cool,new}$0, normalized to the cosmic value, dips strongly around $\dot{M}_{\rm cool,new}$1 and rises again at both lower and higher masses, producing a U-shaped feature. The paper attributes this cavity almost entirely to the hot gas component: the normalized hot gas fraction exhibits a corresponding depression over the same mass range (Contini et al., 14 Jul 2025).

On cluster scales, AGNeject2 yields a baryon fraction of approximately $\dot{M}_{\rm cool,new}$2 of the universal value and a hot gas fraction of approximately $\dot{M}_{\rm cool,new}$3. The paper states that this implies that approximately $\dot{M}_{\rm cool,new}$4 of the baryons inside massive cluster halos are in hot gas, with the remainder in stars and negligible cold gas (Contini et al., 14 Jul 2025).

A notable feature of AGNeject2 is that these strong changes in the halo baryon budget do not visibly affect the stellar-to-halo mass relation for central galaxies. Both AGNeject1 and AGNeject2 are calibrated to the same observed stellar mass functions from $\dot{M}_{\rm cool,new}$5 to $\dot{M}_{\rm cool,new}$6, and both reproduce them well. AGNeject2 matches the Moster (2013) empirical stellar-to-halo mass relation at $\dot{M}_{\rm cool,new}$7, agrees with observational estimates and with the SHARK2 semi-analytic model at $\dot{M}_{\rm cool,new}$8, and does not visibly differ from AGNeject1 in this relation (Contini et al., 14 Jul 2025).

The paper also emphasizes that the hot gas ejection mode is constructed to preserve cold gas and stars. Detailed HI or H$\dot{M}_{\rm cool,new}$9 plots are not presented, but the stated design principle is that AGNeject2 leaves cold gas and stars untouched, modifying only the hot and ejected gas budgets. The main observational signatures are therefore expected in X-ray and SZ inferences of hot gas fractions and total baryon fractions, rather than in cold-gas scaling relations (Contini et al., 14 Jul 2025).

6. Relation to simulations, observations, and the broader FEGA25 framework

AGNeject2 is compared to major hydrodynamical simulations at $$\dot{M}_{\rm cool} < 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$0. In this comparison, EAGLE exhibits a monotonic rise of baryon fraction with halo mass, whereas IllustrisTNG and SIMBA show a pronounced cavity in the group regime. AGNeject1 resembles EAGLE in producing no cavity, while AGNeject2 produces a cavity similar in spirit to IllustrisTNG and SIMBA, though with different depth and mass location (Contini et al., 14 Jul 2025).

The model is also compared to observational constraints on total baryon fractions and hot gas fractions from X-ray and SZ compilations, including datasets associated with Chiu et al. (2016), Akino et al. (2022), and a range of studies summarized in the paper. Both AGNeject1 and AGNeject2 match observed hot gas fractions reasonably well over the mass range where data exist, namely $$\dot{M}_{\rm cool} < 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$1 at $$\dot{M}_{\rm cool} < 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$2. The cavity predicted by AGNeject2 is reported to be consistent with the scatter in current data, especially because observational uncertainties are large below $$\dot{M}_{\rm cool} < 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$3. The paper therefore concludes that current data cannot yet rule out either a cavity-like or a monotonic baryon fraction relation, and identifies more precise measurements below $$\dot{M}_{\rm cool} < 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$4 as crucial (Contini et al., 14 Jul 2025).

Within FEGA25, AGNeject2 is one component of a three-mode AGN feedback architecture:

1. Negative radio mode, which suppresses cooling via the radio-mode accretion and cooling-subtraction equations.
2. Positive mode, triggered when $$\dot{M}_{\rm cool} < 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$5, with

$$\dot{M}_{\rm cool} < 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$6

1. Hot gas ejection mode, implemented as either AGNeject1 or AGNeject2, but not both in the same run.

Supernova feedback coexists with these AGN modes by heating cold gas, transferring it to the hot phase, and ejecting some hot gas into the ejected reservoir through its own energy budget. In the FEGA25 + AGNeject2 configuration, the combined feedback system matches stellar mass functions and stellar-to-halo mass relation evolution while using AGNeject2 to selectively remove hot halo gas (Contini et al., 14 Jul 2025).

7. Interpretation, limitations, and open issues

The paper presents AGNeject2 as more physically motivated than AGNeject1 because it ties ejection to an explicit excess-energy criterion rather than directly to black hole growth. Even so, it also states clear limitations. The mapping from surplus AGN energy to ejected mass remains phenomenological, particularly through the simple linear factor $$\dot{M}_{\rm cool} < 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$7. The reincorporation physics is likewise simplified, being governed by a single parameter $$\dot{M}_{\rm cool} < 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$8 and a timescale $$\dot{M}_{\rm cool} < 2 \frac{\dot{E}_{\rm radio}}{V_{200}^2}.$$9 that do not depend on environment or detailed outflow physics (Contini et al., 14 Jul 2025).

Another limitation is that FEGA25 is calibrated only on stellar mass functions. Baryon and hot gas fractions are therefore predictions rather than calibration targets. This is methodologically significant: AGNeject2 is not fitted directly to the gas observables that motivate it. The paper also notes degeneracies with supernova feedback, since both SN and AGN contribute to gas ejection and different combinations of efficiencies can yield similar baryon fractions (Contini et al., 14 Jul 2025).

Future development is described in terms of more physical AGN–gas coupling prescriptions, potentially based on jet mode versus quasar mode, Eddington ratio, or black hole spin; environment-dependent reincorporation; and joint calibration to stellar and gas or baryon observables (Contini et al., 14 Jul 2025). This suggests that AGNeject2 should be understood as an intermediate-level phenomenological model: more constrained by physical intuition than a purely empirical scaling, but not yet a first-principles treatment of AGN-driven halo gas ejection.

In that broader perspective, AGNeject2 occupies a specific conceptual niche in galaxy-formation modeling. It is an energy-budget–driven ejective AGN feedback channel designed to resolve the hot-gas excess of intermediate-mass halos while preserving the successful reproduction of stellar observables. Its characteristic prediction is a late-time, group-scale depletion of hot halo gas that produces a U-shaped baryon-fraction feature at $M_{\rm excess}$0, closely linking AGN feedback energetics to the modeled baryon cycle (Contini et al., 14 Jul 2025).