AGNeject1: Hot Gas Ejection in Galaxy Evolution

• AGNeject1 is a feedback channel in the FEGA25 framework that selectively ejects hot gas beyond the virial radius, distinct from other AGN modes.
• It continuously scales with radio-mode black-hole accretion and halo virial velocity to ensure smooth, redshift-independent hot gas depletion.
• The mechanism addresses observed baryon deficits in group-scale halos by preventing excessive hot gas retention while preserving cold gas and stars.

AGNeject1 is a feedback channel in the FEGA25 semi-analytic framework for galaxy formation and evolution, introduced as a third AGN mode to eject hot gas beyond $R_{\rm vir}$ without affecting cold gas or stars. It was designed to address a persistent discrepancy in semi-analytic models and hydrodynamical simulations: halos of group scale, $\log M_{\rm halo}\approx 12\!-\!13$, tend to retain too much hot gas, whereas X-ray and Sunyaev–Zel’dovich observations suggest that these systems are significantly baryon-depleted. Within FEGA25, AGNeject1 is distinct from the negative mode, which suppresses cooling, and the positive mode, which boosts a residual starburst; its defining feature is selective removal of the hot phase through a continuous coupling to radio-mode black-hole accretion, producing a smooth, nearly redshift-independent depletion of hot gas (Contini et al., 14 Jul 2025).

1. Physical motivation and problem setting

In FEGA25, the introduction of AGNeject1 is tied to the difficulty of reproducing the baryonic content of low- and intermediate-mass halos when only supernova and conventional AGN feedback channels are used. The specific problem is the overestimation of hot-gas fractions in halos of group scale. Supernova feedback alone cannot eject hot gas out of these relatively deep potential wells without also over-quenching star formation in lower-mass systems. Traditional AGN radio-mode feedback, formulated only as mechanical heating that offsets cooling, likewise leaves hot baryons inside the virial volume.

The observational motivation is correspondingly specific. X-ray and Sunyaev–Zel’dovich constraints indicate that group-scale systems are baryon-depleted. AGNeject1 was therefore conceived as a physically motivated mechanism that removes hot gas entirely beyond $R_{\rm vir}$, rather than only reducing the net cooling rate. In the broader FEGA25 results, supernova feedback dominates gas ejection in halos with $\log M_{\rm halo}<$ approximately $12$, while AGN feedback becomes increasingly important at higher halo masses (Contini et al., 14 Jul 2025).

2. Position within the FEGA25 feedback architecture

FEGA25 separates AGN feedback into multiple channels. The negative mode is a mechanical-heating channel that offsets cooling and reduces the net cooling rate. The positive mode operates when the radio energy is insufficient to fully quench the flow; in that case, any residual cooling triggers a secondary starburst proportional to black-hole growth. Neither of these channels removes hot gas from the halo.

AGNeject1 is the third AGN mode. It postulates that some fraction of the same mechanical power that suppresses cooling can instead, or in addition, drive an outflow of hot gas beyond $R_{\rm vir}$. Its conceptual distinction from AGNeject2 is central. AGNeject1 does not wait for excess energy beyond that needed to offset cooling. Instead, it continuously scales with the instantaneous black-hole accretion and halo virial velocity, so that ejection is active at all epochs and produces a smooth, nearly redshift-independent depletion of hot gas. By construction, it acts on the hot reservoir only and does not perturb the cold phase (Contini et al., 14 Jul 2025).

3. Mathematical formulation

In FEGA25, the hot gas ejected by AGN in AGNeject1 during a timestep $dt$ is

$$M_{\rm ejected} = \left(\frac{\delta M_{\rm BH}}{M_{\rm BH}}\right) \left(\frac{M_{\rm hot}}{10^{8}\,M_\odot/h}\right) \left(1-\frac{V_{200}}{V_{\rm scale}}\right),$$

where $\delta M_{\rm BH}=\dot M_{\rm BH}\,dt$ is the black-hole mass growth by radio-mode accretion, $M_{\rm BH}$ is the instantaneous black-hole mass, $\log M_{\rm halo}\approx 12\!-\!13$0 is the hot-gas mass in the halo, $\log M_{\rm halo}\approx 12\!-\!13$1 is the halo circular velocity at $\log M_{\rm halo}\approx 12\!-\!13$2, and $\log M_{\rm halo}\approx 12\!-\!13$3 is a tunable velocity threshold. Whenever $\log M_{\rm halo}\approx 12\!-\!13$4, $\log M_{\rm halo}\approx 12\!-\!13$5 is set to zero.

The black-hole accretion rate in the standard radio mode is

$\log M_{\rm halo}\approx 12\!-\!13$6

The corresponding mechanical power is

$\log M_{\rm halo}\approx 12\!-\!13$7

and the modified cooling rate is

$\log M_{\rm halo}\approx 12\!-\!13$8

Because AGNeject1 multiplies the fractional black-hole growth $\log M_{\rm halo}\approx 12\!-\!13$9 by the hot-gas reservoir, normalized to $R_{\rm vir}$0, and by a factor that weakens with increasing $R_{\rm vir}$1, it ensures that more massive halos are harder to purge, while the ejection channel remains continuously active whenever black-hole accretion proceeds (Contini et al., 14 Jul 2025).

4. Free parameters and calibration

The free parameters in AGNeject1 are $R_{\rm vir}$2, the radio-mode accretion efficacy; $R_{\rm vir}$3, the velocity threshold in the ejection law; and $R_{\rm vir}$4, the reincorporation efficiency governing how ejected gas returns. The reincorporation timescale $R_{\rm vir}$5 enters later in the model.

These parameters were constrained via Markov Chain Monte Carlo against the observed stellar mass functions from $R_{\rm vir}$6 to $R_{\rm vir}$7, using merger trees from the YS50HR, YS200, and YS300 $R_{\rm vir}$8-body simulations. For the AGNeject1 configuration, the best-fit values are as follows (Contini et al., 14 Jul 2025).

Parameter	Role	Best-fit value
$R_{\rm vir}$9	radio-mode accretion efficacy	$\log M_{\rm halo}<$0
$\log M_{\rm halo}<$1	velocity threshold	$\log M_{\rm halo}<$2
$\log M_{\rm halo}<$3	reincorporation efficiency	$\log M_{\rm halo}<$4

No explicit redshift-dependent modifiers are included in AGNeject1. Its activation therefore depends only on the evolving $\log M_{\rm halo}<$5, $\log M_{\rm halo}<$6, and $\log M_{\rm halo}<$7. This is the formal basis for its time-smooth behavior.

5. Redshift behavior and baryon-fraction trends

Because AGNeject1 scales directly with $\log M_{\rm halo}<$8 and does not require a threshold excess energy above that needed to quench cooling, it operates smoothly whenever the central black hole is accreting in radio mode. In practice, $\log M_{\rm halo}<$9 evolves steadily from high to low redshift, and $12$0 grows only gradually with halo assembly, so the combination in the ejection law yields a nearly constant ejection efficacy across cosmic time.

The impact on halo baryons is quantified through the total baryon fraction

$12$1

For AGNeject1, $12$2 rises monotonically from $12$3 at $12$4 to $12$5 at $12$6, with almost no evolution from $12$7 to $12$8. There is no U-shaped cavity; the behavior is a gentle, mass-dependent rise. The normalized hot-gas mass, $12$9, climbs from $R_{\rm vir}$0 to $R_{\rm vir}$1 over the same mass range, again with minimal redshift drift. By continuously ejecting hot gas in all halos above the supernova-driven regime, AGNeject1 reproduces the broad observational constraints on baryon-to-halo mass scaling without generating redshift-dependent cavity features (Contini et al., 14 Jul 2025).

6. Preservation of the cold phase, stellar-halo relation, and contrast with AGNeject2

AGNeject1 acts exclusively on the hot phase by transferring $R_{\rm vir}$2 from the hot reservoir to an external ejecta reservoir. It therefore leaves the cold gas disk and existing stellar populations untouched. In FEGA25, the star-formation history and final stellar masses of central galaxies remain governed by the standard cooling and supernova-regulated star-formation cycle. Consistent with that construction, AGNeject1 matches the empirical and semi-empirical stellar-to-halo mass relations of Moster (2013) and observational estimates out to $R_{\rm vir}$3, with no degradation relative to the version without hot ejection.

The contrast with AGNeject2 clarifies the meaning of AGNeject1. AGNeject2 ties hot-gas removal to surplus radio-mode energy,

$R_{\rm vir}$4

together with the same $R_{\rm vir}$5 factor. In that formulation, hot-gas ejection remains negligible until $R_{\rm vir}$6, when AGN energy increasingly exceeds cooling needs. The resulting late-time onset generates a characteristic cavity, a U-shaped feature in the baryon fraction at redshift zero, similar to trends observed in SIMBA and IllustrisTNG. AGNeject1 avoids that behavior: it yields a smoother, redshift-independent evolution. Within the FEGA25 framework, it is therefore a minimal, continuous hot-gas removal channel linked to the same black-hole physics that drives standard radio-mode feedback, while preserving the stellar and cold-gas components and reproducing the stellar-to-halo mass relation up to redshift $R_{\rm vir}$7 (Contini et al., 14 Jul 2025).