Cooling and AGN Heating

This page covers how gas moves from the hot/CGM reservoir into the cold disk, how AGN radio-mode feedback suppresses that flow, and how SAGE26’s two-regime CGM model selects between classical hot-halo cooling and precipitation-driven CGM cooling.

Source: src/model_cooling_heating.c

Called from: Per-halo physics loop – step 8 of the substep ordering.

The two cooling regimes

A central galaxy is classified once per snapshot by determine_and_store_regime() based on the Dekel & Birnboim (2006) shock mass M_shock ~ 6 x 10^11 Msun (modulated by redshift via Z_CRIT_DB06 = 1.5):

Regime 0 (CGM): halo is below M_shock (or above it but at z < z_crit where cold streams penetrate). Cooling proceeds via the Voit (2015) precipitation criterion on the CGMgas reservoir.
Regime 1 (hot halo): halo is above M_shock and has a stable virial shock. Cooling proceeds via the classical Croton+06 isothermal recipe on the HotGas reservoir, optionally with a Dekel & Birnboim cold-stream fraction blended in.

When CGMrecipeOn = 0, every galaxy uses Regime 1 unconditionally and the CGMgas reservoir is unused.

Dispatcher – `cooling_recipe_regime_aware()`

The top-level entry point. Both regimes can produce some cooling from both reservoirs:

Galaxy regime	Primary path	Secondary path
Regime 0 (CGM)	`cooling_recipe_cgm()` on `CGMgas`	–
Regime 1 (hot)	`cooling_recipe_hot()` on `HotGas`	`cooling_recipe_cgm()` on any residual `CGMgas`

The secondary CGM path for Regime 1 ensures that any leftover CGMgas (typical of a halo that crossed M_shock mid-life) drains naturally rather than being frozen.

After computing the cooled masses, the dispatcher transfers them into ColdGas in-place, tracking metallicity from each donor reservoir separately.

`cooling_recipe_hot()` – Regime 1 (classical hot halo)

Compute the virial temperature T_vir = VIRIAL_TEMP_COEFF * Vvir^2 = 35.9 * Vvir^2 (K, with Vvir in km/s).
Look up the metal-dependent cooling rate Lambda(T, Z) from the Sutherland & Dopita (1993) tables via get_metaldependent_cooling_rate().
Compute the cooling radius r_cool from the isothermal beta-model: the density at which t_cool = t_dyn = R_vir / V_vir.
Pick the cooling regime:
- If r_cool > R_vir: cold accretion – the whole HotGas reservoir cools on the dynamical time.
- If r_cool <= R_vir: hot-halo cooling – mass flux is (HotGas / R_vir) * (r_cool / (2 * t_cool)) per unit time.
If CGMrecipeOn = 1 (Regime 1 only), blend in a Dekel & Birnboim (2006) cold-stream fraction f_stream = (M_vir / M_shock)^(-4/3) * (1 + z) / 2, capped at 0.5 and hard-cut to 0 at z < 1.5 for halos above M_shock.
Apply do_AGN_heating() if AGNrecipeOn > 0.
Return the net cooled mass to the dispatcher.

`cooling_recipe_cgm()` – Regime 0 (precipitation)

The CGM recipe replaces the isothermal cooling-radius construction with a Voit (2015) precipitation criterion based on the ratio of cooling time to free-fall time.

Step 1 – density profile

The CGM gas distribution is selected by CGMDensityProfile (Regime 0 only; Regime 1 always uses uniform for the residual CGMgas drain):

Value	Profile
0	Uniform
1	NFW (concentration from Duffy+08)
2	Beta profile with `beta = 2/3`, core radius `r_c = 0.1 R_vir`

Helper functions nfw_density(), beta_density(), and cgm_density_at_radius() evaluate the profile; cgm_enclosed_mass() returns the enclosed mass at any radius for free-fall calculations.

Step 2 – cooling radius

solve_for_rcool() iteratively finds the radius at which t_cool(r) = t_ff(r). The cooling time is t_cool = (3/2) * mu * m_p * k_B * T / (rho(r) * Lambda(T, Z)), and the free-fall time at that radius is t_ff = sqrt(2 r / g) with g = G M_enc(r) / r^2.

Step 3 – characteristic radius

The precipitation criterion is evaluated at r_cool itself – the traditional Voit-style choice.

Step 4 – precipitation fraction

A smooth logistic sigmoid centred on t_cool / t_ff = 10 with characteristic width 2 sets the precipitation fraction. It falls back to standard cooling on the cooling timescale when the sigmoid is negligible (f < 0.01).

When the gas is “stable” (t_cool / t_ff well above threshold), it cools slowly on the cooling timescale: dM/dt = CGMgas / t_cool. When it is “unstable” (below threshold), it precipitates on the free-fall timescale: dM/dt = f_precip * CGMgas / t_ff.

Step 5 – AGN heating (Regime 0 only)

The CGM cooling is passed to the standard r_heat ratchet, identical to the hot-halo path but capped at R_vir. Suppression formula: coolingGas *= (1 - r_heat / r_cool).

CGMAGNOn = 0 disables CGM-regime AGN coupling entirely (so no accretion from CGMgas); the r_heat suppression still applies so quenching persists after the AGN turns off.

Step 6 – diagnostics

cooling_recipe_cgm() populates several diagnostic fields on the galaxy: tcool, tff, tcool_over_tff, tdeplete, RcoolToRvir. These are the values reported in the HDF5 output for plotting.

AGN radio-mode heating

Two functions implement the AGN suppression for the two regimes. Both share the accretion calculation via the file-private agn_accretion_compute() helper.

`agn_accretion_compute()` – the shared accretion calculation

Computes the BH accretion rate from one of three recipes (AGNrecipeOn = 1, 2, 3), applies the Eddington limit, and derives the corresponding heating mass. Three recipes:

`AGNrecipeOn`	Recipe	Source
1	Empirical Croton+06 eq. 10: scales with `BH_mass / 10^8 Msun`, `(V_vir/200)^3`, `HotGas / M_vir`	Croton+06
2	Bondi-Hoyle accretion: `dM/dt = 2.5 pi G * (3/8) * 0.6 * x * BH_mass * eta`	Bondi (1952)
3	Cold-cloud accretion: triggers when `BH_mass > 1e-4 * M_vir * (r_cool / R_vir)^3`	—

Accretion is then capped at the Eddington rate. The resulting heating mass is converted from accreted mass via AGNheating = (1.34e5 / V_vir)^2 * AGNaccreted (with the coefficient derived from sqrt(2 * eta * c^2)).

`do_AGN_heating()` – Regime 1 (hot halo)

The classical Croton+06 ratchet:

Suppress cooling by (1 - r_heat / r_cool). If r_heat >= r_cool, cooling is fully zeroed.
Compute accretion via agn_accretion_compute(), draw it from HotGas, credit it to BlackHoleMass.
Update r_heat monotonically: `r_heat_new = (AGNheating / coolingGas)
- r_cool; if larger than the stored r_heat`, replace it.

The ratchet is never reduced, so r_heat can only grow over time. In the hot-halo path there is no R_vir cap – once r_heat >= r_cool, cooling stays fully suppressed for that substep.

`do_AGN_heating_cgm()` – Regime 0 (CGM)

Differences from the hot-halo path:

Accretion draws from CGMgas, not HotGas.
After the ratchet updates r_heat, the value is capped at R_vir so the heating radius cannot grow past the halo boundary.

`cool_gas_onto_galaxy()`

For the original SAGE path (CGMrecipeOn = 0), cooling_recipe() calls cool_gas_onto_galaxy() to transfer the cooled gas from HotGas to ColdGas with metallicity tracking. In the regime-aware path the dispatcher does the transfer itself.

Switches and parameters

Parameter	Effect
`CGMrecipeOn`	0 disables the two-regime split entirely; 1 enables it.
`CGMDensityProfile`	CGM density profile: 0 uniform, 1 NFW, 2 beta.
`CGMAGNOn`	Enables AGN heating coupling in the CGM regime.
`AGNrecipeOn`	Radio-mode BH accretion recipe: 0 off, 1 empirical, 2 Bondi-Hoyle, 3 cold-cloud.
`RadioModeEfficiency`	Overall scaling on radio-mode accretion.
`QuasarModeEfficiency`	Used by the merger-driven AGN path – see Mergers and disruption.

See parameters.md for full descriptions and defaults.

References

White & Frenk (1991), ApJ 379, 52 – classical halo cooling framework.
Sutherland & Dopita (1993), ApJS 88, 253 – metal-dependent cooling tables.
Croton et al. (2006), MNRAS 365, 11 – original SAGE cooling and AGN radio-mode prescriptions.
Dekel & Birnboim (2006), MNRAS 368, 2 – shock-mass criterion and cold streams.
McCourt et al. (2012), MNRAS 419, 3319 – thermal instability criterion.
Sharma et al. (2012), MNRAS 420, 3174 – precipitation-limited cooling.
Voit (2015), ApJL 808, L30 – precipitation criterion at t_cool/t_ff = 10.
Duffy et al. (2008), MNRAS 390, L64 – NFW concentration scaling.
Bondi (1952), MNRAS 112, 195 – accretion onto compact objects.
Rybicki & Lightman (1979) – Eddington luminosity.