Mergers and Disruption

This page covers what happens when two galaxies merge or when a satellite is tidally destroyed: how the events are classified, how mass and metals flow between the merging pair, how the starburst and quasar-mode AGN operate, and how the bulge grows in the two-channel SAGE26 model.

Source: src/model_mergers.c

Called from: Per-halo physics loop – step 10 of the substep ordering (the satellite/merger block after the per-galaxy cooling and SF loop).

When this step fires

Each satellite carries a MergTime set when it first becomes a Type 1 (by estimate_merging_time(), computed from a dynamical-friction estimate based on satellite/host mass ratio and the satellite’s orbital radius at infall). At each substep:

MergTime is decremented by deltaT / effective_steps.
If M_vir / baryon_mass <= ThresholdSatDisruption (or the satellite has zero baryons), the satellite is flagged for an event.
If MergTime > 0, the satellite is disrupted to ICS via disrupt_satellite_to_ICS().
If MergTime <= 0, the satellite has reached the central – the event is a merger handled by deal_with_galaxy_merger().

Type 1 satellites merge into the central of the host halo. Type 2 (orphan) satellites merge into whatever was their central at the time their subhalo was lost.

`deal_with_galaxy_merger()` – the merger dispatcher

The function classifies and processes one merger event. Mass ratio is computed from baryonic mass (StellarMass + ColdGas):

mass_ratio = min(m_sat, m_central) / max(m_sat, m_central)

The threshold mass_ratio > ThreshMajorMerger (default 0.3) classifies the event as a major merger; otherwise it is minor. Before any reservoir transfers happen, the function decides where burst stars will go:

Merger type	Central morphology	Burst destination
Major	irrelevant	Merger-driven bulge
Minor	disk-dominated (disk > 0.5 stellar)	Instability bulge
Minor	spheroid-dominated	Merger-driven bulge

This morphology-aware routing is the key SAGE26 change to the original Croton+06 merger model – minor mergers onto disks no longer pollute the merger-driven bulge channel.

Step-by-step execution

add_galaxies_together() – transfers the satellite’s gas, stars, metals, BH mass, and ICS into the central. Regime-aware for the gas reservoirs (CGMgas vs HotGas). The satellite’s existing BulgeMass, MergerBulgeMass, and InstabilityBulgeMass are added to the central’s like-for-like.

The satellite’s disk mass (StellarMass - BulgeMass) is then routed by the central’s post-add morphology:
- Disk-dominated central (disk fraction > 0.5): the satellite’s disk mass joins InstabilityBulgeMass and InstabilityBulgeRadius is updated via Tonini+2016 incremental evolution.
- Spheroid-dominated central: the satellite’s disk mass joins MergerBulgeMass.
Note this is independent of the burst-stars routing decided in deal_with_galaxy_merger() (which uses the pre-add morphology captured before this step runs).
grow_black_hole() – quasar-mode BH accretion if AGNrecipeOn > 0 (see below).
collisional_starburst_recipe() – the merger-driven starburst (see below).
get_bulge_radius() – recomputes the displayed BulgeRadius after bulge masses changed.
calculate_merger_remnant_radius() – energy-conservation calculation for the post-merger bulge radius.
Major merger branch: make_bulge_from_burst() destroys the disk (all stellar mass becomes bulge), sets MergerBulgeRadius from the energy-conservation calculation, stamps TimeOfLastMajorMerger, and marks the satellite mergeType = 2.
Minor merger branch: mark mergeType = 1, stamp TimeOfLastMinorMerger, and either update InstabilityBulgeRadius (disk-dominated central) or MergerBulgeRadius (spheroid-dominated) from the energy-conservation calculation.

Quasar-mode AGN – `grow_black_hole()`

Triggered on every merger (major or minor). Accreted mass is:

BHaccrete = BlackHoleGrowthRate * mass_ratio
            * ColdGas / (1 + (280 km/s / V_vir)^2)

So accretion scales with merger violence and is suppressed in shallow potential wells (the V_vir = 280 km/s floor is hard-coded from Croton+06). The accreted gas is removed from ColdGas with metallicity tracking, deposited into BlackHoleMass, and tallied in QuasarModeBHaccretionMass.

`quasar_mode_wind()` – ejection from quasar-mode energy

Each merger then computes the quasar wind energy:

E_quasar = QuasarModeEfficiency * 0.1 * BHaccrete * c^2

(the 0.1 is the radiative efficiency.) The function compares E_quasar against successive reservoir binding energies:

If E_quasar > 0.5 * ColdGas * V_vir^2, the entire cold reservoir is ejected to EjectedMass.
Then it checks against the hot reservoir (regime-aware: HotGas for Regime 1, CGMgas for Regime 0). If E_quasar exceeds the combined cold + hot energy, the hot reservoir is ejected too.

This is what gives bright quasars the ability to expel the entire baryonic content of low-mass hosts.

`collisional_starburst_recipe()` – the merger starburst

Implements the Somerville+2001 / Cox PhD-thesis form:

eburst = STARBURST_FRAC_COEFF * mass_ratio^STARBURST_MASS_POWER
       = 0.56 * mass_ratio^0.7    (mergers, mode == 0)
eburst = mass_ratio               (disk instabilities, mode == 1)

stars_burst = eburst * gas_for_starburst becomes the burst stellar mass. The gas_for_starburst is normally ColdGas, but when StarburstColdGasOn = 0 and an H2-tracking SFprescription is in use, it is recomputed from the current ColdGas using the same H2 recipe as the disk SF path – this avoids the stale stored H2gas value if SF and feedback have already depleted cold gas earlier in the substep.

The burst then applies SN feedback through the same update_from_feedback() helper used by starformation_and_feedback(), including FIRE scaling when FIREmodeOn = 1, and routes the burst stars into either the MergerBulgeMass or InstabilityBulgeMass channel per the burst_to_merger_bulge flag set in deal_with_galaxy_merger().

The SFR is recorded into SfrBulge[step] (separate from disk SF, which goes into SfrDisk[step]).

The two-channel bulge model

Every bulge-growth path in SAGE26 routes its contribution into one of two channels:

Channel	Mass field	Radius field	Sources
Merger	`MergerBulgeMass`	`MergerBulgeRadius`	Major mergers (whole disk); minor merger bursts onto spheroid-dominated centrals
Instability	`InstabilityBulgeMass`	`InstabilityBulgeRadius`	Toomre instability; minor merger bursts onto disk-dominated centrals

The two channels are tracked independently so that the bulge formation history can be decomposed into merger-driven and secular contributions. The combined BulgeMass = MergerBulgeMass + InstabilityBulgeMass and the displayed BulgeRadius is a mass-weighted average computed by get_bulge_radius() in model_misc.c (Tonini+2016 prescription, BulgeSizeOn = 3).

Merger remnant radii are set via energy conservation (calculate_merger_remnant_radius() – Covington+11). The function uses baryonic mass (stellar + cold gas) and a mass-weighted half-mass radius for each progenitor (disk half-mass = 1.68 * DiskScaleRadius, bulge half-mass = BulgeRadius):

E_init = M1^2 / R1 + M2^2 / R2                  (self-binding)
E_orb  = M1 * M2 / (R1 + R2)                    (orbital interaction)
E_rad  = C_rad * E_init * f_gas                 (radiative dissipation)
R_final = (M1 + M2)^2 / (E_init + E_orb + E_rad)

with C_rad = 2.75 from Covington+11 and f_gas = (ColdGas_1 + ColdGas_2) / (M1 + M2). If the total energy comes out non-positive (very gas-rich pairs at the cap of E_rad), the function falls back to a mass-weighted average of the progenitor radii.

Satellite disruption – `disrupt_satellite_to_ICS()`

When the satellite has reached the central before the merger clock runs out, it is disrupted instead of merged. This is the primary formation channel for intracluster stars – see the dedicated Intracluster stars (ICS) page for the full lifecycle of the ICS reservoir. The function:

Transfers gas to the central (regime-aware: total ColdGas + HotGas + CGMgas goes to the central’s CGMgas if Regime 0 or HotGas if Regime 1).
Transfers ejected mass and pre-existing ICS unchanged.
Disrupts the satellite’s stellar mass – splits it between the central’s ICS and the central’s stellar mass (BCG accretion). The split is controlled by DynamicDisruptionSplit:

Value	Split	Formula
0	Fixed	`f_ICS = FractionDisruptedToICS`
1	Mass-ratio	`f_ICS = 1 - (infallMvir / Mhost)^DisruptionSplitAlpha` – low mass-ratio satellites are stripped on wider orbits and contribute more to ICS. Uses the satellite’s `infallMvir` (frozen at the time of infall), not its current `Mvir`.
2	Mass-ratio with concentration weighting	as mode 1, but with `alpha_eff = DisruptionSplitAlpha * DisruptionSplitCref / c_sat` – concentrated satellites resist stripping and deposit more onto the BCG

The infallMvir / Mhost ratio is clipped to 1.0. If either mass is zero or unknown, the function falls back to the fixed FractionDisruptedToICS.

Records assembly history if TrackICSAssembly = 1: ICS_disrupt accumulates the satellite stellar mass newly disrupted into ICS; ICS_accrete accumulates ICS that the satellite already carried in. ICS_sum_mt tracks the mass-weighted deposit time so that the mean ICS-assembly time reflects when the stars were originally stripped, not when this packet transferred into the central.

The satellite is then marked mergeType = 4 (disrupted to ICS) and will be skipped on subsequent substeps. mergeType values defined in core_allvars.h are: 0 (still active / no event), 1 (minor merger), 2 (major merger), 3 (reserved for disk instability; not currently set by any code path), 4 (disrupted to ICS).

What is NOT in this module

Radio-mode AGN. Handled in model_cooling_heating.c. See Cooling and AGN heating.
Disk SF. Handled in model_starformation_and_feedback.c. See Star formation and feedback.
Toomre disk instability. Implemented in model_disk_instability.c. The starburst it triggers reuses collisional_starburst_recipe(mode=1).
BulgeRadius calculation. Implemented in model_misc.c (get_bulge_radius()). The merger code only sets MergerBulgeRadius and lets get_bulge_radius() derive the displayed BulgeRadius.

Switches and parameters

Parameter	Effect
`AGNrecipeOn`	0 disables quasar-mode BH growth and wind during mergers.
`BlackHoleGrowthRate`	Scaling for `grow_black_hole()` accretion.
`QuasarModeEfficiency`	Coupling between BH accretion energy and wind energy.
`ThreshMajorMerger`	Mass-ratio threshold for major vs minor classification.
`ThresholdSatDisruption`	M_vir/baryon threshold below which a satellite is eligible for an event.
`StarburstColdGasOn`	0 forces the burst to recompute H2 from current ColdGas; 1 uses the stored value.
`DynamicDisruptionSplit`	ICS-vs-BCG split mode for disrupted satellites (0 fixed, 1 mass-ratio, 2 mass-ratio with concentration weighting).
`FractionDisruptedToICS`	Fixed-split fraction (mode 0) or fallback.
`DisruptionSplitAlpha`	Exponent in the mass-ratio split (modes 1 and 2).
`DisruptionSplitCref`	Reference concentration for mode 2.
`BulgeSizeOn`	Bulge radius model (0 off, 1-2 Shen+2003, 3 Tonini+2016 multi-channel).
`TrackICSAssembly`	Record `ICS_disrupt` and `ICS_accrete` assembly history.
`SFprescription`	Used to pick the H2 recipe in the burst when `StarburstColdGasOn = 0`.
`FIREmodeOn`	Applies FIRE scaling to burst SN feedback if enabled.

See parameters.md for full descriptions and defaults.

References

Croton et al. (2006), MNRAS 365, 11 – original SAGE merger and AGN prescriptions.
Somerville et al. (2001), MNRAS 320, 504 – collisional starburst form.
Cox et al. (2008), MNRAS 384, 386 – merger-driven SF efficiency calibration.
Covington et al. (2011), ApJ 743, 76 – energy-conservation remnant radius.
Tonini et al. (2016), MNRAS 459, 4109 – two-channel bulge formation.
Shen et al. (2003), MNRAS 343, 978 – bulge size-mass relation.
Hopkins et al. (2010), MNRAS 401, 1099 – merger-driven bulge growth.
Dynamical-friction merger timescale: Binney & Tremaine (2008) eq. 8.12.