How Do Dynamical Friction and Tidal Stripping Define BCG and Intracluster Light?

Why the BCG-ICL split lacked a physical basis

In galaxy clusters, stellar mass is conventionally divided into the brightest cluster galaxy (BCG) at the centre, smaller orbiting satellites, and the diffuse intracluster light (ICL). In practice the BCG-ICL boundary is not clean: the outer envelope of the BCG blends smoothly into low-surface-brightness light extending to larger radii, and in simulations the remaining stellar distribution around the main halo is similarly continuous.

Because no sharp physical transition is identifiable, studies have adopted a wide range of operational definitions. Simulations often use fixed physical apertures around the central galaxy, of order 30-100 kpc, or a multiple of the stellar half-mass radius. Observations frequently identify the ICL using isophotal thresholds. Dynamical approaches use unbinding criteria or split the stellar component kinematically into a cold central component embedded in a hotter diffuse envelope. No single choice has emerged as uniquely physical or universally applicable.

The paper argues this ambiguity is not merely a naming convention. The light profile of the central galaxy often merges smoothly into the ICL, so the BCG-ICL split is usually imposed on a continuous stellar distribution rather than read from a sharply bimodal one. The study's aim is therefore to define the two components by their dynamical origin instead of by an a posteriori spatial cut.

Tracing BCG stars back through the merger hierarchy

The authors use cluster zoom simulations from the Three Hundred project and begin with a hindcasting approach: they trace stars from the centres of present-day clusters back through the merger hierarchy. The hindcasting sample is 107 clusters, selected because their cluster main branch and the main progenitor of the central stars remain identical to lookback times greater than 10 Gyr (z = 1.77).

That selection is deliberately conservative. In a major merger the object being tracked is not unique: the dark-matter halo identified by the halo finder and merger tree, and the galaxy at its centre identified by its stellar content, need not stay aligned. Halo labels can swap between snapshots, and the dominant stellar core can switch from one galaxy halo to another. The 107 clusters are those where the central halo and central galaxy have a consistent ancestry over the period relevant to the study. Cluster 1, the largest cluster in the study, fails this test by briefly swapping its central galaxy at z = 0.59, so cluster 2, the largest cluster that passes, is used as the example cluster in the plots.

The hindcast result is oligarchic assembly: the majority of the final BCG stellar mass is typically contributed by the central galaxies of only 3 to 5 progenitor haloes, and half of the final BCG stellar mass is typically contributed by only 3-5 infall events. Most accreted galaxies contribute no stars to the BCG, instead surviving as satellites or depositing stellar material throughout the cluster.

Dynamical friction delivers only massive progenitors

The mechanism behind this oligarchic assembly is the mass-ratio dependence of orbital decay. Dynamical friction is stronger for more massive perturbers because the deceleration scales approximately with the perturber mass, so high mass-ratio mergers take much longer to sink while nearly equal mass-ratio mergers decay much more quickly. Using the Boylan-Kolchin et al. (2008) merger-time formula with standard coefficients, the expected merger time rises steeply as the satellite-to-host mass ratio decreases. Massive satellites therefore have a plausible route to becoming part of the central galaxy within a Hubble time; low-mass satellites generally do not.

Tidal stripping works against this delivery. As a satellite orbits through the host potential, its outer dark-matter halo is stripped first, reducing the bound mass that drives further dynamical friction, and continued stripping can remove stars from loosely bound outer stellar envelopes. Tidal stripping therefore lengthens the dynamical friction timescale of infalling objects.

The consequence is a strong mass-ratio dependence in the fate of accreted stellar mass. Once stripped, stars join the diffuse cluster potential and no longer experience the coherent orbital decay of a self-bound galaxy; they may later contribute to the central regions statistically, but not through direct delivery of an infalling central stellar system. By contrast, the dense inner cores of sufficiently massive galaxies can survive long enough to reach the centre and merge violently with the existing BCG, so the stars they carry are far more likely to become part of the central galaxy itself.

Forecasting the BCG and ICL from dynamical fates

The hindcast result motivates a forecasting method that partitions stars using resolved halo memberships and merger-tree ancestry rather than an imposed radial or kinematic decomposition. The authors take the histories of all 324 cluster haloes, drop the four clusters whose halo history does not extend to z = 3.5, and define the set of stars exclusively belonging to each halo, so a star is only a member of the least massive object it is bound to.

Stars are then identified as BCG or ICL via the dynamical fates of their originating stellar systems. The physically defined BCG is the stellar component originating from the central cores of progenitor systems with low merger mass ratios whose central galaxies are delivered to the cluster centre through efficient dynamical friction prior to disruption. The ICL is the complementary population: stars stripped from galaxies or groups during their passage through the cluster, which populate the broader cluster potential.

Applying this to 261 clusters, the resulting components remain spatially interleaved but occupy distinct regions of phase space. This explains why the BCG and ICL can be physically distinct while remaining spatially interleaved: they are not separated by a sharp edge in radius but correspond to different assembly channels, one associated with efficient incorporation of infalling central galaxies into the bottom of the potential well, the other with partial stripping, incomplete assimilation, and broader dispersal of stellar debris through the cluster halo.

How well the physical BCG matches aperture selections

The physically defined BCG matches conventional aperture-based selections with high completeness. Within an aperture of about 100 kpc the stellar mass of the compact, dynamically cold central component dominates over the ICL mass, and an aperture selection method is highly complete and pure within such a radius. The paper reports that within 147.6 kpc the forecast BCG component and the aperture selection correspond closely.

The correspondence weakens only mildly towards the highest-mass systems. Both matching fractions exhibit weak negative correlations with M200c. For the fraction of stellar mass within 147.6 kpc assigned to the forecast BCG component, the authors find rs = -0.127 (p = 0.041); for the fraction of the total forecast BCG component contained within the same aperture, rs = -0.216 (p = 4.3 x 10^-4). When the sample is divided into three equal-number mass bins, the median fractions decrease only from 0.721 to 0.699 and from 0.899 to 0.881 between the lowest- and highest-mass thirds, changes that are small compared with the cluster-to-cluster scatter.

The authors interpret this as showing that the hindcast and forecast approaches are closely aligned for relaxed systems, and that deviations arise primarily in dynamically complex environments where no simple geometric definition of the BCG is expected to perform well. Care should be taken with dynamically disturbed central systems, which can be asymmetrical.

Resolution changes the central component most

The authors test robustness to numerical resolution by comparing the GIZMO_3k runs with 45 available higher-resolution GIZMO_7k runs. The same minimum threshold of 100 star particles is applied at both resolutions; because GIZMO_7k particle masses are eight times smaller, this corresponds to an approximately eight-times lower stellar-mass scale and allows substantially smaller progenitors to be followed.

The overall stacked decomposition is very similar between resolutions. The GIZMO_7k clusters produce a crossover between BCG- and ICL-dominated regimes at a smaller radius, but the profiles are otherwise comparable. The ICL, galaxy, and dark-matter halo velocity dispersions lie close to the one-to-one relation, indicating that these broader and dynamically hotter components are only weakly affected by the change in resolution.

The BCG population shows a small systematic offset: GIZMO_7k runs yield slightly lower dispersions by roughly 50 km/s on average, and the BCG contribution extends to somewhat smaller radii. The authors explain this as physically plausible because BCG stars are the most centrally concentrated stellar population and therefore the most sensitive to the star formation and energy feedback model and to the detailed structure of the inner potential. The main qualitative picture is unchanged, and the unresolved low-mass progenitor population does not dominate either central BCG assembly or diffuse ICL structure.

What the decomposition does not transfer to

Several quantities introduced here remain intrinsically model-dependent. Observations cannot normally determine the R200max of an individual disrupted progenitor, follow the orbital energy loss of that progenitor through time, or identify which present-day diffuse stars were associated with a particular infall event. The precise decomposition into merger-delivered and stripped populations, the BCG progenitor fraction fcen, and quantities such as N50 are therefore most naturally regarded as simulation-derived diagnostics.

Their observational value lies instead in the predictions they generate: the radial variation of stellar populations, the relative kinematics of the central and diffuse components, the frequency and masses of BCG companions, and the redshift evolution of the BCG and ICL fractions. The proposed separation scheme should therefore be viewed as a physical calibration for observable proxies rather than as a classification that can be applied directly to imaging data.

Some quantitative aspects are model- or definition-dependent. The absolute BCG and ICL mass fractions, the precise cluster-centric crossover radius, and the detailed extent of the central component depend on the adopted BCG progenitor central radius and, to some degree, on numerical resolution and galaxy-formation physics. This is consistent with the homogeneous comparison of four hydrodynamical simulation suites by Brown et al. (2026), who find that absolute ICL fractions and their apparent redshift evolution are highly sensitive to the adopted BCG-ICL definition, while differences between simulations become much smaller when a common definition is imposed. The authors therefore regard the assembly pathways and their dynamical ordering as the robust result, rather than any particular numerical BCG-ICL boundary.

The assembly pathway is the robust result

The paper's central conclusion is that the BCG-ICL division is real in terms of assembly history and dynamics, but not as a sharp structural boundary. It reflects a dynamical sorting of a common stellar population, governed by the interplay between dynamical friction and tidal stripping during hierarchical growth. Forecasting allows these components to be separated physically even though they remain interleaved in configuration space.

The central stellar component is best understood as a superposition of two populations: one formed in-situ within the central region of the cluster, and one formed near the centres of progenitor systems and subsequently delivered to the cluster centre through strong dynamical friction. While star formation within a particular simulation depends on the adopted subgrid star formation and feedback model, gravitational dynamics determines how these stars are redistributed, producing a continuous transition from a compact central core to an extended diffuse envelope.

For readers weighing how to use this result, the paper-specific priority is the distinction between assembly pathway and spatial boundary. The robust claim is that BCG stars trace a small number of major mergers whose central galaxies sank efficiently, while ICL stars trace stripping from all infalling systems; the fragile claim is any particular numerical BCG-ICL boundary, absolute mass fraction, or crossover radius. Aperture-based selections should be expected to work well in relaxed systems and to break down in dynamically complex ones, which is exactly the scenario split this framework predicts.

Sources used in this answer