The origin of early mass segregation in young star clusters: dynamical subcluster-merger inheritance versus primordial segregation

Very young star clusters often show a central concentration of massive stars (mass segregation) that standard two-body relaxation cannot produce on the cluster's age, and it has been debated for nearly three decades whether this segregation is imprinted by the star-formation process (primordial segregation) or generated dynamically during the early, hierarchical, out-of-equilibrium assembly of the cluster. McMillan, Vesperini & Portegies Zwart (2007) proposed and simulated a dynamical route: small stellar clumps that are segregated at formation, or segregate internally before merging, pass their segregation on to the merged cluster, provided the clump system is dynamically cool. Subsequent literature confirms the dynamical route in idealized N-body experiments and in modern simulations with gas dynamics and stellar feedback, while independent observational and theoretical work argues for substantial primordial segregation at birth. No quantitative, environment-dependent decomposition of the relative importance of the two channels exists; the question remains explicitly debated in 2025–2026 work.

Background

Mass segregation is the radial ordering of a star cluster by stellar mass: massive stars concentrate toward the center and low-mass stars populate the outskirts. In an initially smooth, mixed cluster it is produced by two-body relaxation, the cumulative effect of weak gravitational encounters between stars, which drives the system toward energy equipartition on a timescale of order the half-mass relaxation time $t_r$ — typically many crossing times and, for clusters with $N \gtrsim 10^3$ stars, much longer than a few Myr. The problem arose when very young systems such as the Orion Nebula Cluster were found to be significantly mass segregated at ages of roughly 1 Myr (Hillenbrand & Hartmann 1998), far too short for global two-body relaxation from unsegregated initial conditions (Bonnell & Davies 1998). Two families of explanations compete. Formation-driven (primordial) segregation posits that massive stars are born in the central, densest parts of the natal cloud, a prediction made by competitive accretion (stars in cluster centers accrete more from the shared gas reservoir) and by monolithic core collapse (massive stars form in situ near the potential center). Dynamical explanations posit that segregation is produced after (or during) star formation but faster than standard relaxation. The key dynamical mechanism studied here is the clump-merger route of McMillan, Vesperini & Portegies Zwart (2007): stars form in small clumps; each clump, having few members, has a short internal segregation timescale ($t_{seg} \sim 0.1\,t_r$ of the clump); if the system of clumps is dynamically cool, with virial ratio $q_c \lesssim 0.1$ (kinetic energy small compared to self-gravitational energy, i.e. cold, subvirial, nearly at rest), the clumps merge on a global free-fall time $t_{ff}$; when $\tau = t_{ff}/t_{seg} > 1$ segregation develops inside the clumps before they merge, and the merged cluster inherits the clumps' segregation. Their N-body experiments (clump numbers $N_c = 2$–$8$, clump mass ratios 1–4, two impact parameters, mass–radius scalings with exponent $0$–$1/2$) showed that the segregation measure $f_{seg} = R_h/R_h^{(heavy)}$ (ratio of the cluster half-mass radius to that of the massive component) is approximately conserved through the merger, and that clumpy assembly reaches a given segregation level roughly $7$–$10$ times faster in dynamical time than a standard unsegregated Plummer-model sphere (a common spherical equilibrium initial condition). The 2007 papers themselves note only limited open issues: the simulations neglect initial binaries (proceedings Sec. 2: 'We neglect initial binaries and concentrate on two stellar mass distributions'), the companion ApJL letter's conclusions state that its results 'cover only a small portion of the possible initial conditions for the clumpy systems of interest here', with a fuller survey promised elsewhere, and on frequency the proceedings conclude that the required cool condition 'would be met for even a modest number of clumps or moderate clumping'. The wider set of open issues that frame the present problem — residual gas, stellar evolution, and massive-star feedback and dynamical ejection during the merger epoch, the frequency with which sufficiently cool clump systems arise in real star-forming environments, and the scaling across cluster masses and assembly histories — was raised by later work. Observationally, segregation is usually measured with the minimum-spanning-tree statistic $\Lambda_{MSR}$ (the ratio of the mean edge length of the network spanning the most massive stars to that of a random equal-number sample), which allows comparison between simulated and observed clusters.

Problem Statement

For young star clusters whose observed mass segregation is inconsistent with two-body relaxation acting on an initially smooth, unsegregated, virialized system, determine the relative importance of (a) formation-driven primordial segregation — massive stars born centrally concentrated through fragmentation, competitive accretion, or monolithic core collapse — versus (b) purely dynamical production and inheritance of segregation through the hierarchical merger of dynamically cool subclusters, versus (c) subsequent ordinary two-body relaxation acting on the assembled cluster after the merger epoch. Attribute each contribution to exactly one channel: segregation already present in the subclusters at their formation counts as primordial channel (a) regardless of whether it is later inherited through a merger; channel (b) covers only segregation generated dynamically inside the subclusters before they merge; and channel (c) covers only segregation generated by two-body relaxation acting on the already-assembled cluster. The objective is a quantitative, observationally testable decomposition of the origin of early mass segregation valid across cluster masses and star-forming environments.

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