Star-by-star simulations that form clusters from turbulent magnetized gas with stellar feedback (Polak et al. 2025, A&A 695, A188, the third paper of the 'Massive star cluster formation' series) show that hierarchical assembly drives dynamical mass segregation within about 2 Myr even with no primordial segregation by construction; however, massive stars that segregate into the collapsing core are also preferentially ejected, and the segregation diagnostic fluctuates strongly on 0.1-0.3 Myr timescales. The open problem posed by that work is to complete this picture quantitatively under realistic gas dynamics and feedback: (1) how dynamical ejection of massive stars competes with and limits collapse-driven segregation; (2) whether primordial mass segregation on the sub-cluster scale - including that imposed by sub-grid star-formation prescriptions placing massive stars preferentially at sub-cluster centers - survives the full assembly process or is transient; (3) how primordial massive-star multiplicity and a fully resolved initial mass function change the timing, amplitude, and longevity of early segregation across cluster masses; and (4) the expected statistical distribution of the mass segregation ratio over many stochastic realizations for a cluster of given mass and age, together with the observational selection effects of incomplete low-mass-star detection in dense cores. The ejection-segregation balance, primordial-segregation survival with gas dynamics, resolved-IMF high-mass runs, and ensemble statistics remain open.

Background

Mass segregation - the concentration of the most massive stars toward the center of a star cluster - is observed in many young clusters, but its origin is debated: massive stars may form already concentrated ('primordial' segregation) or migrate inward dynamically after birth. Classical two-body relaxation theory (the gradual exchange of energy in gravitational encounters between stars) predicts that segregation should take a relaxation time comparable to or longer than the ages of few-Myr-old clusters, so observed early segregation has often been interpreted as primordial. Purely stellar-dynamical N-body experiments by Allison et al. (2009) overturned this intuition: when a cluster assembles hierarchically, i.e. through sub-clusters (locally dense groups of newly formed stars) merging into a dense central core with a short crossing time (the time a typical star needs to cross the cluster), dynamical segregation can occur on sub-Myr timescales. The standard observational and numerical diagnostic is the mass segregation ratio Λ\Lambda (ΛMSR\Lambda_{\rm MSR}): the average tree length of random sets of NN stars divided by the length of the minimum spanning tree (the shortest network of straight segments connecting a given set of stars) through the NN most massive stars; Λ>1\Lambda>1 signals segregation and its magnitude measures the degree.

Three results frame the current problem. First, simulations forming individual stars self-consistently from turbulent gas in the STARFORGE framework (Guszejnov et al. 2022) found that sub-clusters emerge already primordially segregated. Second, ALMA (Atacama Large Millimeter/submillimeter Array) observations of 11 massive protoclusters (Xu et al. 2024, ASSEMBLE survey) detect significant segregation of prestellar and protostellar cores on sub-cluster scales, supporting primordial segregation at the core scale. Third, the source paper - Polak et al. 2025, using the Torch framework, which couples magnetohydrodynamics of the star-forming gas, star-by-star formation via sink particles (point masses that condense out of dense gas and accrete), direct N-body stellar dynamics, stellar evolution, and radiation, wind, and supernova feedback through the AMUSE (Astrophysical Multipurpose Software Environment) coupling framework - simulated cluster formation from 10410^{4}, 10510^{5}, and 106 M⊙10^{6}\,M_\odot turbulent clouds. With no primordial segregation by construction, all three clusters become dynamically mass segregated within 2 2\,Myr of the onset of star formation, reaching the levels observed in young Galactic clusters. Two features qualify this conclusion: massive stars that segregate into the collapsing core are prone to dynamical ejection in few-body encounters, which can reduce the segregation level again, and Λ\Lambda fluctuates strongly, with segregated episodes lasting only 0.10.1-0.3 0.3\,Myr during assembly. The models also omit primordial binaries and, for computational tractability, merge ('agglomerate') stars below 4 M⊙4\,M_\odot into fewer dynamical particles, leaving the initial mass function (the distribution of stellar birth masses, IMF) incompletely resolved.

The unresolved problem is the quantitative completion of this picture under realistic gas dynamics and feedback: how ejection competes with segregation, whether primordial sub-cluster-scale segregation survives assembly, what stellar multiplicity and resolved IMF sampling do to the segregation signal, and what distribution of Λ\Lambda should statistically be expected for a cluster of given mass and age.

Problem Statement

Determine, in star-cluster formation simulations that include gas dynamics and stellar feedback during hierarchical assembly, the physical origin, robustness, and expected observational signature of early mass segregation. Establish:

(1) Ejection-segregation interplay: quantify the competition between collapse-driven dynamical segregation and dynamical ejection of the most massive stars - how frequently ejections erase or limit the central concentration built during collapse, and the expected longevity of the segregated state as a function of cluster mass.

(2) Survival of primordial segregation: whether primordial mass segregation present at the sub-cluster (core) scale - as indicated by core-scale observations, and as imposed, for example, by sub-grid star-formation prescriptions that place massive stars preferentially at sub-cluster centers - survives the full assembly process when gas dynamics and feedback are included, or is transient (erased, or subsequently destroyed, for instance because centrally concentrated massive stars are more easily ejected).

(3) Multiplicity and IMF sampling: establish how realistic primordial massive-star multiplicity and a fully resolved initial mass function (no low-mass agglomeration) change the timing, amplitude, and longevity of early mass segregation across the cluster-mass range (10410^{4}-106 M⊙10^{6}\,M_\odot clouds).

(4) Stochasticity and selection effects: determine the distribution of the mass segregation ratio Λ\Lambda over an ensemble of independent realizations of the same initial cloud conditions, for clusters of given mass and age (given its 0.1-0.3 Myr episodic variability), and quantify the magnitude of the observational bias from incomplete detection of low-mass stars in dense cluster cores.

These four questions are all required, and jointly they answer whether observed early mass segregation in young massive clusters can be produced and maintained by dynamics alone, and whether a primordial contribution can be distinguished from a dynamical one.

References

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