Hubble–Lemaître fragmentation and the path to equilibrium of merger-driven cluster formation

Abstract

This paper discusses a new method to generate self-coherent initial conditions for young substructured stellar cluster. The expansion of a uniform system allows stellar sub-structures (clumps) to grow from fragmentation modes by adiabatic cooling. We treat the system mass elements as stars, chosen according to a Salpeter mass function, and the time-evolution is performed with a collisional N-body integrator. This procedure allows to create a fully-coherent relation between the clumps' spatial distribution and the underlying velocity field. The cooling is driven by the gravitational field, as in a cosmological Hubble-Lema\^itre flow. The fragmented configuration has a `fractal'-like geometry but with a self-grown velocity field and mass profile. We compare the characteristics of the stellar population in clumps with that obtained from hydrodynamical simulations and find a remarkable correspondence between the two in terms of the stellar content and the degree of spatial mass-segregation. In the fragmented configuration, the IMF power index is ~0.3 lower in clumps in comparison to the field stellar population, in agreement with observations in the Milky Way. We follow in time the dynamical evolution of fully fragmented and sub-virial configurations, and find a soft collapse, leading rapidly to equilibrium (timescale of 1 Myr for a ~ 10^4 Msun system). The low-concentration equilibrium implies that the dynamical evolution including massive stars is less likely to induce direct collisions and the formation of exotic objects. Low-mass stars already ejected from merging clumps are depleted in the end-result stellar clusters, which harbour a top-heavy stellar mass function.