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.

• The paper introduces a novel computational method using cosmological-inspired adiabatic cooling to generate self-consistent initial conditions for stellar cluster formation simulations.
• Simulations show fragmented clusters can reach equilibrium in ~1 million years for 10^4 Msun masses, leading to low-concentration configurations.
• The model predicts mass segregation within clumps and a top-heavy stellar mass function in the field population, aligning with observational data.

Overview of Hubble-Lemaître Fragmentation in Merger-Driven Cluster Formation

The paper "Hubble-Lemaître Fragmentation and the Path to Equilibrium of Merger-Driven Cluster Formation" presents an innovative approach to understanding the formation and evolution of stellar clusters through a cosmological-inspired expansion mechanism. This research investigates the dynamical processes underlying young, substructured stellar clusters and introduces a novel computational method to model these systems' initial conditions, bridging the gap between star formation and their subsequent dynamical evolution.

Key Concepts and Methodology

The central innovation of this work lies in its adaptation of an adiabatic cooling mechanism to generate self-consistent initial conditions for stellar clusters. This involves allowing a uniform system to expand, enabling the formation of clumps akin to those observed in the cosmological Hubble-Lemaître flow. The study employs an N-body integrator to simulate the temporal evolution, treating stellar mass elements according to a Salpeter mass function.

The authors' method creates a coherent relationship between the clumps' spatial distribution and the underlying velocity field. As the system undergoes expansion, gravitational effects drive cooling and facilitate fragmentation into clumps, which possess a fractal geometry bolstered by a self-grown velocity field and mass profile. This approach aligns the spatial distribution and velocities, offering a more realistic starting point for simulating stellar cluster evolution compared to traditional uniform or fractal initial conditions.

Results and Analysis

The paper highlights several significant findings derived from the simulations:

• Cluster Dynamics: Fragmented configurations can achieve equilibrium within approximately 1 million years for stellar masses around $10^4 M_\odot$. The equilibrium state is characterized by low concentration, implying that direct stellar collisions and the formation of exotic objects are less likely.
• Mass Segregation: The study finds mass segregation within the clumps, where the initial mass function (IMF) power index in clumps is approximately 0.3 lower than in the field stellar population. This observation is consistent with empirical data from the Milky Way and suggests that mass segregation is a fundamental aspect of the cluster formation process.
• Clump Dynamics: Low-mass stars ejected from merging clumps contribute to a mass-depleted field population within the resulting stellar clusters. The simulations show that these clusters have a top-heavy stellar mass function, largely influenced by the initial conditions set by massive stars acting as nucleation sites for clump growth.

Implications and Future Directions

The implications of this research are multifaceted. The model aligns well with observational data on young stellar populations, creating potential for improved predictions about the evolutionary paths of these clusters. The findings suggest that the initial mass function and early dynamical interactions have lasting impacts, shaping the distribution and subsequent dynamics of stars within clusters.

Future research could extend this model by incorporating more complex physical processes, such as hydrodynamical effects and radiative feedback, to further refine predictions. The approach offers a promising avenue for simulating star formation in diverse environments, potentially leading to a deeper understanding of different stellar populations and their evolutionary contexts.

The novel method for generating initial conditions may be particularly useful for simulations seeking to explore the formation of dense stellar systems, such as globular clusters or nuclear star clusters. Moreover, the insights from this study could be extrapolated to larger cosmological contexts, providing a framework for analyzing the hierarchical assembly of galactic structures.

In conclusion, this paper contributes a robust computational tool that aligns theoretical models with observational evidence, outlining a coherent pathway from star formation to cluster evolution while emphasizing the significance of early dynamical processes in shaping stellar populations.