Dynamical equivalence, the origin of the Galactic field stellar and binary population, and the initial radius--mass relation of embedded clusters

TL;DR

This study confirms the existence of dynamical equivalence in stellar clusters, linking initial conditions to observed Galactic field populations and deriving a radius-mass relation consistent with molecular cloud observations.

Contribution

It demonstrates the existence of dynamically equivalent embedded cluster solutions and derives a radius-mass relation aligned with observed molecular cloud clumps.

Findings

Dynamically equivalent solutions exist for embedded clusters.

The radius-mass relation matches observed molecular cloud clumps.

Time to reach dynamical equivalence is about 0.5 Myr.

Abstract

In order to allow a better understanding of the origin of Galactic field populations, dynamical equivalence of stellar-dynamical systems has been postulated by Kroupa and Belloni et al. to allow mapping of solutions of the initial conditions of embedded clusters such that they yield, after a period of dynamical processing, the Galactic field population. Dynamically equivalent systems are defined to initially and finally have the same distribution functions of periods, mass ratios and eccentricities of binary stars. Here we search for dynamically equivalent clusters using the {\sc mocca} code. The simulations confirm that dynamically equivalent solutions indeed exist. The result is that the solution space is next to identical to the radius--mass relation of Marks \& Kroupa, $\left( r_h/{\rm pc} \right)= 0.1^{+0.07}_{-0.04}\, \left( M_{\rm ecl}/{\rm M}_\odot \right)^{0.13\pm0.04}$. This relation is in good agreement with the observed density of molecular cloud clumps. According to the solutions, the time-scale to reach dynamical equivalence is about 0.5~Myr which is, interestingly, consistent with the lifetime of ultra-compact HII regions and the time-scale needed for gas expulsion to be active in observed very young clusters as based on their dynamical modelling.