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

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, $\left(r_h/\mathrm{pc}\right)=0.1_{-0.04}^{+0.07}{\left(M_{\mathrm{ecl}}/{\mathrm{M}}_{\odot }\right)}^{0.13\pm 0.04}$. 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.

6 pages, 2 figures; accepted for publication in MNRAS, minor changes made to the text after proofs

References in corpus (10)

• Binary interaction dominates the evolution of massive stars
• Dependency of dynamical ejections of O stars on the masses of very young star clusters
• The formation of NGC 3603 young starburst cluster: "prompt" hierarchical assembly or monolithic starburst?
• The bound fraction of young star clusters
• On the initial binary population for star cluster simulations
• Characterizing the Brown Dwarf Formation Channels from the Initial Mass Function and Binary-star Dynamics
• The state of globular clusters at birth II: primordial binaries
• A perfect starburst cluster made in one go: the NGC 3603 young cluster
• Mass Evaporation Rate of Globular Clusters in a Strong Tidal Field
• Using binary statistics in Taurus-Auriga to distinguish between brown dwarf formation processes

Cited by in corpus (1)

• The initial mass function of stars and the star-formation rates of galaxies