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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, $left( r_h/{rm pc} right)= 0.1^{+0.07}_{-0.04}, left( M_{rm ecl}/{rm M}_odot right)^{0.13pm0.04}$. 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.
Young stellar clusters across nearly five orders of magnitude in mass appear to follow a power-law mass-radius relationship (MRR), $R_{star} propto M_{star}^{alpha}$, with $alpha approx 0.2 - 0.33$. We develop a simple analytic model for the cluster
The stellar initial mass function (IMF) plays a crucial role in determining the number of surviving stars in galaxies, the chemical composition of the interstellar medium, and the distribution of light in galaxies. A key unsolved question is whether
Most globular clusters have half-mass radii of a few pc with no apparent correlation with their masses. This is different from elliptical galaxies, for which the Faber-Jackson relation suggests a strong positive correlation between mass and radius. O
Observations and semianalytical galaxy formation and evolution models (SAMs) have suggested the existence of a stellar mass-stellar metallicity relation (MZR), which is shown to be universal for different types of galaxies over a large range of stell
Early-type galaxies obey a narrow relation traced by their stellar content between the mass and size (Mass- Radius relation). The wealth of recently acquired observational data essentially confirms the classical relations found by Burstein, Bender, F