Characterizing the dynamical state of star clusters from snapshots of their spatial distributions

TL;DR

This paper investigates how the distribution of stellar surface densities and the Q-parameter can be used together to determine the current dynamical state and history of star clusters, despite degeneracies in density distributions.

Contribution

It demonstrates that combining b-parameter measurements with surface density distributions allows inferring the dynamical evolution of star clusters from snapshots.

Findings

b-distribution alone cannot determine initial densities due to rapid evolution.

Using b-parameter with b-distribution reveals substructure and dynamical history.

Substructure erases quickly, affecting binary and planetary systems.

Abstract

We determine the distribution of stellar surface densities, \Sigma, from models of static and dynamically evolving star clusters with different morphologies, including both radially smooth and substructured clusters. We find that the \Sigma distribution is degenerate, in the sense that many different cluster morphologies (smooth or substructured) produce similar cumulative distributions. However, when used in tandem with a measure of structure, such as the Q-parameter, the current spatial and dynamical state of a star cluster can be inferred. The effect of cluster dynamics on the \Sigma distribution and the Q-parameter is investigated using N-body simulations and we find that, depending on the assumed initial conditions, the \Sigma distribution can rapidly evolve from high to low densities in less than 5Myr. This suggests that the \Sigma distribution can only be used to assess the current density of a star forming region, and provides little information on its initial density. However, if the \Sigma distribution is used together with the Q-parameter, then information on the amount of substructure can be used as a proxy to infer the amount of dynamical evolution that has taken place. Substructure is erased quickly through dynamics, which can disrupt binary star systems and planets, as well as facilitate dynamical mass segregation. Therefore, dynamical processing in young star forming regions could still be significant, even without currently observed high densities.