The mass function and dynamical mass of young star clusters: Why their initial crossing-time matters crucially

TL;DR

This paper investigates how the initial crossing-time of young star clusters influences their dynamical evolution and mass function during violent relaxation, emphasizing the importance of initial density conditions.

Contribution

It introduces models linking initial crossing-time to cluster evolution, highlighting the role of initial density in shaping mass function changes during violent relaxation.

Findings

Mass-dependent evolutionary rates affect the cluster mass function shape during violent relaxation.

Constant mean volume density preserves the initial mass function shape throughout evolution.

Compact clusters with rapid evolution can reach equilibrium regions within a few Myr after gas expulsion.

Abstract

We highlight the impact of cluster-mass-dependent evolutionary rates upon the evolution of the cluster mass function during violent relaxation, that is, while clusters dynamically respond to the expulsion of their residual star-forming gas. Mass-dependent evolutionary rates arise when the mean volume density of cluster-forming regions is mass-dependent. In that case, even if the initial conditions are such that the cluster mass function at the end of violent relaxation has the same shape as the embedded-cluster mass function (i.e. infant weight-loss is mass-independent), the shape of the cluster mass function does change transiently {\it during} violent relaxation. In contrast, for cluster-forming regions of constant mean volume density, the cluster mass function shape is preserved all through violent relaxation since all clusters then evolve at the same mass-independent rate. On the scale of individual clusters, we model the evolution of the ratio between the dynamical mass and luminous mass of a cluster after gas expulsion. Specifically, we map the radial dependence of the time-scale for a star cluster to return to equilibrium. We stress that fields-of-view a few pc in size only, typical of compact clusters with rapid evolutionary rates, are likely to reveal cluster regions which have returned to equilibrium even if the cluster experienced a major gas expulsion episode a few Myr earlier. We provide models with the aperture and time expressed in units of the initial half-mass radius and initial crossing-time, respectively, so that our results can be applied to clusters with initial densities, sizes, and apertures different from ours.