Star Cluster Formation from Turbulent Clumps. II. Gradual Star Cluster Formation

TL;DR

This study models the dynamical evolution of star clusters forming gradually from turbulent molecular clumps, highlighting how formation timescales and efficiencies influence cluster structure, stellar ejections, and age gradients.

Contribution

It introduces a model of star cluster formation with gradual star formation rates, contrasting with instantaneous models, and explores how formation timescales affect cluster dynamics and observable properties.

Findings

Longer formation times lead to more runaway stars.

Radial age gradients depend on star formation efficiency.

Slow formation rates match observed age gradients.

Abstract

We investigate the dynamical evolution of star clusters during their formation, assuming that they are born from a turbulent starless clump of a given mass that is embedded within a parent self-gravitating molecular cloud characterized by a particular mass surface density. In contrast to the standard practice of most $N$-body studies, we do not assume that all stars are formed at once. Rather, we explore the effects of different star formation rates on the global structure and evolution of young embedded star clusters, also considering various primordial binary fractions and mass segregation levels. Our fiducial clumps studied in this paper have initial masses of $M_{\rm cl} = 3000\,M_\odot$, are embedded in ambient cloud environments of $\Sigma_{\rm cloud} = 0.1$ and 1 g cm$^{-2}$, and gradually form stars with an overall efficiency of 50% until the gas is exhausted. We investigate star formation efficiencies per free-fall time in the range $\epsilon_{\rm ff}=0.01$ to 1, and also compare to the instantaneous case ($\epsilon_{\rm ff}=\infty$) of Paper I. We show that most of the interesting dynamical processes that determine the future of the cluster, happen during the early formation phase. In particular, the ejected stellar population is sensitive to the duration of star cluster formation: for example, clusters with longer formation times produce more runaway stars, since these clusters remain in a dense state for longer, thus favouring occurrence of dynamical ejections. We also show that the presence of radial age gradients in star clusters depends sensitively on the star formation efficiency per free fall time, with observed values being matched best by our slowest forming clusters with $\epsilon_{\rm ff}\lesssim0.03$.