The puzzle of the cluster-forming core mass-radius relation and why it matters

Abstract

We highlight how the mass–radius relation of cluster‐forming cores combined with an external tidal field can influence infant weight‐loss and disruption likelihood of clusters at the end of their violent relaxation, namely, when their dynamical response to the expulsion of their residual star‐forming gas is over. Specifically, building on the cluster N‐body model grid of Baumgardt & Kroupa (2007), we study how the relation between the bound fraction of stars staying in clusters at the end of violent relaxation and the cluster‐forming core mass is affected by the slope and normalization of the core mass–radius relation. Assuming mass‐independent star formation efficiency and gas‐expulsion time‐scale τGExp/τcross and a given external tidal field, it is found that constant surface density cores and constant radius cores have the potential to lead to the preferential removal of high‐ and low‐mass clusters, respectively. In contrast, constant volume density cores result in mass‐independent cluster infant weight‐loss, as suggested by some observations. These trends result from how core volume density and core mass scale with each other. Infant weight‐loss is quantified for cluster‐forming cores with number density , surface density Σcore≃ 0.5 g cm−2 or radius rcore= 0.3 pc. Our modelling includes predictions about the evolution of high‐mass cluster‐forming cores (say mcore > 105 M⊙), a regime not yet covered by the observations. We show how, for a given external tidal field, the core mass–radius diagram constitutes a straightforward diagnostic tool to assess whether the tidal field influences the fate of clusters after gas expulsion. An overview of various issues directly affected by the nature of the core mass–radius relation is presented. In relation to the tidal field impact, these are the evolution of the cluster mass function at young ages (i.e. over the first ≃30 Myr), and our ability to reconstruct the star formation history of galaxies from their cluster age distribution. Independently of the tidal field impact, the slope and/or normalization of the cluster‐forming core mass–radius relation also influences the mass–metallicity relation of old globular clusters predicted by self‐enrichment models, and the duration of cluster violent relaxation. Finally, we emphasize that observational mass–radius data sets of dense gas regions must be handled with caution as they may be the imprint of the molecular tracer used to map them, rather than reflecting cluster formation conditions.

From the molecular-cloud- to the embedded-cluster-mass function with a density threshold for star formation

“…To satisfy the observed requirement of mass‐independent cluster infant weight‐loss, r h / r t must be independent of the CFRg mass. Parmentier & Kroupa (2011) demonstrate that – for given local SFE, gas expulsion time‐scale and external tidal field – this constrain is robustly satisfied for CFRgs with constant mean volume density. This is because their half‐mass radius r h and tidal radius r t scale alike with the embedded‐cluster mass m ecl , namely r h ∝ m 1/3 ecl and r t ∝ m 1/3 ecl .…”

“…See also fig. 1 and section 3 in Parmentier & Kroupa (2011) for a discussion. Several studies have therefore suggested that star formation requires a gas volume (or number ) density threshold (e.g.…”

Volume density thresholds for overall star formation imply mass-size thresholds for massive star formation

“…We stress here that the mass–radius relations defined by Kauffmann et al (2010a,b) on the one hand and by Parmentier & Kroupa (2011) on the other have distinct physical significance. While in Kauffmann et al (2010a,b), the mass–radius relation describes the radial distribution of the mass of the molecular gas regions, the mass–radius relation discussed in depth by Parmentier & Kroupa (2011) in the framework of the early survival of star clusters in a tidal field refers to the mass–radius relations of populations of clumps , that is, the relation between the total mass of individual clumps and their radius at their outer edge. For instance, the two clumps of Fig.…”

The big problems in star formation: The star formation rate, stellar clustering, and the initial mass function

“…Fall et al (2010) focus on the early phase when f cl = 1, and argue that the observed β ≈ 2 slope for young clusters can be reproduced naturally if the gas clouds have roughly constant densities, and if the process responsible for stellar feedback is a momentum-driven mechanism such as radiation pressure. Parmentier & Kroupa (2011) and Parmentier & Baumgardt (2012) argue that a constant density initial condition provides a better explanation for the observed similarity between the cloud and cluster mass functions.…”