Local-density-driven clustered star formation

¹ Astronomisches Rechen-Institut, Zentrum für Astronomie, Heidelberg Universität, Mönchhofstr. 12-14, 69120 Heidelberg, Germany
² Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
³ Argelander-Institut für Astronomie, Bonn Universität, Auf dem Hügel 71, 53121 Bonn, Germany
e-mail: gparm@ari.uni-heidelberg.de

Received: 22 May 2012
Accepted: 23 October 2012

Abstract

Context. A positive power-law trend between the local surface densities of molecular gas, Σ_gas, and young stellar objects, Σ _⋆ , in molecular clouds of the solar neighbourhood has recently been identified. How it relates to the properties of embedded clusters, in particular to the recently established radius-density relation, has so far not been investigated.

Aims. We model the development of the stellar component of molecular clumps as a function of time and initial local volume density. Our study provides a coherent framework able to explain both the molecular-cloud and embedded-cluster relations quoted above.

Methods. We associate the observed volume density gradient of molecular clumps to a density-dependent free-fall time. The molecular clump star formation history is obtained by applying a constant star formation efficiency per free-fall time, ϵ_ff.

Results. For the volume density profiles typical of observed molecular clumps (i.e. power-law slope  ≃ −1.7), our model gives a star-gas surface-density relation of the form Σ_⋆ ∝ Σ_gas², which agrees very well with the observations. Taking the case of a molecular clump of mass M₀ ≃ 10⁴   M_⊙ and radius R ≃ 6   pc experiencing star formation during 2 Myr, we derive what star formation efficiency per free-fall time matches the normalizations of the observed and predicted (Σ _⋆ , Σ_gas) relations best. We find ϵ_ff ≃ 0.1. We show that the observed growth of embedded clusters, embodied by their radius-density relation, corresponds to a surface density threshold being applied to developing star-forming regions. The consequences of our model in terms of cluster survivability after residual star-forming gas expulsion are that, owing to the locally high star formation efficiency in the inner part of star-forming regions, global star formation efficiency as low as 10% can lead to the formation of bound gas-free star clusters.