Formation of a protocluster: A virialized structure from gravoturbulent collapse

Abstract

Context. Most stars are born in the gaseous protocluster environment where the gas is reprocessed after the global collapse from the diffuse molecular cloud. The knowledge of this intermediate step gives more accurate constraints on star formation characteristics. Aims. We demonstrate that a virialized globally supported structure, in which star formation happens, is formed out of a collapsing molecular cloud, and we derive a mapping from the parent cloud parameters to the protocluster to predict its properties with a view to confront analytical calculations with observations and simulations. Methods. We decomposed the virial theorem into two dimensions to account for the rotation and the flattened geometry. Equilibrium was found by balancing rotation, turbulence, and self-gravity, while turbulence was maintained through accretion driving and it dissipates in one crossing time. We estimated the angular momentum and the accretion rate of the protocluster from the parent cloud properties.Results. The two-dimensional virial model predicts the size and velocity dispersion given the mass of the protocluster and that of the parent cloud. The gaseous protoclusters lie on a sequence of equilibrium with the trend R ∼ M 0.5 with limited variations, depending on the evolutionary stage, parent cloud, and parameters that are not well known, such as turbulence driving efficiency by accretion and turbulence anisotropy. The model reproduces observations and simulation results successfully. Conclusions. The properties of protoclusters follow universal relations and they can be derived from that of the parent cloud. The gaseous protocluster is an important primary stage of stellar cluster formation, and should be taken into account when studying star formation. Using simple estimates to infer the peak position of the core mass function (CMF) we find a weak dependence on the cluster mass, suggesting that the physical conditions inside protoclusters may contribute to set a CMF, and by extension an initial mass function (IMF), that appears to be independent of the environment.

Star Clusters Across Cosmic Time

“…The final star formation efficiency is ultimately be dictated by the efficiency of feedback at ejecting gas, and if the ratio of mass ejected by feedback to mass converted into stars is 1, then the final value of * is large even if ff is always fairly small. This scenario is consistent with observed values of ff , naturally produces an accelerating rate of star formation, and also yields a cluster mass-size relation in good agreement with observations (Matzner & Jumper 2015;Lee & Hennebelle 2016b). Because the final mass that goes into a cluster was never assembled in a single cloud all at once, there is no problem with finding clouds dense enough to be the progenitors of the densest clusters.…”

Structure and Rotation of Young Massive Star Clusters in a Simulated Dwarf Starburst

“…For example in Mapelli (2017) all clusters except those with stellar masses below 100 M showed signatures of ordered rotation, even though their initial conditions were non-rotating. Lee & Hennebelle (2016b) in turn showed how the properties of the forming protoclusters can be derived from the initial star-forming cloud. The high level of turbulence and strong tidal torques commonly found in the high-pressure environments where star clusters tend to form, such as starbursts and mergers studied here, makes it difficult to form a non-rotating massive .…”

Scale-free gravitational collapse as the origin of ρ ∼ r−2 density profile – a possible role of turbulence in regulating gravitational collapse

“…The model shares a common view with many of the previous ones, e.g. Murray & Chang (2015); Lee & Hennebelle (2016); Li (2017). We consider a clump with a density profile ρ(r) and an infall velocity profile v infall (r).…”