The initial mass function of star clusters that form in turbulent molecular clouds

Abstract

We simulate the formation and evolution of young star clusters using the combination of smoothed-particle hydrodynamical (SPH) simulations and direct N -body simulations. We start by performing SPH simulations of the giant molecular cloud with a turbulent velocity field, a mass of 4 × 10 4 to 5 × 10 6 M ⊙ , and a density between ρ ∼ 1.7×10 3 and 170cm −3 . We continue the hydrodynamical simulations for a free-fall time scale (t ff ≃ 0.83 Myr and 2.5 Myr), and analyze the resulting structure of the collapsed cloud. We subsequently replace a density-selected subset of SPH particles with stars by adopting a local star-formation efficiency proportional to ρ 1/2 . As a consequence, the local star formation efficiency exceeds 30 per cent, whereas globally only a few per cent of the gas is converted to stars. The stellar distribution by the time gas is converted to stars is very clumpy, with typically a dozen bound conglomerates that consist of 100 to 10 4 stars. We continue to evolve the stars dynamically using the collisional N -body method, which accurately treats all pairwise interactions, stellar collisions and stellar evolution. We analyze the results of the N -body simulations when the stars have an age of 2 Myr and 10 Myr. During the dynamical simulations, massive clusters grow via hierarchical merging of smaller clusters. The shape of the cluster mass function that originates from an individual molecular cloud is consistent with a Schechter function with a power-law slope of β = −1.73 at 2 Myr and β = −1.67 at 10 Myr, which fits to observed cluster mass function of the Carina region. The superposition of mass functions have a power-law slope of < ∼ − 2, which fits the observed mass function of star clusters in the Milky Way, M31 and M83. We further find that the mass of the most massive cluster formed in a single molecular cloud with a mass of M g scales with 6.1M 0.51 g which also agrees with recent observation of the GMC and young clusters in M51.

Simulating radiative feedback and star cluster formation in GMCs – II. Mass dependence of cloud destruction and cluster properties

“…This relation has been found in both observations (Hughes et al 2013) and simulations (Fujii & Portegies Zwart 2015) to take the form Mc,max ∝M 0.5 GM C , where Mc,max is the maximum mass cluster that forms out of a GMC of mass MGMC .…”

Rotation in young massive star clusters

“…However, the adopted tree code (employing a second-order leap-frog scheme) is not particularly suited to investigate close stellar encounters in detail. Only few studies attempt to trace the dynamical evolution of star clusters born from hydrodynam- ical simulations of molecular clouds (Fujii & Portegies Zwart 2015;McMillan et al 2015;Fujii 2015;Fujii & Portegies Zwart 2016), because the problem is a numerical challenge (e.g. Pelupessy & Portegies Zwart 2012;Hubber et al 2013).…”

Formation of a protocluster: A virialized structure from gravoturbulent collapse

“…Ballesteros-Paredes et al (2015) used SPH to simulate a 10 3 M cloud to characterize the impact of self-gravity on the high-mass end slope of the IMF. To study the transition from cloud to stellar cluster and the link between their properties and, in particular, the later evolution of stellar clusters, Moeckel & Bate (2010) and Fujii & Portegies Zwart (2015) performed SPH simulations of a molecular cloud for one free-fall time, converted the dense gas to stars, and then evolved with N-body simulations to form clusters. These studies do not explicitly address in great detail how the gas, which is converted into clustered stars, is assembled and whether and how the properties of the stellar clusters are inherited from the gas phase.…”