Simulating Star Clusters Across Cosmic Time: I. Initial Mass Function, Star Formation Rates and Efficiencies

Abstract

We present radiation-magneto-hydrodynamic simulations of star formation in self-gravitating, turbulent molecular clouds, modeling the formation of individual massive stars, including their UV radiation feedback. The set of simulations have cloud masses between $m_{\mathrm{gas}}=10^3$~M${}_{\odot }$ to $3\times 10^5$~M${}_{\odot }$ and gas densities typical of clouds in the local universe (${\overline{n}}_{\mathrm{gas}}\sim 1.8\times 10^2$~cm${}^{-3}$) and 10$\times$ and 100$\times$ denser, expected to exist in high-redshift galaxies. The main results are: {\it i}) The observed Salpeter power-law slope and normalisation of the stellar initial mass function at the high-mass end can be reproduced if we assume that each star-forming gas clump (sink particle) fragments into stars producing on average a maximum stellar mass about $40\%$ of the mass of the sink particle, while the remaining $60\%$ is distributed into smaller mass stars. Assuming that the sinks fragment according to a power-law mass function flatter than Salpeter, with log-slope $0.8$, satisfy this empirical prescription. {\it ii}) The star formation law that best describes our set of simulation is $d\ddot{I}{}_{\ast }/dt\propto \ddot{I}{}_{gas}^{1.5}$ if ${\overline{n}}_{gas}<n_{cri}\approx 10^3$~cm${}^{-3}$, and $d\ddot{I}{}_{\ast }/dt\propto \ddot{I}{}_{\mathrm{gas}}^{2.5}$ otherwise. The duration of the star formation episode is roughly $6$ cloud's sound crossing times (with $c_s=10$~km/s). {\it iii}) The total star formation efficiency in the cloud is $f_{\ast }=2\%(m_{\mathrm{gas}}/10^4{M}_{\odot }{)}^{0.4}(1+{\overline{n}}_{\mathrm{gas}}/n_{\mathrm{cri}}{)}^{0.91}$, for gas at solar metallicity, while for metallicity $Z<0.1$~Z${}_{\odot }$, based on our limited sample, $f_{\ast }$ is reduced by a factor of $\sim 5$. {\it iv)} The most compact and massive clouds appear to form globular cluster progenitors, in the sense that star clusters remain gravitationally bound after the gas has been expelled.

21 pages, 18 figures, Published in MNRAS. References added; Fig. 5 and Fig. 15 added