Simulating star clusters across cosmic time – I. Initial mass function, star formation rates, and efficiencies

Abstract

ABSTRACT We present radiation-magneto-hydrodynamic simulations of star formation in self-gravitating, turbulent molecular clouds, modelling the formation of individual massive stars, including their UV radiation feedback. The set of simulations have cloud masses between mgas = 103 M⊙ and 3 × 105 M⊙ and gas densities typical of clouds in the local Universe ($\overline{n}_{\rm gas} \sim 1.8\times 10^2$ cm−3) and 10× and 100× denser, expected to exist in high-redshift galaxies. The main results are as follows. (i) The observed Salpeter power-law slope and normalization 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 $40{{\ \rm per\ cent}}$ of the mass of the sink particle, while the remaining $60{{\ \rm per\ cent}}$ 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. (ii) The star formation law that best describes our set of simulation is ${\rm d}\rho _*/{\rm d}t \propto \rho _{\rm gas}^{1.5}$ if $\overline{n}_{\rm gas}\lt n_{\rm cri}\approx 10^3$ cm−3, and ${\rm d}\rho _*/{\rm d}t \propto \rho _{\rm gas}^{2.5}$ otherwise. The duration of the star formation episode is roughly six cloud’s sound crossing times (with cs = 10 km s−1). (iii) The total star formation efficiency in the cloud is $f_*=2{{\ \rm per\ cent}} (m_{\rm gas}/10^4~\mathrm{M}_\odot)^{0.4}(1+\overline{n}_{\rm gas}/n_{\rm cri})^{0.91}$, for gas at solar metallicity, while for metallicity Z < 0.1 Z⊙, based on our limited sample, f* is reduced by a factor of ∼5. (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.