The Formation of a Star Cluster: Predicting the Properties of Stars and Brown Dwarfs

We present results from the largest numerical simulation of star formation to resolve the fragmentation process down to the opacity limit. The simulation follows the collapse and fragmentation of a large-scale turbulent molecular cloud to form a stellar cluster and, simultaneously, the formation of circumstellar discs and binary stars. This large range of scales enables us to predict a wide variety of stellar properties for comparison with observations. The calculation clearly demonstrates that star formation is a highly-dynamic and chaotic process. Star-disc encounters form binaries and truncate discs. Stellar encounters disrupt bound multiple systems. The cloud produces roughly equal numbers of stars and brown dwarfs, with masses down to the opacity limit for fragmentation (~5 Jupiter masses). The initial mass function is consistent with a Salpeter slope (Gamma=-1.35) above 0.5 Msun, a roughly flat distribution (Gamma=0) in the range 0.006-0.5 Msun, and a sharp cutoff below ~0.005 Msun. This is consistent with recent observational surveys. The brown dwarfs form by the dynamical ejection of low-mass fragments from dynamically unstable multiple systems before the fragments have been able to accrete to stellar masses. Close binary systems (with separations <10 AU) are not formed by fragmentation in situ. Rather, they are produced by hardening of initially wider multiple systems through a combination of dynamical encounters, gas accretion, and/or the interaction with circumbinary and circumtriple discs. Finally, we find that the majority of circumstellar discs have radii less than 20 AU due to truncation in dynamical encounters. This is consistent with observations of the Orion Trapezium Cluster and implies that most stars and brown dwarfs do not form large planetary systems.