We report the statistical properties of stars, brown dwarfs and multiple systems obtained from the largest radiation hydrodynamical simulation of star cluster formation to date that resolves masses down to the opacity limit for fragmentation (a few Jupiter masses). The initial conditions are identical to those of previous barotropic calculations published by Bate, but this time the calculation is performed using a realistic equation of state and radiation hydrodynamics. The calculation uses sink particles to model 183 stars and brown dwarfs, including 28 binaries and 12 higher-order multiple systems, the properties of which are compared to the results from observational surveys.
We find that the radiation hydrodynamical/sink particle simulation reproduces many observed stellar properties very well. In particular, whereas using a barotropic equation of state produces more brown dwarfs than stars, the inclusion of radiative feedback results in a stellar mass function and a ratio of brown dwarfs to stars in good agreement with observations of Galactic star-forming regions. In addition, many of the other statistical properties of the stars and brown dwarfs are in reasonable agreement with observations, including multiplicity as a function of primary mass, the frequency of very low mass binaries, and general trends for the mass ratio and separation distributions of binaries. We also examine the velocity dispersion of the stars, the distributions of disc truncation radii due to dynamical interactions, and coplanarity of orbits and sink particle spins in multiple systems. Overall, the calculation produces a cluster of stars whose statistical properties are difficult to distinguish from observed systems, implying that gravity, hydrodynamics and radiative feedback are the primary ingredients for determining the origin of the statistical properties of low-mass stars.