  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 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.
