  We perform SPH simulations of the collapse and fragmentation of low-mass
cores having different initial levels of turbulence
(alpha_turb=0.05,0.10,0.25). We use a new treatment of the energy equation
which captures the transport of cooling radiation against opacity due to both
dust and gas (including the effects of dust sublimation, molecules, and H^-
ions). We also perform comparison simulations using a standard barotropic
equation of state. We find that -- when compared with the barotropic equation
of state -- our more realistic treatment of the energy equation results in more
protostellar objects being formed, and a higher proportion of brown dwarfs; the
multiplicity frequency is essentially unchanged, but the multiple systems tend
to have shorter periods (by a factor ~3), higher eccentricities, and higher
mass ratios. The reason for this is that small fragments are able to cool more
effectively with the new treatment, as compared with the barotropic equation of
state. We find that the process of fragmentation is often bimodal. The first
protostar to form is usually, at the end, the most massive, i.e. the primary.
However, frequently a disc-like structure subsequently forms round this
primary, and then, once it has accumulated sufficient mass, quickly fragments
to produce several secondaries. We believe that this delayed fragmentation of a
disc-like structure is likely to be an important source of very low-mass
hydrogen-burning stars and brown dwarfs.
