Protostellar feedback in turbulent fragmentation: consequences for stellar clustering and multiplicity

Stars are strongly clustered on both large (∼pc) and small (∼binary) scales, but there are few analytic or even semi-analytic theories for the correlation function and multiplicity of stars. In this paper, we present such a theory, based on our recently developed semi-analytic framework called MISFIT (Minimalistic Star Formation Including Turbulence), which models gravitoturbulent fragmentation, including the suppression of fragmentation by protostellar radiation feedback. We compare the results including feedback to a control model in which it is omitted. We show that both classes of models robustly reproduce the stellar correlation function at >0.01 pc scales, which is well approximated by a power law that follows generally from scale-free physics (turbulence plus gravity) on large scales. On smaller scales, protostellar disc fragmentation becomes dominant over common core fragmentation, leading to a steepening of the correlation function. Multiplicity is more sensitive to feedback: we found that a model with the protostellar heating reproduces the observed multiplicity fractions and mass ratio distributions for both Solar and sub-Solar mass stars (in particular, the brown dwarf desert), while a model without feedback fails to do so. The model with feedback also produces an at-formation period distribution consistent with the one inferred from observations. However, it is unable to produce short-range binaries below the length-scale of protostellar discs. We suggest that such close binaries are produced primarily by disc fragmentation and further decrease their separation through orbital decay.