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

Abstract

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, which models gravito-turbulent 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 disk 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 disks. We suggest that such close binaries are produced primarily by disk fragmentation and further decrease their separation through orbital decay.