Mapping the Present-Day Prestellar Core Mass Function into the Stellar IMF

Abstract

The fact that the shapes of the Present-Day Prestellar Core Mass Function (PDPCMF) and the Stellar Initial Mass Function (StIMF) appear to be very similar is purely coincidental, unless the mapping from the PDPCMF to the StIMF is statistically self similar. Either way, there is a huge amount of physics that occurs between a prestellar core and a protostar, and theories for the genesis of the PDPCMF should be presented as such, not as theories for the origin of the StIMF. Here we explore the constraints that the observed statistical properties of stars place on self-similar mappings. We find a simple mapping that is able to deliver the observed StIMF, the binary frequency as a function of primary mass, and the distribution of mass ratios for binaries with Sun-like primaries. This mapping implies that the local efficiency is high (typically a core spawns ∼ 4 stars, and these stars comprise ∼ 87% of the core’s initial mass); that most of the stars spawned by a single core have masses within a factor ∼ 4 of each other; that most cores deliver one long-lasting binary into the field, and in ∼ 75% of cases this binary involves the two most massive stars formed in the core; that the remaining ∼ 25% of binaries involve random pairings of the stars formed in the core.