Mapping the core mass function onto the stellar IMF: multiplicity matters

TL;DR

This paper investigates how the core mass function (CMF) maps onto the stellar initial mass function (IMF), emphasizing the role of multiplicity and binary statistics in constraining the parameters of this mapping.

Contribution

It introduces a method to estimate key parameters of the CMF-IMF mapping using binary star statistics, challenging the assumption of a purely self-similar relationship.

Findings

Estimated eta = 1.0 +/- 0.3, N0 = 4.3 +/- 0.4, sigma0 = 0.3 +/- 0.03, alpha = 0.9 +/- 0.6.

Binary statistics support a near-unity fraction of core mass forming stars.

The shape inheritance from CMF to IMF remains plausible given current data.

Abstract

Observations indicate that the central portions of the Present-Day Prestellar Core Mass Function (CMF) and the Stellar Initial Mass Function (IMF) both have approximately log-normal shapes, but that the CMF is displaced to higher mass than the IMF by a factor F = 4+/-1. This has lead to suggestions that the shape of the IMF is directly inherited from the shape of the CMF - and therefore, by implication, that there is a self-similar mapping from the CMF onto the IMF. If we assume a self-similar mapping, it follows (i) that F = N0/eta, where eta is the mean fraction of a core's mass that ends up in stars, and N0 is the mean number of stars spawned by a single core; and (ii) that the stars spawned by a single core must have an approximately log-normal distribution of relative masses, with universal standard deviation sigma0. Observations can be expected to deliver ever more accurate estimates of F, but this still leaves a degeneracy between eta and N0; and sigma0 is also unconstrained by observation. Here we show that these parameters can be estimated by invoking binary statistics. Specifically, if (a) each core spawns one long-lived binary system, and (b) the probability that a star of mass M is part of this long-lived binary is proportional to M^alpha, current observations of the binary frequency as a function of primary mass and the distribution of mass ratios strongly favour eta = 1.0 +/- 0.3, N0 = 4.3 +/- 0.4, sigma0 = 0.3 +/- 0.03 and alpha = 0.9 +/- 0.6. The mapping from CMF to IMF is not necessarily self-similar - there are many possible motivations for a non self-similar mapping - but if it is not, then the shape of the IMF cannot be inherited from the CMF. Given the limited observational constraints currently available and the ability of a self-similar mapping to satisfy them, the possibility that the shape of the IMF is inherited from the CMF cannot be ruled out at this juncture.