Mapping the core mass function to the initial mass function

TL;DR

This paper develops analytic models linking turbulent fragmentation in molecular clouds to the initial mass function (IMF), predicting the IMF's slope and turnover mass based on turbulence and equation of state effects.

Contribution

It extends analytic models of turbulent fragmentation to include hierarchical core collapse, predicting the IMF's slope and turnover mass with dependencies on turbulence and EOS.

Findings

IMF slope is slightly steeper than CMF slope due to collapse dynamics.

Turnover mass is influenced by the sonic scale and equation of state.

Stiffening the EOS at low densities reproduces observed IMF turnover.

Abstract

It has been shown that fragmentation within self-gravitating, turbulent molecular clouds ("turbulent fragmentation") can naturally explain the observed properties of protostellar cores, including the core mass function (CMF). Here, we extend recently-developed analytic models for turbulent fragmentation to follow the time-dependent hierarchical fragmentation of self-gravitating cores, until they reach effectively infinite density (and form stars). We show that turbulent fragmentation robustly predicts two key features of the IMF. First, a high-mass power-law scaling very close to the Salpeter slope, which is a generic consequence of the scale-free nature of turbulence and self-gravity. We predict the IMF slope (-2.3) is slightly steeper then the CMF slope (-2.1), owing to the slower collapse and easier fragmentation of large cores. Second, a turnover mass, which is set by a combination of the CMF turnover mass (a couple solar masses, determined by the `sonic scale' of galactic turbulence, and so weakly dependent on galaxy properties), and the equation of state (EOS). A "soft" EOS with polytropic index $\gamma<1.0$ predicts that the IMF slope becomes "shallow" below the sonic scale, but fails to produce the full turnover observed. An EOS which becomes "stiff" at sufficiently low surface densities $\Sigma_{\rm gas} \sim 5000\,M_{\odot}\,{\rm pc^{-2}}$, and/or models where each collapsing core is able to heat and effectively stiffen the EOS of a modest mass ($\sim 0.02\,M_{\odot}$) of surrounding gas, are able to reproduce the observed turnover. Such features are likely a consequence of more detailed chemistry and radiative feedback.