Analytical theory for the initial mass function: II. Properties of the flow

TL;DR

This paper extends an analytical model for the initial mass function of prestellar cores by incorporating non-isothermal effects, turbulence, and thermal physics, and compares predictions with simulations and observations.

Contribution

It introduces a generalized analytical IMF accounting for non-isothermality and thermal physics, improving agreement with observed IMFs in high-density environments.

Findings

The polytropic exponent significantly affects the low-mass IMF.

Good agreement with observed IMF occurs in high-density cloud conditions.

The derived analytical IMF can serve as a practical template for observations and simulations.

Abstract

Recently, Hennebelle and Chabrier (2008) derived an analytical theory for the mass spectrum of non self-gravitating clumps associated with overdensities in molecular clouds and for the initial mass function of gravitationally bound prestellar cores, as produced by the turbulent collapse of the cloud. In this companion paper, we examine the effects of the non-isothermality of the flow, of the turbulence forcing and of local fluctuation of the velocity dispersion, on the mass function. In particular, we investigate the influence of a polytropic equation of state and of the effective adiabatic exponent $\gamma$ and find that it has a drastic influence on the low mass part of the IMF. We also consider a barotropic equation of state (i.e. a piecewise polytropic eos) that mimics the thermal behaviour of the molecular gas and compare the prediction of our theory with the results of numerical simulations and with the observationally-derived IMF, for cloud parameters which satisfy Larson's type relations. We find that for clouds whose density is, at all scales, almost an order of magnitude larger than the density inferred for the CO clumps in the Galaxy, a good agreement is obtained between the theory and the observed IMF, suggesting that star formation preferentially occurs in high density environments. We derive an analytical expression for the IMF which generalizes the expression previously obtained for the isothermal case. This easy-to-implement analytical IMF should serve as a template to compare observational or numerical results with the theory.