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Recently, Hennebelle and Chabrier (2008) derived an analytical theory for themass spectrum of non self-gravitating clumps associated with overdensities inmolecular clouds and for the initial mass function of gravitationally boundprestellar cores, as produced by the turbulent collapse of the cloud. In thiscompanion 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 apolytropic 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. Wealso consider a barotropic equation of state (i.e. a piecewise polytropic eos)that mimics the thermal behaviour of the molecular gas and compare theprediction of our theory with the results of numerical simulations and with theobservationally-derived IMF, for cloud parameters which satisfy Larson's typerelations. We find that for clouds whose density is, at all scales, almost anorder of magnitude larger than the density inferred for the CO clumps in theGalaxy, a good agreement is obtained between the theory and the observed IMF,suggesting that star formation preferentially occurs in high densityenvironments. We derive an analytical expression for the IMF which generalizesthe expression previously obtained for the isothermal case. Thiseasy-to-implement analytical IMF should serve as a template to compareobservational or numerical results with the theory.

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