The dependence of the IMF on the density- temperature relation of pre-stellar gas

It has been recently shown by several authors that fragmentation of pre-stellar gas (i.e. at densities from 10⁴ to 10¹⁰ particles cm⁻³ and temperatures of order 10-30 K) depends on the gas thermodynamics much more than it was anticipated in earlier studies, in which only an isothermal behaviour has been assumed for the gas. Here we review the results of a number of numerical hydrodynamic simulations (e.g. Li et al. 2003, Jappsen et al. 2005, Bonnell et al. 2006) in which departure from isothermality has been attempted by employing a polytropic equation of state (eos) with exponent different from unity. In particular, in these studies it has been shown that the dominant fragmentation scale of pre-stellar gas, and hence the peak of the initial mass function (IMF), depends on a polytropic exponent that changes value, from below to above unity, at a critical density (Larson 2005). Furthermore, this piecewise polytropic eos depends on the gas metallicity and fundamental constants. Therefore, the peak of the IMF depends, in turn, also on the gas metallicity and fundamental constants rather than on initial conditions, as it has been previously suggested (e.g. Larson 1995). Hence, we are for the first time in a position to infer theoretically the notion of a universal IMF (at least for its low-mass end).