The stellar mass spectrum from non-isothermal gravoturbulent fragmentation

The thermodynamic state of star-forming gas determines its fragmentation behavior and thus plays a crucial role in determining the stellar initial mass function (IMF). We address the issue by studying the effects of a piecewise polytropic equation of state (EOS) on the formation of stellar clusters in turbulent, self-gravitating molecular clouds using three-dimensional, smoothed particle hydrodynamics simulations. In these simulations stars form via a process we call gravoturbulent fragmentation, i.e., gravitational fragmentation of turbulent gas. To approximate the results of published predictions of the thermal behavior of collapsing clouds, we increase the polytropic exponent γ from 0.7 to 1.1 at a critical density n_c, which we estimated to be 2.5 × 103 cm^-3. The change of thermodynamic state at n_c selects a characteristic mass scale for fragmentation M _ch, which we relate to the peak of the observed IMF. A simple scaling argument based on the Jeans mass M_J at the critical density n _c leads to M_ch ∝ n_c^-0.95. We perform simulations with 4.3 × 10⁴ cm^-3 < n _c < 4.3 × 10⁷ cm^-3 to test this scaling argument. Our simulations qualitatively support this hypothesis, but we find a weaker density dependence of M_ch ∝ n_c ^-0.5±0.1. We also investigate the influence of additional environmental parameters on the IMF. We consider variations in the turbulent driving scheme, and consistently find M_J is decreasing with increasing n_c. Our investigation generally supports the idea that the distribution of stellar masses depends mainly on the thermodynamic state of the star-forming gas. The thermodynamic state of interstellar gas is a result of the balance between heating and cooling processes, which in turn are determined by fundamental atomic and molecular physics and by chemical abundances. Given the abundances, the derivation of a characteristic stellar mass can thus be based on universal quantities and constants.