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 gamma from 0.7 to 1.1 at a critical density n(c), which we estimated to be 2.5 x 10(5) 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) proportional to n(c)(-0.95). We perform simulations with 4.3 x 10(4) cm(-3) < n(c) < 4.3 x 10(7) cm(-3) to test this scaling argument. Our simulations qualitatively support this hypothesis, but we find a weaker density dependence of M(ch) proportional to 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.