The stellar mass spectrum from non-isothermal gravoturbulent fragmentation

¹ Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany e-mail: akjappsen@aip.de
² Department of Astronomy, Yale University, New Haven, CT 06520-8101, USA
³ Department of Astrophysics, American Museum of Natural History, 79th Street at Central Park West, New York, NY 10024-5192, USA
⁴ Department of Astronomy, Columbia University, New York, NY 10027, USA

Received: 14 October 2004
Accepted: 12 January 2005

Abstract

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 . 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 at the critical density leads to . We perform simulations with to test this scaling argument. Our simulations qualitatively support this hypothesis, but we find a weaker density dependence of . We also investigate the influence of additional environmental parameters on the IMF. We consider variations in the turbulent driving scheme, and consistently find is decreasing with increasing . 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.