The Formation of Stellar Clusters in Turbulent Molecular Clouds: Effects of the Equation of State

We study numerically the effect of varying the equation of state (EOS) on the formation of stellar clusters in turbulent molecular clouds. Our results show that the EOS plays an important role in the fragmentation of the clouds, and the determination of the initial mass function (IMF) of the protostellar cores. Fragmentation decreases with increasing adiabatic index $\gamma$ in the range $0.2 < \gamma < 1.4$, although the total amount of mass accreted appears to remain roughly constant through that range, resulting in more massive cores at higher $\gamma$. Fragmentation and collapse ceases entirely for $\gamma > 1.4$ as expected from analytic arguments. Primordial gas may have effective $\gamma > 1$, in which case these results may help explain why models of the formation of the first stars produce isolated, massive objects.