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

We study the effect of varying the equation of state on the formation of stellar clusters in turbulent molecular clouds using three-dimensional, smoothed particle hydrodynamics simulations. Our results show that the equation of state helps determine how strongly self-gravitating gas fragments. The degree of fragmentation decreases with increasing polytropic exponent γ in the range 0.2 < γ < 1.4, although the total amount of mass accreted onto collapsed fragments appears to remain roughly constant through that range. Low values of γ are expected to lead to the formation of dense clusters of low-mass stars, while γ > 1 probably results in the formation of isolated and massive stars. Fragmentation and collapse ceases entirely for γ > 1.4, as expected from analytic arguments. The mass spectrum of overdense gas clumps is roughly lognormal for non -self-gravitating turbulent gas, but changes to a power law under the action of gravity. The spectrum of collapsed cores, on the other hand, remains lognormal for γ ≤ 1 but flattens markedly for γ > 1. The density probability function approaches lognormal, with widths that decrease with increasing γ. Primordial gas may have effective γ > 1, in which case these results could help explain why models of the formation of the first stars tend to produce isolated, massive objects.