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 gamma in the range 0.2 < gamma < 1.4, although the total amount of mass accreted onto collapsed fragments appears to remain roughly constant through that range. Low values of gamma are expected to lead to the formation of dense clusters of low-mass stars, while gamma > 1 probably results in the formation of isolated and massive stars. Fragmentation and collapse ceases entirely for gamma > 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 gamma less than or equal to 1 but flattens markedly for gamma > 1. The density probability function approaches lognormal, with widths that decrease with increasing gamma. Primordial gas may have effective gamma > 1, in which case these results could help explain why models of the formation of the first stars tend to produce isolated, massive objects.