The Formation of Stellar Clusters: Gaussian Initial Conditions II

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Abstract
Using hydrodynamic simulations we investigate the time evolution and fragmentation of regions within molecular clouds which have lost their turbulent support leading to gravitational contraction. The initial density distributions are described by random Gaussian fluctuations with varying slopes x of the power spectrum P(k) ~ k^-x, covering the range from flat (x=0) to very steep spectra (x=3). We consider molecular cloud volumes containing different masses relative to the average Jeans mass M_J, from 1 M_J to 222 M_J. This parameter study extends the detailed analysis of systems with initially P(k) ~ k^-2 and mass 222 M_J presented by Klessen & Burkert (2000). The dynamical evolution of the simulated molecular cloud regions is insensitive to the slope of the initial density fluctuation spectrum. The system evolves into a complicated network of intersecting filaments and collapsing clumps leading to the formation of a compact cluster of accreting and interacting embedded protostellar cores. The cluster builds up as bound entity, but dissolves later due to collisional effects. In all simulations, the mass spectrum of collapsed cores is very broad, has approximately log-normal shape and peaks roughly at the average Jeans mass. This supports the hypothesis that the average Jeans mass is the main parameter determining the peak in the stellar spectrum, and suggests that the interplay between self-gravity on the one side and thermal and turbulent pressure on the other side is the dominant process that regulates the formation of stellar clusters.

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