The Formation of Stellar Clusters: Mass Spectra from Turbulent Molecular Cloud Fragmentation

Star formation is intimately linked to the dynamical evolution of molecular clouds. Turbulent fragmentation determines where and when protostellar cores form, and how they contract and grow in mass via competitive accretion from the surrounding cloud material. This process is investigated, using numerical models of self-gravitating molecular cloud dynamics, where no turbulent support is included, where turbulence is allowed to decay freely, and where it is continuously replenished on large, intermediate and small scales, respectively. Molecular cloud regions without turbulent driving sources, or where turbulence is driven on large scales, exhibit rapid and efficient star formation in a clustered mode, whereas interstellar turbulence that carries most energy on small scales results in isolated star formation with low efficiency. The clump mass spectrum of shock-generated density fluctuations in pure hydrodynamic, supersonic turbulence is not well fit by a power law, and it is too steep at the high-mass end to be in agreement with the observational data. When gravity is included in the turbulence models, local collapse occurs, and the spectrum extends towards larger masses as clumps merge together, a power-law description dN/dM ∝ M becomes possible with slope ν ∼< −2. In the case of pure gravitational contraction, i.e. in regions without turbulent support, the clump mass spectrum is shallower with ν ≈ −3/2. The mass spectrum of protostellar cores in regions without turbulent support and where turbulence is replenished on large-scales, however, is well described by a log-normal or by multiple power laws, similar to the stellar IMF at low and intermediate masses. The model clusters are not massive enough to allow for comparison with the high-mass part of the IMF. In the case of small-scale turbulence, the core mass spectrum is too flat compared to the IMF for all masses. Subject headings: hydrodynamics – ISM: clouds – ISM: kinematics and dynamics – ISM: clump mass spectrum – stars: formation – stars: IMF – turbulence