The formation of stellar clusters: gaussian cloud conditions. II.

Using hydrodynamic simulations, we investigate the time evolution and fragmentation of regions within molecular clouds that have lost their turbulent support, leading to gravitational contraction. The initial density distributions are described by random Gaussian fluctuations with varying slopes nu of the power spectrum P(k) proportional to k(-nu), covering the range from flat (nu = 0) to very steep (nu = 3) spectra. We consider molecular cloud volumes containing different masses relative to the average Jeans mass M(J), from 1M(J) to 222M(J). This parameter study extends a previous detailed analysis of systems with, initially, P(k) proportional to k(-2) and mass 222M(J). 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 complex 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 a 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.