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

Using hydrodynamic simulations, we investigate the time evolution and fragm entation of regions within molecular clouds that have lost their turbulent support, leading to gravitational contraction. The initial density distribu tions 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 v olumes containing different masses relative to the average Jeans mass M-J, from 1M(J) to 222M(J). This parameter study extends a previous detailed ana lysis of systems with, initially, P(k) proportional to k(-2) and mass 222M( J). The dynamical evolution of the simulated molecular cloud regions is ins ensitive to the slope of the initial density fluctuation spectrum. The syst em evolves into a complex network of intersecting filaments and collapsing clumps, leading to the formation of a compact cluster of accreting and inte racting embedded protostellar cores. The cluster builds up as a bound entit y but dissolves later due to collisional effects. In all simulations, the m ass spectrum of collapsed cores is very broad, has approximately log-normal shape, and peaks roughly at the average Jeans mass. This supports the hypo thesis that the average Jeans mass is the main parameter determining the pe ak in the stellar spectrum and suggests that the interplay between self-gra vity on the one side and thermal and turbulent pressure on the other side i s the dominant process that regulates the formation of stellar clusters.