The Formation of Stellar Clusters: Gaussian Cloud Conditions. I.

The isothermal dynamical evolution of a clumpy molecular cloud region and its fragmentation into a protostellar cluster is investigated numerically. The initial density distributions are generated from different realizations of a Gaussian random field with power spectrum P(k) ∝ k^-2. During the evolution of the system, the one-point probability distribution functions (PDFs) of the gas density and of the line-of-sight velocity centroids develop considerable distortions away from the initial Gaussian behavior. The density PDF can be best described by power-law distributions, whereas the velocity PDF exhibits extended tails. As a result of the interplay between gas pressure and gravitational forces, a quasi-equilibrium clump mass spectrum emerges with a power-law distribution dN/dM ∝ M^-1.5. Being part of a complex network of filaments, individual clumps are elongated, centrally condensed objects with 2 : 1 to 4 : 1 axis ratios with outer r^-2 density distributions. Dense, Jeans-unstable gas clumps collapse and form protostellar cores that evolve through competitive accretion and N-body interactions with other cores. In contrast to the clumps, the core mass spectrum is best described by a lognormal distribution that peaks approximately at the average Jeans mass of the system. Scaled to physical conditions typical for star-forming molecular clouds, the mass function is in good agreement with the initial mass function (IMF) of multiple stellar systems. The final dynamical state of the newly formed stellar cluster closely resembles observed young stellar clusters. It has a core/halo structure, which is typical for collision dominated N-body systems. The two-point correlation function of the spatial stellar distribution can be described by two power laws with a break in the slope at the transition point from the binary to the large-scale clustering regime. The protostellar cluster is marginally bound and would be easily disrupted if the conversion of cores into stars were inefficient.