Understanding the formation and evolution of protostellar discs is a key ingredient in star-formation theory. Due to angular momentum conservation, almost all matter falling onto a protostellar object first accretes onto a disc-like structure. The size, ma ss and stability of such a protostellar disc determines the probability of sub- fragmentation into a binary or higher-order multiple system, as well as the properties of the planetary system that may build up in the late phases of disc evolution. We invest igate star formation and protostellar disc evolution in turbulent interstellar gas clouds using Smoothed Particle Hydrodynamics (SPH) with Particle Splitting to follow the time evolution of the system. Previous SPH simulations of turbulent clouds without P article Splitting have lead to the formation of clusters of protostars. The large-scale characteristics of these clusters greatly resemble those of observed young clusters, like the Trapezium. However, so far the numerical resolution has not been adequate for the detailed modelling of the protostellar discs. With Particle Splitting we will ensure that the numerical resolution of the simulations is always sufficient for the modelling of self-gravitating gas at all scales. This will allow us to study star and planet formation in unprecedented detail, and to investigate the complex dynamical interplay between gas on cluster scales and the evolution of individual protostellar discs on very small scales. We aim to understand the frequency of binary/multiple stell ar systems, the overall efficiency of star-cluster formation, the boundedness of such clusters, the resulting stellar and planetary mass spectrum, the probability for planet formation in the disc, and in particular, the efficiency of disc fragmentation as a mechanism for forming gas giant planets, the radial distribution of the planets formed, and the formation of gaps in the discs as a result of accretion onto protoplanetary objects.
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