Protostellar collapse:: a comparison between smoothed particle hydrodynamics and adaptative mesh refinement calculations

Context. The rapid development of parallel supercomputers is enabling the detailed study of the collapse and the fragmentation of prestellar cores with increasingly accurate numerical simulations. Due to the advances also in sub-millimeter observation technology, we are now able to consider many different modes of low-mass star formation using observations of a range of initials conditions. The challenge for the simulations is to reproduce the observational results. Aims. Two main numerical methods, namely AMR and SPH, are widely used to simulate the collapse and the fragmentation of prestellar cores. We thoroughly compare these two methods within their standard framework. Methods. We use the AMR code RAMSES and the SPH code DRAGON. Our simplified physical model consists of an isothermal sphere rotating about the z-axis. First we study the conservation of angular momentum as a function of the resolution. Then, we explore a wide range of simulation parameters to study the fragmentation of prestellar cores. Results. There appears to be convergence between the two methods, provided numerical resolution in each case is sufficient. We deduced numerical resolution criteria adapted to our physical cases, in terms of resolution per Jeans mass, for an accurate description of the formation of protostellar cores. This convergence is encouraging for future work in simulations of low-mass star formation, providing the aforementioned criteria are fulfilled.