Fragmentation and evolution of molecular clouds. I. Algorithm and first results

We present a series of simulations of the fragmentation of a molecular cloud, leading to the formation of a cluster of protostellar cores. We use Gaussian initial conditions with a power spectrum P(k) alpha k(-2), assume an isothermal equation of state, and neglect turbulence and magnetic fields. The purpose of these simulations is to address a specific numerical problem called artificial fragmentation, which plagues simulations of cloud fragmentation. We argue that this is a serious problem, and that the only reasonable and practical way to address it within the smoothed particle hydrodynamics (SPH) algorithm is to use a technique called particle splitting. We performed three simulations, with N-gen 0, 1, and 2 levels of particle splitting. All simulations start up with 643 SPH particles, but their effective resolutions correspond to 643, 1283, and 2563 particles, respectively. The third simulation properly resolves the Jeans mass throughout the entire system, at all times, thus preventing artificial fragmentation. The high resolution of our simulations results in the formation of a large number of protostellar cores, nearly 3000 for the largest simulation. The final mass distribution of cores is lognormal, and the distribution shifts down in mass as the resolution improves. The width of the distribution is about 1.5 (e. g., a factor of 30 in the mass), and the low-mass edge of the distribution corresponds to the lowest core mass that the code can resolve. This result differs from previous claims of a relationship between the mean of the distribution and the initial Jeans mass.