GRAPESPH with Fully Periodic Boundary Conditions: Fragmentation of Molecular Clouds

A method of adapting smoothed particle hydrodynamics (SPH) with periodic boundary conditions for use with the special purpose device GRAPE is presented. GRAPE (GRAvity PipE) solves the Poisson and force equations for an N-body system by direct summation on a specially designed chip and in addition returns the neighbour list for each particle. Due to its design, GRAPE cannot treat periodic particle distributions directly. This limitation of GRAPESPH can be overcome by computing a correction force for each particle due to periodicity (Ewald correction) on the host computer using a PM-like method. This scheme is applied to study the fragmentation process in giant molecular clouds. Assuming a pure isothermal model, we follow the dynamical evolution in the interior of a molecular cloud starting from an Gaussian initial density distribution to the formation of selfgravitating clumps until most of the gas is consumed in these dense cores. Despite its simplicity, this model can reproduce some fundamental properties of observed molecular clouds, like a clump mass distribution of the form $dN/dm \propto m^n$, with $n ~ -1.5$.