Ionization-induced star formation - I. The collect-and-collapse model

We conduct smoothed particle hydrodynamics simulations of the 'collect-and-collapse' scenario for star formation triggered by an expanding H II region. We simulate the evolution of a spherical uniform molecular cloud with an ionizing source at its centre. The gas in the cloud is self-gravitating, although the cloud is prevented from globally collapsing. We find that the shell driven by the H II region fragments to form numerous self-gravitating objects. We repeat our calculations at four numerical resolutions to ensure that they are converged. We compare our results to the analytical model of Whitworth et al. and show that our simulations and the predictions of Whitworth et al. are in good agreement in the sense that the shell fragments at the time and radius predicted by Whitworth et al. to within 20 and 25 per cent, respectively. Most of the fragments produced in our two highest resolution calculations are approximately half the mass of those predicted by Whitworth et al., but this conclusion is robust against both numerical resolution and the presence of random noise (local fluctuations in density of a factor of similar to 2) in the initial gas distribution. We conclude that such noise has little impact on the fragmentation process.