Simulating star clusters across cosmic time - II. Escape fraction of ionizing photons from molecular clouds

We calculate the hydrogen- and helium-ionizing radiation escaping star-forming molecular clouds, as a function of the star cluster mass and compactness, using a set of high-resolution radiation-magnetohydrodynamic simulations of star formation in self-gravitating, turbulent molecular clouds. In these simulations, presented in He et al., the formation of individual massive stars is well resolved, and their UV radiation feedback and lifetime on the main sequence are modelled self-consistently. We find that the escape fraction of ionizing radiation from molecular clouds, < f_esc^{MC}> , decreases with increasing mass of the star cluster and with decreasing compactness. Molecular clouds with densities typically found in the local Universe have negligible < f_esc^{MC}> , ranging between 0.5 per cent and 5 per cent. 10 times denser molecular clouds have < f_esc^{MC}> ≈ 10 per cent-20 per cent, while 100× denser clouds, which produce globular cluster progenitors, have < f_esc^{MC}> ≈ 20 per cent-60 per cent. We find that < f_esc^{MC}> increases with decreasing gas metallicity, even when ignoring dust extinction, due to stronger radiation feedback. However, the total number of escaping ionizing photons decreases with decreasing metallicity because the star formation efficiency is reduced. We conclude that the sources of reionization at z > 6 must have been very compact star clusters forming in molecular clouds about 100× denser than in today's Universe, which lead to a significant production of old globular clusters progenitors.