Galactic porosity and a star formation threshold for the escape of ionizing radiation from galaxies

The spatial distribution of star formation within galaxies strongly affects the resulting feedback processes. Previous work has considered the case of a single, concentrated nuclear starburst, and also that of distributed single supernovae (SNe). Here, we consider interstellar medium (ISM) structuring by SNe originating in spatially distributed clusters having a cluster membership spectrum given by the observed H II region luminosity function. We show that, in this case, the volume of H I cleared per SN is considerably greater than in either of the two cases considered hitherto. We derive a simple relationship between the 'porosity' of the ISM and the star formation rate (SFR), and deduce a critical SFRcrit, at which the ISM porosity is unity. This critical value describes the case in which the SN mechanical energy output over a time-scale (t(e)) is comparable with the ISM 'thermal' energy contained in random motions; t(e) is the duration of SN mechanical input per superbubble. This condition also defines a critical gas consumption time-scale t(exh), which for a Salpeter initial mass function and random velocities of similar or equal to10 km s(-1) is roughly 10(10) yr. We draw a link between porosity and the escape of ionizing radiation from galaxies, arguing that high escape fractions are expected if SFR greater than or similar to SFRcrit. The Lyman break galaxies, which are presumably subject to infall on a time-scale <t(exh), meet this criterion, as is consistent with the significant leakage of ionizing photons inferred in these systems. We suggest the utility of this simple parametrization of the escape fraction in terms of the SFR for semi-empirical models of galaxy formation and evolution and for modelling mechanical and chemical feedback effects.