An improved model of H II bubbles during the epoch of reionization

The size distribution of ionized regions during the epoch of reionization - a key ingredient in understanding the H I power spectrum observable by 21 cm experiments - can be modelled analytically using the excursion set formalism of random walks in the smoothed initial density field. To date, such calculations have been based on simplifying assumptions carried forward from the earliest excursion set models of two decades ago. In particular, these models assume that the random walks have uncorrelated steps and that haloes can form at arbitrary locations in the initial density field. We extend these calculations by incorporating recent technical developments that allow us to (a) include the effect of correlations in the steps of the walks induced by a realistic smoothing filter and (b) more importantly, account for the fact that dark matter haloes preferentially form near peaks in the initial density. A comparison with previous calculations shows that including these features, particularly the peaks constraint on halo locations, has large effects on the size distribution of the H II bubbles surrounding these haloes. For example, when comparing models at the same value of the globally averaged ionized volume fraction, the typical bubble sizes predicted by our model are more than a factor of 2 larger than earlier calculations. Our results can potentially have a significant impact on estimates of the observable H I power spectrum.