A bubble size distribution model for the Epoch of Reionization

The bubble size distribution is a summary statistics that can be computed from the observed 21-cm signal from the Epoch of Reionization. As it depends only on the ionization field and is not limited to gaussian information, it is an interesting probe, complementary to the power spectrum of the full 21-cm signal. Devising a flexible and reliable theoretical model for the bubble size distribution paves the way for using it for astrophysical parameters inference. The proposed model is built from the excursion set theory and a functional relation between the bubble volume and the collapsed mass in the bubble. Unlike previous models it accommodates any functional relation or distributions. Using parameterized relations allows us to test the predictive power of the model by performing a minimization best-fit to the bubble size distribution obtained from a high resolution, fully coupled radiative hydrodynamics simulations, HIRRAH-21. Our model is able to provide a better fit to the numerical bubble size distribution at ionization fraction of $x_{\text{H}_{\text{II}}} \sim 1\%$ and $3\%$ than other existing models. Moreover, the bubble volume to collapsed mass relation corresponding to the best-fit parameters, which is not an observable, is compared to numerical simulation data. A good match is obtained, confirming the possibility to infer this relation from an observed bubble size distribution using our model. Finally we present a simple algorithm that empirically implements the process of percolation. We show that it extends the usability of our bubble size distribution model up to $x_{\text{H}_{\text{II}}} \sim 30\%$.