A bubble size distribution model for the Epoch of Reionization

Abstract

Aims. 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 that is 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 its use in astrophysical parameter inference. Methods. The proposed model was 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 can accommodate any functional relation or distribution. The use of 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 simulation known as HIRRAH-21. Results. Our model is able to provide a better fit to the numerical bubble size distribution at an ionization fraction of xH II ∼ 1% and 3%, as compared to other existing models. Moreover, we compare the relation between the bubble volume and the collapsed mass corresponding to the best-fit parameters, which is not an observable, to the numerical simulation data. A good match is obtained, confirming the possibility of inferring 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 xH II ∼ 30%.