On the Properties of Cosmological Ionization Fronts

We investigate the properties of cosmological ionization fronts during the Epoch of Reionization using the CROC simulations. By analyzing reionization timing maps, we characterize ionization front velocities and curvatures and their dependence on the density structure of the intergalactic medium (IGM). The velocity distribution of ionization fronts in the simulations indicates that while the barrier-crossing analytical model captures the overall shape in high-velocity regions, it fails to reproduce the low-velocity tail, highlighting the non-Gaussian nature of the IGM's density field. Ionization front velocities are inversely correlated with local density, propagating faster in underdense regions and more slowly in overdense environments. Faster ionization fronts also lead to higher post-ionization temperatures, reaching a plateau at $\sim 2 \times 10^4$ K for velocities exceeding 3000 km/s. Examining curvature statistics further establishes a connection between ionization front structure and the normalized density contrast $\nu$, with trends in overdense regions aligning well with barrier-crossing model predictions, while deviations appear in underdense environments due to model limitations. These results provide a detailed characterization of ionization front dynamics and their interaction with the underlying density field, bridging small-scale reionization physics with large-scale observables such as the 21 cm signal and the IGM's thermal history.