Studying neutral hydrogen structures during the epoch of reionization using fractal dimensions

Fractal dimensions can be used to characterize the clustering and lacunarities in density distributions. We use generalized fractal dimensions to study the neutral hydrogen distribution (H i) during the epoch of reionization. Using a semi-numeric model of ionized bubbles to generate the H i field, we calculate the fractal dimensions for length-scales ∼10 h−1cMpc. We find that the H i field displays significant multifractal behaviour and is not consistent with homogeneity at these scales when the mass-averaged neutral fraction |x̄_ H\, IM 0.5|⁠. This multifractal nature is driven entirely by the shapes and distribution of the ionized regions. The sensitivity of the fractal dimension to the neutral fraction implies that it can be used for constraining reionization history. We find that the fractal dimension is relatively less sensitive to the value of the minimum mass of ionizing haloes when it is in the range ∼109–1010h−1M⊙. Interestingly, the fractal dimension is very different when the reionization proceeds inside-out compared to when it is outside-in. Thus, the multifractal nature of H i density field at high redshifts can be used to study the nature of reionization.