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

TL;DR

This study uses fractal dimensions to analyze the clustering of neutral hydrogen during reionization, revealing multifractal behavior that depends on the reionization process and neutral fraction, offering a new way to constrain reionization history.

Contribution

It introduces the application of generalized fractal dimensions to HI density fields, highlighting their sensitivity to reionization stages and the morphology of ionized regions.

Findings

HI field shows significant multifractality at certain scales.

Fractal dimension varies with neutral fraction and reionization mode.

Less sensitivity to minimum halo mass in a specific range.

Abstract

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 (HI) during the epoch of reionization. Using a semi-numeric model of ionized bubbles to generate the HI field, we calculate the fractal dimensions for length scales $\sim 10 h^{-1}$ cMpc. We find that the HI field displays significant multifractal behaviour and is not consistent with homogeneity at these scales when the mass averaged neutral fraction $\bar{x}_{\rm HI}^M \gtrsim 0.5$. 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 $\sim 10^9 - 10^{10} h^{-1} M_{\odot}$. 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 HI density field at high redshifts can be used to study the nature of reionization.