Reionization Through the Lens of Percolation Theory

TL;DR

This paper models cosmic reionization as a percolation phase transition, revealing an abrupt formation of a giant ionized region at a critical ionized fraction, with implications for understanding the distribution of ionized and neutral gas.

Contribution

It introduces a formal percolation theory framework to analyze reionization, identifying critical thresholds and distribution patterns of ionized regions during the process.

Findings

Infinitely-large ionized region appears at ~0.1 ionized fraction

Near power-law distribution of ionized regions before transition

Most of the intergalactic medium is divided into two large regions during reionization

Abstract

The reionization of intergalactic hydrogen has received intense theoretical scrutiny over the past two decades. Here, we approach the process formally as a percolation process and phase transition. Using semi-numeric simulations, we demonstrate that an infinitely-large ionized region abruptly appears at an ionized fraction of ~0.1 and quickly grows to encompass most of the ionized gas: by an ionized fraction of 0.3, nearly ninety percent of the ionized material is part of this region. Throughout most of reionization, nearly all of the intergalactic medium is divided into just two regions, one ionized and one neutral, and both infinite in extent. We also show that the discrete ionized regions that exist before and near this transition point follow a near-power law distribution in volume, with equal contributions to the total filling factor per logarithmic interval in size up to a sharp cutoff in volume. These qualities are generic to percolation processes, with the detailed behavior a result of long-range correlations in the underlying density field. These insights will be crucial to understanding the distribution of ionized and neutral gas during reionization and provide precise meaning to the intuitive description of reionization as an "overlap" process.