Reionization through the lens of percolation theory

MNRAS 000, 1–16 (2015) Preprint 27 January 2016 Compiled using MNRAS L A TEX style file v3.0 Reionization through the lens of percolation theory Steven R. Furlanetto, 1? and S. Peng Oh 2 1 Department 2 Department of Physics & Astronomy, University of California, Los Angeles, Los Angeles, CA 90095, USA of Physics, University of California, Santa Barbara, Santa Barbara, CA 93106, USA arXiv:1511.01521v2 [astro-ph.CO] 25 Jan 2016 Accepted XXX. Received YYY; in original form ZZZ 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 x i ≈ 0.1 and quickly grows to encompass most of the ionized gas: by x i ∼ 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. Key words: cosmology: theory – intergalactic medium – dark ages, reionization, first stars – large scale structure of Universe INTRODUCTION The reionization of neutral hydrogen in the intergalactic medium (IGM) at z > ∼ 6 is one of the landmark events in the early history of structure formation in our Universe (e.g., Loeb & Furlanetto 2013). In addition to marking the point at which galaxy formation affected every baryon in the Uni- verse, it also represents the last major phase transition in the history of the Universe and has profound effects on the fuel supply for future generations of galaxies. As such, reioniza- tion has been a prime focus of diverse observational efforts including studies of the cosmic microwave background (Hin- shaw et al. 2013; Planck Collaboration et al. 2015), galaxy emission line studies (e.g., Kashikawa et al. 2006; Fontana et al. 2010; Schenker et al. 2012; Treu et al. 2012), and the nascent field of low-frequency radio observations of the red- shifted 21-cm line (Bowman & Rogers 2010; Paciga et al. 2011; Parsons et al. 2014; Dillon et al. 2015; Ali et al. 2015). As it presents a crucial constraint on galaxy formation, many studies of galaxies at z > ∼ 6 also focus their interpretation on the process of reionization (e.g., Robertson et al. 2015; Bouwens et al. 2015). One of the most fundamental aspects of the reionization E-mail: sfurlane@astro.ucla.edu (SRF) c 2015 The Authors process is the intermingled structure of the ionized and neu- tral material. Furlanetto et al. (2004) developed an analytic model to describe the growth of ionized bubbles from clus- tered sources during reionization. Using excursion set the- ory and a simple “photon-counting” criterion to determine whether a region is ionized, their model predicted the mass (or volume) distribution of ionized regions. The physical principles of that model have since been applied to a num- ber of “semi-numeric” algorithms to generate realizations of the ionization field from linear or quasilinear theory, includ- ing the public codes DexM (Mesinger & Furlanetto 2007) and 21cmFAST (Mesinger et al. 2011) amongst others (see Zahn et al. 2011). Meanwhile, fully numerical simulations have increased in both size and sophistication over the past decade, incorporating radiative transfer and hydrodynamics to study the reionization problem over a wide range of scales (e.g., So et al. 2014; Gnedin & Kaurov 2014; Iliev et al. 2014; Trac et al. 2015). In particular, the excursion set formalism is generally considered to provide a reasonably accurate pic- ture of the ionized bubbles throughout reionization, and its qualitative predictions have guided much of our intuition about the reionization process. To this point, the structure of ionized regions has typi- cally been quantified only crudely, through the power spec- trum of the ionization field (or the closely-related 21-cm in-