Simulating cosmic reionization: how large a volume is large enough?

Abstract

We present the largest-volume (425 h −1 Mpc = 607 Mpc on a side) full radiative transfer simulation of cosmic reionization to date. We show that there is significant additional power in density fluctuations at very large scales. Although the halo power spectra are unaffected by this, there is strong modulation of the halo abundance reaching very large scales. We systematically investigate the effects this additional power has on the progress, duration and features of reionization, as well as on selected reionization observables. We find that comoving simulation volume of ∼ 100 h −1 Mpc per side is sufficient for deriving a convergent mean reionization history, but that the reionization patchiness is significantly underestimated. In the large-scale volume the isolated ionized regions reach volumes up to 4-10 times larger (depending on the measure being used) than they do in a smaller, 114 h −1 = 163 Mpc volume with the same source properties and reionization history, though the abundance of smaller ionized patches agrees well in the two cases. We use jackknife splitting of the large simulation volume to quantify the convergence of reionization properties with simulation volume for both mean-density and variable-density sub-regions. We find that sub-volumes of ∼ 100 h −1 Mpc per side or larger yield convergent reionization histories, except for the earliest times (corresponding to z ∼ > 20 − 25 for our parameters), but smaller volumes of ∼ 50 h −1 Mpc or less are not well converged at any redshift. Reionization history milestones, defined here as the redshifts at which the ionized fraction by mass reaches 10%, 50%, 90% and 99%, show significant scatter between the sub-volumes, of ∆z = 0.6 − 1 for ∼ 50 h −1 Mpc volumes, decreasing to ∆z = 0.3 − 0.5 for ∼ 100h −1 Mpc volumes, and ∆z ∼ 0.1 for ∼ 200 h −1 Mpc volumes. If we only consider mean-density sub-regions the scatter decreases, but remains at ∆z ∼ 0.1 − 0.2 for the different size sub-volumes. Consequently, many potential reionization observables like 21-cm rms, 21-cm PDF skewness and kurtosis all show good convergence for volumes of ∼ 200 h −1 Mpc, but retain considerable scatter for smaller volumes. In contrast, the three-dimensional 21-cm power spectra at large scales (k ∼ < 0.25 h Mpc −1 ) do not fully converge for any sub-volume size. These additional large-scale fluctuations significantly enhance the 21-cm fluctuations. At the rough beam-and bandwidth resolution expected for the LOFAR EoR experiment (3' and 440 kHz) and for our simulation parameters, the peak value of the rms 21-cm brightness temperature fluctuations as a function of frequency, derived from the large volume is ∼ 10% higher than for a ∼ 100 h −1 Mpc volume. At late times (high frequency), close to the overlap epoch, the signal derived from the large volume is up to 2.5 times larger, which should improve the prospects of detection considerably, given the lower foregrounds and greater interferometer sensitivity at higher frequencies.

Direct collapse black hole formation from synchronized pairs of atomic cooling haloes

“…Iliev et al 2014). At higher redshift, the density of the IGM will be greater leading to an increased rate of recombination.…”

The reionization of carbon

“…Its amplitude then jumps when reionization completes (z = 6.5). This is a well-known numerical artefact of computing reionization in small volumes (Barkana & Loeb 2004;Iliev et al 2014), and owes to an overly-rapid increase in the mean free path of ionizing photons.…”

“…These discrepancies can be traced to two factors. First, the tendency for the simulated τLyα to evolve too quickly is a well-known artefact of small volumes (Barkana & Loeb 2004;Iliev et al 2014) that will improve through increased dynamic range. Second, the Lyman-α forest is increasingly sensitive to rare voids at high redshifts (Bolton & Becker 2009); these are systematically absent from small volumes.…”

Non-linear bias of cosmological halo formation in the early universe

“…in the study of cosmic reionization, due to the very large dynamic gap between the very small galaxies believed to be the main drivers of reionization (see e.g. Ciardi & Ferrara 2005, for a review) and the large characteristic scales of the reionization patchiness (Friedrich et al 2011;Iliev et al 2014). Barkana & Loeb (2004) used a hybrid halo bias scheme to study the fluctuation of the 21cm background from the fluctuating halo distribution during the epoch of reionization (EoR).…”