This paper describes the open-source code Enzo, which uses block-structured adaptive mesh refinement to provide high spatial and temporal resolution for modeling astrophysical fluid flows. The code is Cartesian, can be run in 1, 2, and 3 dimensions, and supports a wide variety of physics including hydrodynamics, ideal and non-ideal magnetohydrodynamics, N-body dynamics (and, more broadly, self-gravity of fluids and particles), primordial gas chemistry, optically-thin radiative cooling of primordial and metal-enriched plasmas (as well as some optically-thick cooling models), radiation transport, cosmological expansion, and models for star formation and feedback in a cosmological context. In addition to explaining the algorithms implemented, we present solutions for a wide range of test problems, demonstrate the code's parallel performance, and discuss the Enzo collaboration's code development methodology.

We use high-quality echelle spectra of 24 quasi-stellar objects to provide a calibrated measurement of the total amount of Lyα forest absorption (DA) over the redshift range 2.2 < z < 3.2. Our measurement of DA excludes absorption from metal lines or the Lyα lines of Lyman-limit systems and damped Lyα systems. We use artificial spectra with realistic flux calibration errors to show that we are able to place continuum levels that are accurate to better than 1 per cent. When we combine our results with our previous results between 1.6 < z < 2.2, we find that the redshift evolution of DA is well described over 1.6 < z < 3.2 as A (1 +z) γ , where A = 0.0062 and γ = 2.75. We detect no significant deviations from a smooth power-law evolution over the redshift range studied. We find less H I absorption than expected at z = 3, implying that the ultraviolet background is ∼40 per cent higher than expected. Our data appears to be consistent with an H I ionization rate of ∼ 1.4 × 10 −12 s −1 .

We use a fully self-consistent cosmological simulation including dark matter dynamics, multispecies hydrodynamics, chemical ionization, flux limited diffusion radiation transport, and a parameterized model of star formation and feedback (thermal and radiative) to investigate the epoch of hydrogen reionization in detail. Our numerical method is scalable with respect to the number of radiation sources, size of the mesh, and the number of computer processors employed, and is described in Paper I of this series. In this the first of several application papers, we investigate the mechanics of reionization from stellar sources forming in high-z galaxies, the utility of various formulations for the gas clumping factor on accurately estimating the effective recombination time in the IGM, and the photon budget required to achieve reionization. We also test the accuracy of the static and time-dependent models of Madau et al. as predictors of reionization completion/maintenance.We simulate a WMAP7 ΛCDM cosmological model in a 20 Mpc comoving cube, resolved with 800 3 uniform fluid cells and dark matter particles. By tuning our star formation recipe to approximately match the observed high redshift star formation rate density and galaxy luminosity function, we have created a fully coupled radiation hydrodynamical realization of hydrogen reionization which begins to ionize at z ≈ 10 and completes at z ≈ 5.8 without further tuning. The complicated events during reionization that lead to this number can be generally described as inside-out, but in reality the narrative depends on the level of ionization of the gas one attributes to as ionized. We find that roughly 2 ionizing photons per H atom are required to convert the neutral IGM to a highly ionized state, which supports the "photon starved" reionization scenario discussed by Bolton & Haehnelt. We find that the formula for the ionizing photon production rateṄ ion (z) needed to maintain the IGM in an ionized state derived by Madau et al. should not be used to predict the epoch of reionization completion because it ignores history-dependent terms in the global ionization balance which are not ignorable. We find that the time-dependent model for the ionized volume fraction Q HII is more predictive, but overestimates the redshift of reionization completion z reion by ∆z ≈ 1. We propose a revised formulation of the time-dependent model which agrees with our simulation to high accuracy. Finally, we use our simulation data to estimate a globally averaged ionizing escape fraction due to circumgalactic gas resolved on our meshf esc (CGM ) ≈ 0.7.

Enzo (Enzo Developers, 2019a) is a block-structured adaptive mesh refinement code that is widely used to simulate astrophysical fluid flows (primarily, but not exclusively, cosmological structure formation, star formation, and turbulence). The code is a community project with dozens of users, and has contributed to hundreds of peer-reviewed publications in astrophysics, physics, and computer science. The code utilizes a Cartesian mesh can be run in one, two, or

We describe an extension of the Enzo code to enable fully-coupled radiation hydrodynamical simulation of inhomogeneous reionization in large ∼ (100M pc) 3 cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. (2009) differing principally in the operator splitting algorithm we we use to advance the system of equations. Radiation transport is done in the grey flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200 3 Eulerian grid cells and dark matter particles.