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.

Starlight from galaxies plays a pivotal role throughout the process of cosmic reionisation. We present the statistics of dwarf galaxy properties at z > 7 in haloes with masses up to 10 9 M , using a cosmological radiation hydrodynamics simulation that follows their buildup starting with their Population III progenitors. We find that metal-enriched star formation is not restricted to atomic cooling (T vir 10 4 K) haloes, but can occur in haloes down to masses ∼ 10 6 M , especially in neutral regions. Even though these smallest galaxies only host up to 10 4 M of stars, they provide nearly 30 per cent of the ionising photon budget. We find that the galaxy luminosity function flattens above M UV ∼ −12 with a number density that is unchanged at z 10. The fraction of ionising radiation escaping into the intergalactic medium is inversely dependent on halo mass, decreasing from 50 to 5 per cent in the mass range log M/M = 7.0 − 8.5. Using our galaxy statistics in a semi-analytic reionisation model, we find a Thomson scattering optical depth consistent with the latest Planck results, while still being consistent with the UV emissivity constraints provided by Lyα forest observations at z = 4 − 6.

By definition, Population III stars are metal-free, and their protostellar collapse is driven by molecular hydrogen cooling in the gas-phase, leading to large characteristic masses. Population II stars with lower characteristic masses form when the star-forming gas reaches a critical metallicity of 10 −6 − 10 −3.5 Z ⊙ . We present an adaptive mesh refinement radiation hydrodynamics simulation that follows the transition from Population III to II star formation. The maximum spatial resolution of 1 comoving parsec allows for individual molecular clouds to be well-resolved and their stellar associations to be studied in detail. We model stellar radiative feedback with adaptive ray tracing. A top-heavy initial mass function for the Population III stars is considered, resulting in a plausible distribution of pair-instability supernovae and associated metal enrichment. We find that the gas fraction recovers from 5 percent to nearly the cosmic fraction in halos with merger histories rich in halos above 10 7 M ⊙ . A single pair-instability supernova is sufficient to enrich the host halo to a metallicity floor of 10 −3 Z ⊙ and to transition to Population II star formation. This provides a natural explanation for the observed floor on damped Lyman alpha (DLA) systems metallicities reported in the literature, which is of this order. We find that stellar metallicities do not necessarily trace stellar ages, as mergers of halos with established stellar populations can create superpositions of t − Z evolutionary tracks. A bimodal metallicity distribution is created after a starburst occurs when the halo can cool efficiently through atomic line cooling.

It has been argued that low-luminosity dwarf galaxies are the dominant source of ionizing radiation during cosmological reionization. The fraction of ionizing radiation that escapes into the intergalactic medium from dwarf galaxies with masses less than ∼ 10 9.5 solar masses plays a critical role during this epoch. Using an extensive suite of very high resolution (0.1 pc), adaptive mesh refinement, radiation hydrodynamical simulations of idealized and cosmological dwarf galaxies, we characterize the behavior of the escape fraction in galaxies between 3 × 10 6 and 3 × 10 9 solar masses with different spin parameters, amounts of turbulence, and baryon mass fractions. For a given halo mass, escape fractions can vary up to a factor of two, depending on the initial setup of the idealized halo. In a cosmological setting, we find that the time-averaged photon escape fraction always exceeds 25% and reaches up to 80% in halos with masses above 10 8 solar masses with a top-heavy initial mass function (IMF). The instantaneous escape fraction can vary up to an order of magnitude in a few million years and tends to be positively correlated with star formation rate. We find that the mean of the star formation efficiency times ionizing photon escape fraction, averaged over all atomic cooling (T vir 8000 K) galaxies, ranges from 0.02 for a normal IMF to 0.03 for a top-heavy IMF, whereas smaller, molecular cooling galaxies in minihalos do not make a significant contribution to reionizing the universe due to much lower star formation rates. These results provide the physical basis for cosmological reionization by stellar sources, predominately atomic cooling dwarf galaxies.

The first stars in the universe, forming at redshifts z > 15 in minihalos with masses of order 10 5−6 M ⊙ , may leave behind black holes as their remnants. These objects could conceivably serve as "seeds" for much larger black holes observed at redshifts z 7. We study the growth of the remnant black holes through accretion including for the first time the emitted accretion radiation with adaptive mesh refinement cosmological radiationhydrodynamical simulations. The effects of photo-ionization and heating dramatically affect the accretion flow from large scales, resulting in negligible mass growth of the black hole. We compare cases with the accretion luminosity included and neglected to show that the accretion radiation drastically changes the environment within 100 pc of the black hole, where gas temperatures are increased by an order of magnitude. The gas densities are reduced and further star formation in the same mini-halo prevented for the two hundred million years of evolution we followed. These calculations show that even without the radiative feedback included most seed black holes do not gain mass as efficiently as has been hoped for in previous theories, implying that black hole remnants of Pop III stars that formed in minihalos are not likely to be the origin of miniquasars. Most importantly, however, these calculations demonstrate that if early stellar mass black holes are indeed accreting close to the Bondi-Hoyle rate with ten percent efficiency they have a dramatic local effect in regulating star formation in the first galaxies.

Cosmic reionization is thought to be primarily fueled by the first generations of galaxies. We examine their stellar and gaseous properties, focusing on the star formation rates and the escape of ionizing photons, as a function of halo mass, redshift, and environment using the full suite of the Renaissance Simulations with an eye to provide better inputs to global reionization simulations. This suite, carried out with the adaptive mesh refinement code Enzo, is unprecedented in terms of their size and physical ingredients. The simulations probe overdense, average, and underdense regions of the universe of several hundred comoving Mpc 3 , each yielding a sample of over 3,000 halos in the mass range 10 7 − 10 9.5 M at their final redshifts of 15, 12.5, and 8, respectively. In the process, we simulate the effects of radiative and supernova feedback from 5,000 to 10,000 metal-free (Population III) stars in each simulation. We find that halos as small as 10 7 M are able to form stars due to metal-line cooling from earlier enrichment by massive Population III stars. However, we find such halos do not form stars continuously. Using our large sample, we find that the galaxy-halo occupation fraction drops from unity at virial masses above 10 8.5 M to ∼50% at 10 8 M and ∼10% at 10 7 M , quite independent of redshift and region. Their average ionizing escape fraction is ∼5% in the mass range 10 8 − 10 9 M and increases with decreasing halo mass below this range, reaching 40-60% at 10 7 M . Interestingly, we find that the escape fraction varies between 10-20% in halos with virial masses ∼ 3 × 10 9 M . Taken together, our results confirm the importance of the smallest galaxies as sources of ionizing radiation contributing to the reionization of the universe.

We present the Grackle chemistry and cooling library for astrophysical simulations and models. Grackle provides a treatment of non-equilibrium primordial chemistry and cooling for H, D, and He species, including H 2 formation on dust grains; tabulated primordial and metal cooling; multiple UV background models; and support for radiation transfer and arbitrary heat sources. The library has an easily implementable interface for simulation codes written in C, C++, and Fortran as well as a Python interface with added convenience functions for semi-analytical models. As an open-source project, Grackle provides a community resource for accessing and disseminating astrochemical data and numerical methods. We present the full details of the core functionality, the simulation and Python interfaces, testing infrastructure, performance, and range of applicability. Grackle is a fully open-source project and new contributions are welcome.

Numerous cosmological hydrodynamic studies have addressed the formation of galaxies. Here we choose to study the first stages of galaxy formation, including nonequilibrium atomic primordial gas cooling, gravity, and hydrodynamics. Using initial conditions appropriate for the concordance cosmological model of structure formation, we perform two adaptive mesh refinement simulations of $10 8 M galaxies at high redshift. The calculations resolve the Jeans length at all times with more than 16 cells and capture over 14 orders of magnitude in length scales. In both cases, the dense, 10 5 solar mass, one parsec central regions are found to contract rapidly and have turbulent Mach numbers up to 4. Despite the ever decreasing Jeans length of the isothermal gas, we only find one site of fragmentation during the collapse. However, rotational secular bar instabilities transport angular momentum outward in the central parsec as the gas continues to collapse and lead to multiple nested unstable fragments with decreasing masses down to sub-Jupiter mass scales. Although these numerical experiments neglect star formation and feedback, they clearly highlight the physics of turbulence in gravitationally collapsing gas. The angular momentum segregation seen in our calculations plays an important role in theories that form supermassive black holes from gaseous collapse.