John H. Wise

ENZO: AN ADAPTIVE MESH REFINEMENT CODE FOR ASTROPHYSICS

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 one, two, and three 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 codes parallel performance, and discuss the Enzo collaborations code development methodology.

The Birth of a Galaxy: Primordial Metal Enrichment and Stellar Populations

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 Population 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% to nearly the cosmic fraction in halos with merger histories rich in halos above 107 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 Ly? 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.

RESOLVING THE FORMATION OF PROTOGALAXIES. III. FEEDBACK FROM THE FIRST STARS

The first stars form in dark matter halos of masses ~106 -->M? as suggested by an increasing number of numerical simulations. Radiation feedback from these stars expels most of the gas from the shallow potential well of their surrounding dark matter halos. We use cosmological adaptive mesh refinement simulations that include self-consistent Population III star formation and feedback to examine the properties of assembling early dwarf galaxies. Accurate radiative transport is modeled with adaptive ray tracing. We include supernova explosions and follow the metal enrichment of the intergalactic medium. The calculations focus on the formation of several dwarf galaxies and their progenitors. In these halos, baryon fractions in 108 -->M? halos decrease by a factor of 2 with stellar feedback and by a factor of 3 with supernova explosions. We find that radiation feedback and supernova explosions increase gaseous spin parameters up to a factor of 4 and vary with time. Stellar feedback, supernova explosions, and H2 cooling create a complex, multiphase interstellar medium whose densities and temperatures can span up to 6 orders of magnitude at a given radius. The pair-instability supernovae of Population III stars alone enrich the halos with virial temperatures of 104 K to approximately 10?3 of solar metallicity. We find that 40% of the heavy elements resides in the intergalactic medium (IGM) at the end of our calculations. The highest metallicity gas exists in supernova remnants and very dilute regions of the IGM.

IONIZING PHOTON ESCAPE FRACTIONS FROM HIGH-REDSHIFT DWARF GALAXIES

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 ~109.5 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 × 106 and 3 × 109 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 108 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 birth of a galaxy - III. Propelling reionization with the faintest galaxies

MNRAS 442, 2560–2579 (2014) doi:10.1093/mnras/stu979 The birth of a galaxy – III. Propelling reionization with the faintest galaxies John H. Wise, 1‹ Vasiliy G. Demchenko, 1 Martin T. Halicek, 1 Michael L. Norman, 2 Matthew J. Turk, 3 Tom Abel 4 and Britton D. Smith 5 1 Center for Relativistic Astrophysics, Georgia Institute of Technology, 837 State Street, Atlanta, GA 30332, USA for Astrophysics and Space Sciences, University of California at San Diego, La Jolla, CA 92093, USA 3 Department of Astronomy, Columbia University, 538 West 120th Street, New York, NY 10027, USA 4 Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Menlo Park, CA 94025, USA 5 Institute of Astronomy, University of Edinburgh, Blackford Hill, Edinburgh EH9 3HJ, UK 2 Center Accepted 2014 May 14. Received 2014 May 12; in original form 2014 March 24 Starlight from galaxies plays a pivotal role throughout the process of cosmic reionization. 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 ionizing 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 ionizing 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 reionization 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. Key words: radiative transfer – methods: numerical – galaxies: dwarf – galaxies: formation – galaxies: high-redshift – dark ages, reionization, first stars. 1 I N T RO D U C T I O N Cosmic reionization is an extended process as individual H II regions grow around ionizing sources that gradually coalesce, culminating in a fully ionized Universe by z ∼ 6 (e.g. Gnedin & Ostriker 1997; Razoumov et al. 2002; Ciardi, Ferrara & White 2003; Sokasian et al. 2003; Furlanetto, Zaldarriaga & Hernquist 2004; Iliev et al. 2006; Robertson et al. 2010; Trac & Gnedin 2011; Zahn et al. 2011; So et al. 2014). However, there is still some tension between observational constraints on the timing and duration of reioniza- tion. First, the transmission fraction of z ∼ 6 quasar light blueward of Lyα through the intergalactic medium (IGM) indicates that the Universe was mostly ionized by this epoch (e.g. Gunn & Peterson 1965; Fan et al. 2002, 2006; Willott et al. 2007; Mortlock et al. 2011). Secondly, observations of the cosmic microwave background (CMB) from the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck have measured the optical depth to Thomson scat- tering τ e = 0.089 +0.012 −0.014 , which corresponds to the Universe being E-mail: jwise@physics.gatech.edu ∼50 per cent ionized at z = 11.1 ± 1.1 (Planck Collaboration 2013). But the ionizing emissivity measured at z = 4–6 through Lyα forest observations cannot account for this measured τ e , indi- cating that the end of reionization must be photon starved (Bolton & Haehnelt 2007) and that the emissivity must have been higher during reionization. Third, the duration 1 of reionization has been constrained to occur within z < 7.9 by measuring the kinetic Sunyaev–Zel’dovich effect with the South Pole Telescope (Zahn et al. 2012). These observations suggest that reionization was an extended process, mainly occurring at 6 z 15. What population of ionizing sources drives this global and ex- tended transition? It is clear that quasars and the very brightest galaxies, both of which are too rare, do not significantly contribute to the overall ionizing photon budget of reionization (e.g. Shapiro 1986; Dijkstra et al. 2004; Willott et al. 2010; Grissom, Ballantyne & Wise 2014). Starlight from galaxies is thought to provide the vast majority of the ionizing photon budget from extrapolating the 1 Zahn et al. (2012) define z as the redshift elapsed between 20 and 99 per cent ionized. C 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society Downloaded from http://mnras.oxfordjournals.org/ by guest on September 12, 2016 ABSTRACT

Accretion onto the First Stellar Mass Black Holes

The first stars, forming at redshifts z > 15 in minihalos with M ~ 105-6 M ☉ may leave behind remnant black holes, which could conceivably have been the seeds for the supermassive black holes observed at z 7. We study remnant black hole growth through accretion, including for the first time the radiation emitted due to accretion, with adaptive mesh refinement cosmological radiation-hydrodynamical simulations. The effects of photoionization and heating dramatically affect the large-scale inflow, resulting in negligible mass growth. We compare cases with accretion luminosity included and neglected to show that accretion radiation drastically changes the environment within 100 pc of the black hole, increasing gas temperatures by an order of magnitude. Gas densities are reduced and further star formation in the same minihalo is prevented for the 200 million years we followed. Without 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 population III stars in minihalos are not likely to be miniquasars. Most importantly, however, our calculations demonstrate that if these black holes are indeed accreting close to the Bondi-Hoyle rate with 10% radiative efficiency they have a dramatic local effect in regulating star formation in the first galaxies. This suggests a novel mechanism for massive black hole formation—stellar-mass black holes may have suppressed fragmentation and star formation after falling into halos with virial temperatures ~104 K, facilitating massive black hole formation at their centers.

Resolving the Formation of Protogalaxies. II. Central Gravitational Collapse

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 ~108 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, 105 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.

Resolving the formation of protogalaxies. I. Virialization

Galaxies form in hierarchically assembling dark matter halos. With cosmological three dimensional adaptive mesh refinement simulations, we explore in detail the virialization of baryons in the concordance cosmology, including optically thin primordial gas cooling. We focus on early protogalaxies with virial temperatures of 10 4 K and their progenitors. Without cooling, virial heating occurs in shocks close to the virial radius for material falling in from voids. Material in dense filaments penetrates deeper to about half that radius. With cooling the virial shock position shrinks and also the filaments reach scales as small as a third the virial radius. The temperatures in protogalaxies found in adiabatic simulations decrease by a factor of two from the center and show flat entropy cores. In cooling halos the gas reaches virial equilibrium with the dark matter potential through its turbulent velocities. We observe turbulent Mach numbers ranging from one to three in the cooling cases. This turbulence is driven by the large scale merging and interestingly remains supersonic in the centers of these early galaxies even in the absence of any feedback processes. The virial theorem is shown to approximately hold over 3 orders of magnitude in length scale with the turbulent pressure prevailing over the thermal energy. The turbulent velocity distributions are Maxwellian and by far dominate the small rotation velocities associated with the total angular momentum of the galaxies. Decomposing the velocity field using the Cauchy-Stokes theorem, we show that ample amounts of vorticity are present around shocks even at the very centers of these objects. In the cold flow regime of galaxy formation for halo masses below 10 12 M⊙, this dominant role of virialization driven turbulence should play an important role in for star formation as well as the build up of early magnetic fields. Subject headings: Cosmology: high-redshift—galaxy formation—star formation

SUPPRESSION OF H2 COOLING IN THE ULTRAVIOLET BACKGROUND

The first luminous objects in the concordance cosmology form by molecular hydrogen cooling in dark matter dominated halos of masses ~106 M☉. We use Eulerian adaptive mesh refinement simulations to demonstrate that in the presence of a large soft ultraviolet radiation background, molecular hydrogen is the dominant coolant. Even for very large radiation backgrounds, the halo masses that cool and collapse are up to 2 orders of magnitude smaller than the halos that cool via atomic hydrogen line cooling. The abundance of cooling halos and the cosmic mass fraction contained within them depends exponentially on this critical mass scale. Consequently, the majority of current models of cosmological reionization, chemical evolution, supermassive black hole formation, and galaxy formation underestimate the number of star-forming progenitors of a given system by orders of magnitude. At the highest redshifts, this disagreement is largest. We also show that even in the absence of residual electrons, collisional ionization in central shocks create a sufficient amount of electrons to form molecular hydrogen and cool the gas in halos of virial temperatures far below the atomic cooling limit.

DWARF GALAXY FORMATION WITH H2-REGULATED STAR FORMATION

We describe cosmological galaxy formation simulations with the adaptive mesh refinement code Enzo that incorporate a star formation prescription regulated by the local abundance of molecular hydrogen. We show that this H2-regulated prescription leads to a suppression of star formation in low-mass halos (Mh 1010 M ?) at z > 4, alleviating some of the dwarf galaxy problems faced by theoretical galaxy formation models. H2 regulation modifies the efficiency of star formation of cold gas directly, rather than indirectly reducing the cold gas content with supernova feedback. We determine the local H2 abundance in our most refined grid cells (76 proper parsec in size at z = 4) by applying the model of Krumholz, McKee, & Tumlinson, which is based on idealized one-dimensional radiative transfer calculations of H2 formation-dissociation balance in ~100?pc atomic-molecular complexes. Our H2-regulated simulations are able to reproduce the empirical (albeit lower z) Kennicutt-Schmidt relation, including the low ?gas cutoff due to the transition from atomic to molecular phase and the metallicity dependence thereof, without the use of an explicit density threshold in our star formation prescription. We compare the evolution of the luminosity function, stellar mass density, and star formation rate density from our simulations to recent observational determinations of the same at z = 4-8 and find reasonable agreement between the two.