Tom Abel

The formation of the first star in the universe

We describe results from a fully self-consistent three-dimensional hydrodynamical simulation of the formation of one of the first stars in the Universe. In current models of structure formation, dark matter initially dominates, and pregalactic objects form because of gravitational instability from small initial density perturbations. As they assemble via hierarchical merging, primordial gas cools through ro-vibrational lines of hydrogen molecules and sinks to the center of the dark matter potential well. The high-redshift analog of a molecular cloud is formed. As the dense, central parts of the cold gas cloud become self-gravitating, a dense core of ∼100M ⊙ (whereM ⊙ is the mass of the Sun) undergoes rapid contraction. At particle number densities greater than 109 per cubic centimeter, a 1M ⊙ protostellar core becomes fully molecular as a result of three-body H2formation. Contrary to analytical expectations, this process does not lead to renewed fragmentation and only one star is formed. The calculation is stopped when optical depth effects become important, leaving the final mass of the fully formed star somewhat uncertain. At this stage the protostar is accreting material very rapidly (∼10−2 M ⊙year−1). Radiative feedback from the star will not only halt its growth but also inhibit the formation of other stars in the same pregalactic object (at least until the first star ends its life, presumably as a supernova). We conclude that at most one massive (M ≫ 1 M ⊙) metal-free star forms per pregalactic halo, consistent with recent abundance measurements of metal-poor galactic halo stars.

How small were the first cosmological objects

The minimum mass that a virialized gas cloud must have in order to be able to cool in a Hubble time is computed, using a detailed treatment of the chemistry of molecular hydrogen. With a simple model for halo profiles, we reduce the problem to that of numerically integrating a system of chemical equations. The results agree well with numerically expensive three-dimensional simulations, and our approach has the advantage of being able to explore large regions of parameter space rapidly. The minimum baryonic mass Mb is found to be strongly redshift dependent, dropping from 106 M☉ at z ~ 15 to 5 × 103 M☉ at z ~ 100 as molecular cooling becomes effective. For z 100, Mb rises again, as cosmic microwave background photons inhibit H2 formation through the H- channel. Finally, for z 200, the H -->+2 channel for H2 formation becomes effective, driving Mb down toward Mb ~ 103 M☉. With a standard cold dark matter power spectrum with σ8 = 0.7, this implies that a fraction 10-3 of all baryons may have formed luminous objects by z = 30, which could be sufficient to reheat the universe.

Modeling primordial gas in numerical cosmology

Abstract We have reviewed the chemistry and cooling behavior of low-density (n ≲ 10 4 cm −3 ) primordial gas and devised a model which involves 19 collisional and 9 radiative processes and is applicable for temperatures in the range 1 K T 8 K. In a companion paper (Anninos et al., 1997)[NewA, 2, 209] numerical methods are presented that unify the modeling of non-equilibrium primordial gas chemistry and cooling dicussed here with cosmological hydrodynamics. We derived new fits of rate coefficients for the photo-attachment of neutral hydrogen, the formation of molecular hydrogen via H − , charge exchange beween H 2 and H + , electron detachment of H − by neutral hydrogen, dissociative recombination of H 2 + with slow electrons, photodissociation of H 2 + , and photodissociation of H 2 . Furthermore it was found that the molecular hydrogen produced through the gas-phase processes, H 2 + + H → H 2 + H + , and H − + H → H 2 + e − , is likely to be converted into its para configuration on a faster time scale than the formation time. We have tested the model extensively and shown it to agree well with former studies. We further studied the chemical kinetics in great detail and devised a minimal model which is substantially simpler than the full reaction network but predicts correct abundances. This minimal model shows convincingly that 12 collisional processes are sufficient to model the H, He, H + , H − , He + , He ++ , and H 2 abundances in low density primordial gas for applications with no radiation fields.

YT: A Multi-Code Analysis Toolkit for Astrophysical Simulation Data

The analysis of complex multiphysics astrophysical simulations presents a unique and rapidly growing set of challenges: reproducibility, parallelization, and vast increases in data size and complexity chief among them. In order to meet these challenges, and in order to open up new avenues for collaboration between users of multiple simulation platforms, we present yt (available at http://yt.enzotools.org/) an open source, community-developed astrophysical analysis and visualization toolkit. Analysis and visualization with yt are oriented around physically relevant quantities rather than quantities native to astrophysical simulation codes. While originally designed for handling Enzos structure adaptive mesh refinement data, yt has been extended to work with several different simulation methods and simulation codes including Orion, RAMSES, and FLASH. We report on its methods for reading, handling, and visualizing data, including projections, multivariate volume rendering, multi-dimensional histograms, halo finding, light cone generation, and topologically connected isocontour identification. Furthermore, we discuss the underlying algorithms yt uses for processing and visualizing data, and its mechanisms for parallelization of analysis tasks.

Formation of Primordial Stars in a ΛCDM Universe

We study the formation of the first generation of stars in the standard cold dark matter model. We use a very high resolution cosmological hydrodynamic simulation that achieves a dynamic range of ~1010 in length scale. With accurate treatment of atomic and molecular physics, including the effect of molecular line opacities and cooling by collision-induced continuum emission, it allows us to study the chemothermal evolution of primordial gas clouds to densities up to ρ ~ 2 × 10-8 g cm-3 (nH ~ 1016 cm-3) without assuming any a priori equation of state, an improvement of 6 orders of magnitude over previous three-dimensional calculations. We study the evolution of a primordial star-forming gas cloud in the cosmological simulation in detail. The cloud core becomes marginally unstable against chemothermal instability when the gas cooling rate is increased owing to three-body molecule formation. However, since the core is already compact at that point, runaway cooling simply leads to fast condensation to form a single protostellar seed. During the final dynamical collapse, small angular momentum material collapses faster than the rest of the gas and selectively sinks inward. Consequently, the central regions have little specific angular momentum, and rotation does not halt collapse. We, for the first time, obtain an accurate gas mass accretion rate within a 10 M☉ innermost region around the protostar. We carry out protostellar evolution calculations using the obtained accretion rate. The resulting mass of the first star when it reaches the zero-age main sequence is MZAMS ~ 100 M☉, and less (60 M☉) for substantially reduced accretion rates.

The Radiative Feedback of the First Cosmological Objects

In hierarchical models of structure formation, an early cosmic UV background (UVB) is produced by the small K) halos that collapse before reionization. The UVB at energies below 13.6 eV sup- (T vir ( 104 presses the formation of stars or black holes inside small halos by photodissociating their only cooling agent, molecular We self-consistently compute the buildup of the early UVB in Press-Schechter H 2 . models, coupled with photodissociation both in the intergalactic medium (IGM) and inside virialized H 2 halos. We —nd that the intergalactic has a negligible eUect on the UVB, both because its initial H 2 optical depth is small and because it is photodissociated at an early stage. If the UV sources in ((0.1) the —rst collapsed halos are stars, then their UV —ux suppresses further star formation inside small halos. This results in a pause in the buildup of the UVB, and reionization is delayed until larger halos (T vir Z 104 K) collapse. If the small halos host miniquasars with hard spectra extending to D1 keV, then their X-rays balance the eUects of the UVB, the negative feedback does not occur, and reionization could be caused by the small halos. Subject headings: cosmology: theorydiUuse radiationearly universegalaxies: formation ¨ molecular processesradiative transfer

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 Formation of Population III Binaries from Cosmological Initial Conditions

Genesis of Binary Stars Numerical simulations of collapsing clouds of primordial gas indicate that the first luminous objects to form in the universe were isolated massive stars. Turk et al. (p. 601, published online 9 July) now show that it is possible for single primordial clouds to break up into two dense cores. Three-dimensional calculations, which follow the evolution of primordial gas (composed of hydrogen and helium, with traces of deuterium and lithium) and dark matter starting from realistic, cosmological initial conditions, suggest that these cores may evolve to form binary star systems. Simulations show that binary systems are likely to exist among the first generation of stars. Previous high-resolution cosmological simulations predicted that the first stars to appear in the early universe were very massive and formed in isolation. Here, we discuss a cosmological simulation in which the central 50 M⊙ (where M⊙ is the mass of the Sun) clump breaks up into two cores having a mass ratio of two to one, with one fragment collapsing to densities of 10−8 grams per cubic centimeter. The second fragment, at a distance of ~800 astronomical units, is also optically thick to its own cooling radiation from molecular hydrogen lines but is still able to cool via collision-induced emission. The two dense peaks will continue to accrete from the surrounding cold gas reservoir over a period of ~105 years and will likely form a binary star system.

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.