Greg L. Bryan

Statistical Properties of X-Ray Clusters: Analytic and Numerical Comparisons

We compare the results of Eulerian hydrodynamic simulations of cluster formation against virial scaling relations between four bulk quantities: the cluster mass, the dark matter velocity dispersion, the gas temperature, and the cluster luminosity. The comparison is made for a large number of clusters at a range of redshifts in three different cosmological models (cold plus hot dark matter, cold dark matter, and open cold dark matter). We find that the analytic formulae provide a good description of the relations between three of the four numerical quantities. The fourth (luminosity) also agrees once we introduce a procedure to correct for the fixed numerical resolution. We also compute the normalizations for the virial relations and compare extensively to the existing literature, finding remarkably good agreement. The Press-Schechter prescription is calibrated with the simulations, again finding results consistent with other authors. We also examine related issues such as the size of the scatter in the virial relations, the effect of metallicity with a fixed passband, and the structure of the halos. All of this is done in order to establish a firm groundwork for the use of clusters as cosmological probes. Implications for the models are briefly discussed.

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.

Baryons in the Warm-Hot Intergalactic Medium

Approximately 30%-40% of all baryons in the present-day universe reside in a warm-hot intergalactic medium (WHIM), with temperatures in the range 105 < T < 107 K. This is a generic prediction from six hydrodynamic simulations of currently favored structure formation models having a wide variety of numerical methods, input physics, volumes, and spatial resolutions. Most of these warm-hot baryons reside in diffuse large-scale structures with a median overdensity around 10-30, not in virialized objects such as galaxy groups or galactic halos. The evolution of the WHIM is primarily driven by shock heating from gravitational perturbations breaking on mildly nonlinear, nonequilibrium structures such as filaments. Supernova feedback energy and radiative cooling play lesser roles in its evolution. WHIM gas may be consistent with observations of the 0.25 keV X-ray background without being significantly heated by nongravitational processes because the emitting gas is very diffuse. Our results confirm and extend previous work by Cen & Ostriker and Dave et al.

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.

Supermassive black hole formation by direct collapse: keeping protogalactic gas H2 free in dark matter haloes with virial temperatures Tvir > rsim 104 K

In the absence of H 2 molecules, the primordial gas in early dark matter haloes with virial temperatures just above T vir ≳ 10 4 K cools by collisional excitation of atomic H. Although it cools efficiently, this gas remains relatively hot, at a temperature near T ∼ 8000 K, and consequently might be able to avoid fragmentation and collapse directly into a supermassive black hole. In order for H 2 formation and cooling to be strongly suppressed, the gas must be irradiated by a sufficiently intense ultraviolet (UV) flux. We performed a suite of three-dimensional hydrodynamical adaptive mesh refinement (AMR) simulations of gas collapse in three different protogalactic haloes with T vir ≳ 10 4 K, irradiated by a UV flux with various intensities and spectra. We determined the critical specific intensity, J crit 21 , required to suppress H 2 cooling in each of the three haloes. For a hard spectrum representative of metal-free stars, we find (in units of 10 ―21 erg s ―1 Hz ―1 sr ―1 cm ―2 ) 10 4 < J crit 21 < 10 5 , while for a softer spectrum, which is characteristic of a normal stellar population, and for which H ― dissociation is important, we find 30 < J crit 21 < 300. These values are a factor of 3-10 lower than previous estimates. We attribute the difference to the higher, more accurate H 2 collisional dissociation rate we adopted. The reduction in J crit 21 exponentially increases the number of rare haloes exposed to supercritical radiation. When H 2 cooling is suppressed, gas collapse starts with a delay, but it ultimately proceeds more rapidly. The infall velocity is near the increased sound speed, and an object as massive as M ∼ 10 5 M ⊙ may form at the centre of these haloes, compared to the M ∼ 10 2 M ⊙ stars forming when H 2 cooling is efficient.

The baseline intracluster entropy profile from gravitational structure formation

The radial entropy profile of the hot gas in clusters of galaxies tends to follow a power law in radius outside of the cluster core. Here we present a simple formula giving both the normalization and slope for the power-law entropy profiles of clusters that form in the absence of non-gravitational processes such as radiative cooling and subsequent feedback. It is based on 71 clusters drawn from four separate cosmological simulations, two using smoothed particle hydrodynamics and two using adaptive-mesh refinement (AMR), and can be used as a baseline for assessing the impact of non-gravitational processes on the intracluster medium outside of cluster cores. All the simulations produce clusters with self-similar structure in which the normalization of the entropy profile scales linearly with cluster temperature, and these profiles are in excellent agreement outside of 0.2r 200 . Because the observed entropy profiles of clusters do not scale linearly with temperature, our models confirm that non-gravitational processes are necessary to break the self-similarity seen in the simulations. However, the core entropy levels found by the two codes used here significantly differ, with the AMR code producing nearly twice as much entropy at the centre of a cluster.

Heating cooling flows with jets

Active galactic nuclei are clearly heating gas in ‘cooling flows’. The effectiveness and spatial distribution of the heating are controversial. We use three-dimensional simulations on adaptive grids to study the impact on a cooling flow of weak, subrelativistic jets. The simulations show cavities and vortex rings as in the observations. The cavities are fast-expanding dynamical objects rather than buoyant bubbles as previously modelled, but shocks still remain extremely hard to detect with X-rays. At late times the cavities turn into overdensities that strongly excite the g modes of a cluster. These modes damp on a long time-scale. Radial mixing is shown to be an important phenomenon, but the jets weaken the metallicity gradient only very near the centre. The central entropy density is modestly increased by the jets. We use a novel algorithm to impose the jets on the simulations.

Modified Entropy Models for the Intracluster Medium

We present a set of cluster models that link the present-day properties of clusters to the processes that govern galaxy formation. These models treat the entropy distribution of the intracluster medium as its most fundamental property. Because convection strives to establish an entropy gradient that rises with radius, the observable properties of a relaxed cluster depend entirely on its dark-matter potential and the entropy distribution of its uncondensed gas. Guided by simulations, we compute the intracluster entropy distribution that arises in the absence of radiative cooling and supernova heating by assuming that the gas-density distribution would be identical to that of the dark matter. The lowest-entropy gas would then fall below a critical entropy threshold at which the cooling time equals a Hubble time. Radiative cooling and whatever feedback is associated with it must modify the entropy of that low-entropy gas, changing the overall entropy distribution function and thereby altering the observable properties of the cluster. Using some phenomenological prescriptions for entropy modification based on the existence of this cooling threshold, we construct a remarkably realistic set of cluster models. The surface-brightness profiles, masstemperature relation, and luminosity-temperature relation of observed clusters all naturally emerge from these models. By introducing a single adjustable parameter related to the amount of intracluster gas that can cool within a Hubble time, we can also reproduce the observed temperature gradients of clusters and the deviations of cooling-flow clusters from the standard luminosity-temperature relation. Subject headings: cosmology: theory — galaxies: clusters: general — galaxies: evolution — intergalactic medium — X-rays: galaxies: clusters

Introducing Enzo, an AMR Cosmology Application

In this paper we introduce Enzo, a 3D MPI-parallel Eulerian block-structured adaptive mesh refinement cosmology code. Enzo is designed to simulate cosmological structure formation, but can also be used to simulate a wide range of astrophysical situations. Enzo solves dark matter N-body dynamics using the particle-mesh technique. The Poisson equation is solved using a combination of fast fourier transform (on a periodic root grid) and multigrid techniques (on non-periodic subgrids). Euler’s equations of hydrodynamics are solved using a modified version of the piecewise parabolic method. Several additional physics packages are implemented in the code, including several varieties of radiative cooling, a metagalactic ultraviolet background, and prescriptions for star formation and feedback. We also show results illustrating properties of the adaptive mesh portion of the code. Information on profiling and optimizing the performance of the code can be found in the contribution by James Bordner in this volume.

On the Origin of Intracluster Entropy

The entropy distribution of the intracluster medium and the shape of its confining potential well completely determine the X-ray properties of a relaxed cluster of galaxies, motivating us to explore the origin of intracluster entropy and to describe how it develops in terms of some simple models. We present an analytical model for smooth accretion, including both preheating and radiative cooling, that links a clusters entropy distribution to its mass accretion history and shows that smooth accretion overproduces the entropy observed in massive clusters by a factor of ~2-3, depending on the mass accretion rate. Any inhomogeneity in the accreting gas reduces entropy production at the accretion shock; thus, smoothing of the gas accreting onto a cluster raises its entropy level. Because smooth accretion produces more entropy than hierarchical accretion, we suggest that some of the observed differences between clusters and groups may arise because preheating smooths the smaller scale lumps of gas accreting onto groups more effectively than it smooths the larger scale lumps accreting onto clusters. This effect may explain why entropy levels at the outskirts of groups are ~2-3 times larger than expected from self-similar scaling arguments. The details of how the density distribution of accreting gas affects the entropy distribution of a cluster are complex, and we suggest how to explore the relevant physics with numerical simulations.