Eric J. Hallman

The integrated sunyaev-zeldovich effect as a superior method for measuring the mass of clusters of galaxies

We investigate empirical scaling relations between the thermal Sunyaev-Zeldovich effect (SZE) and cluster mass in simulated clusters of galaxies. The simulated clusters have been compiled from four different samples that differ only in their assumed baryonic physics. We show that the strength of the thermal SZE integrated over a significant fraction of the virialized region of the clusters is relatively insensitive to the detailed heating and cooling processes in the cores of clusters, by demonstrating that the derived scaling relations are nearly identical among the four cluster samples considered. For our synthetic images, the central Comptonization parameter shows significant boosting during transient merging events, but the integrated SZE appears to be relatively insensitive to these events. Most importantly, the integrated SZE closely tracks the underlying cluster mass. Observations through the thermal SZE allow a strikingly accurate mass estimation from relatively simple measurements that do not require either parametric modeling or geometric deprojection and thus avoid assumptions regarding the physics of the intracluster medium or the symmetry of the cluster. This result offers significant promise for precision cosmology using clusters of galaxies.

Cosmological Shocks in Adaptive Mesh Refinement Simulations and the Acceleration of Cosmic Rays

We present new results characterizing cosmological shocks within adaptive mesh refinement N-body/hydrodynamic simulations that are used to predict nonthermal components of large-scale structure. This represents the first study of shocks using adaptive mesh refinement. We propose a modified algorithm for finding shocks from those used on unigrid simulations that reduces the shock frequency of low Mach number shocks by a factor of ~3. We then apply our new technique to a large, (512 h−1 Mpc)3, cosmological volume and study the shock Mach number () distribution as a function of preshock temperature, density, and redshift. Because of the large volume of the simulation, we have superb statistics that result from having thousands of galaxy clusters. We find that the Mach number evolution can be interpreted as a method to visualize large-scale structure formation. Shocks with 20 generally follow accretion onto filaments and galaxy clusters, respectively. By applying results from nonlinear diffusive shock acceleration models using the first-order Fermi process, we calculate the amount of kinetic energy that is converted into cosmic-ray protons. The acceleration of cosmic-ray protons is large enough that in order to use galaxy clusters as cosmological probes, the dynamic response of the gas to the cosmic rays must be included in future numerical simulations.

Why Do Only Some Galaxy Clusters Have Cool Cores

Flux-limited X-ray samples indicate that about half of rich galaxy clusters have cool cores. Why do only some clusters have cool cores while others do not? In this paper, cosmological N-body + Eulerian hydrodynamic simulations, including radiative cooling and heating, are used to address this question as we examine the formation and evolution of cool core (CC) and noncool core (NCC) clusters. These adaptive mesh refinement simulations produce both CC and NCC clusters in the same volume. They have a peak resolution of 15.6 h−1 kpc within a (256 h−1 Mpc)3 box. Our simulations suggest that there are important evolutionary differences between CC clusters and their NCC counterparts. Many of the numerical CC clusters accreted mass more slowly over time and grew enhanced CCs via hierarchical mergers; when late major mergers occurred, the CCs survived the collisions. By contrast, NCC clusters experienced major mergers early in their evolution that destroyed embryonic CCs and produced conditions that prevented CC reformation. As a result, our simulations predict observationally testable distinctions in the properties of CC and NCC beyond the core regions in clusters. In particular, we find differences between CC versus NCC clusters in the shapes of X-ray surface brightness profiles, between the temperatures and hardness ratios beyond the cores, between the distribution of masses, and between their supercluster environs. It also appears that CC clusters are no closer to hydrostatic equilibrium than NCC clusters, an issue important for precision cosmology measurements.

THE NATURE OF THE WARM/HOT INTERGALACTIC MEDIUM. I. NUMERICAL METHODS, CONVERGENCE, AND O VI ABSORPTION

We perform a series of cosmological simulations using Enzo, an Eulerian adaptive-mesh refinement, N-body + hydrodynamical code, applied to study the warm/hot intergalactic medium (WHIM). The WHIM may be an important component of the baryons missing observationally at low redshift. We investigate the dependence of the global star formation rate and mass fraction in various baryonic phases on spatial resolution and methods of incorporating stellar feedback. Although both resolution and feedback significantly affect the total mass in the WHIM, all of our simulations find that the WHIM fraction peaks at z ~ 0.5, declining to 35%-40% at z = 0. We construct samples of synthetic O VI absorption lines from our highest-resolution simulations, using several models of oxygen ionization balance. Models that include both collisional ionization and photoionization provide excellent fits to the observed number density of absorbers per unit redshift over the full range of column densities (1013 cm?2 N O VI 1015 cm?2). Models that include only collisional ionization provide better fits for high column density absorbers (N O VI 1014 cm?2). The distribution of O VI in density and temperature exhibits two populations: one at T ~ 105.5 K (collisionally ionized, 55% of total O VI) and one at T ~ 104.5 K (photoionized, 37%) with the remainder located in dense gas near galaxies. While not a perfect tracer of hot gas, O VI provides an important tool for a WHIM baryon census.

Active Galactic Nuclei Heating and Dissipative Processes in Galaxy Clusters

Recent X-ray observations reveal growing evidence for heating by active galactic nuclei (AGNs) in clusters and groups of galaxies. AGN outflows play a crucial role in explaining the riddle of cooling flows and the entropy problem in clusters. Here we study the effect of AGNs on the intracluster medium in a cosmological simulation using the adaptive mesh refinement FLASH code. We pay particular attention to the effects of conductivity and viscosity on the dissipation of weak shocks generated by the AGN activity in a realistic galaxy cluster. Our three-dimensional simulations demonstrate that both viscous and conductive dissipation play an important role in distributing the mechanical energy injected by the AGNs, offsetting radiative cooling and injecting entropy to the gas. These processes are important even when the transport coefficients are at a level of 10% of the Spitzer value. Provided that both conductivity and viscosity are suppressed by a comparable amount, conductive dissipation is likely to dominate over viscous dissipation. Nevertheless, viscous effects may still affect the dynamics of the gas and contribute a significant amount of dissipation compared to radiative cooling. We also present synthetic Chandra observations. We show that the simulated buoyant bubbles inflated by the AGN, and weak shocks associated with them, are detectable with the Chandra observatory.

Cluster Structure in Cosmological Simulations. I. Correlation to Observables, Mass Estimates, and Evolution

We use Enzo, a hybrid Eulerian adaptive mesh refinement/N-body code including nongravitational heating and cooling,toexplorethemorphologyof theX-raygasinclustersof galaxiesanditsevolutionincurrent-generationcosmological simulations. We employ and compare two observationally motivated structure measures: power ratios and centroidshift.Overall,thestructureof oursimulated clusterscompares remarkablywelltolow-redshift observations, although some differences remain that may point to incomplete gas physics. We find no dependence on cluster structure in the mass-observable scaling relations, TX-M and YX-M, when using the true cluster masses. However, estimates of the total mass based on the assumption of hydrostatic equilibrium, as assumed in observational studies, are systematicallylow.Weshowthatthehydrostaticmassbiasstronglycorrelateswithclusterstructureand,moreweakly, with cluster mass. When thehydrostatic massesareused,themass-observablescalingrelationsandgasmass fractions depend significantly on cluster morphology, and the true relations are not recovered even if the most relaxed clusters are used. We show that cluster structure, via the power ratios, can be used to effectively correct the hydrostatic mass estimatesandmassscalingrelations,suggestingthatwecancalibrateforthissystematiceffectincosmologicalstudies. Similar to observational studies, we find that cluster structure, particularly centroid shift, evolves with redshift. This evolutionismildbutwill leadtoadditionalerrorsathighredshift.Projectionalongthelineof sightleads tosignificant uncertainty in the structure of individual clusters: less than 50% of clusters which appear relaxed in projection based on our structure measures are truly relaxed. Subject headingg galaxies: clusters: general — hydrodynamics — large-scale structure of universe — methods: numerical — X-rays: galaxies: clusters

COSMOLOGICAL MAGNETOHYDRODYNAMIC SIMULATIONS OF GALAXY CLUSTER RADIO RELICS: INSIGHTS AND WARNINGS FOR OBSERVATIONS

Non-thermal radio emission from cosmic-ray electrons in the vicinity of merging galaxy clusters is an important tracer of cluster merger activity, and is the result of complex physical processes that involve magnetic fields, particle acceleration, gas dynamics, and radiation. In particular, objects known as radio relics are thought to be the result of shock-accelerated electrons that, when embedded in a magnetic field, emit synchrotron radiation in the radio wavelengths. In order to properly model this emission, we utilize the adaptive mesh refinement simulation of the magnetohydrodynamic evolution of a galaxy cluster from cosmological initial conditions. We locate shock fronts and apply models of cosmic-ray electron acceleration that are then input into radio emission models. We have determined the thermodynamic properties of this radio-emitting plasma and constructed synthetic radio observations to compare observed galaxy clusters. We find a significant dependence of the observed morphology and radio relic properties on the viewing angle of the cluster, raising concerns regarding the interpretation of observed radio features in clusters. We also find that a given shock should not be characterized by a single Mach number. We find that the bulk of the radio emission comes from gas with T > 5 ? 107 K, ? ~ 10?28-10?27 g cm?3, with magnetic field strengths of 0.1-1.0 ?G, and shock Mach numbers of . We present an analysis of the radio spectral index which suggests that the spatial variation of the spectral index can mimic synchrotron aging. Finally, we examine the polarization fraction and position angle of the simulated radio features, and compare to observations.

GALAXY CLUSTER RADIO RELICS IN ADAPTIVE MESH REFINEMENT COSMOLOGICAL SIMULATIONS: RELIC PROPERTIES AND SCALING RELATIONSHIPS

Cosmological shocks are a critical part of large-scale structure formation, and are responsible for heating the intracluster medium in galaxy clusters. In addition, they are capable of accelerating non-thermal electrons and protons. In this work, we focus on the acceleration of electrons at shock fronts, which is thought to be responsible for radio relics—extended radio features in the vicinity of merging galaxy clusters. By combining high-resolution adaptive mesh refinement/N-body cosmological simulations with an accurate shock-finding algorithm and a model for electron acceleration, we calculate the expected synchrotron emission resulting from cosmological structure formation. We produce synthetic radio maps of a large sample of galaxy clusters and present luminosity functions and scaling relationships. With upcoming long-wavelength radio telescopes, we expect to see an abundance of radio emission associated with merger shocks in the intracluster medium. By producing observationally motivated statistics, we provide predictions that can be compared with observations to further improve our understanding of magnetic fields and electron shock acceleration.

HOW WELL DO COSMOLOGICAL SIMULATIONS REPRODUCE INDIVIDUAL HALO PROPERTIES

Cosmological simulations of galaxy formation often rely on prescriptions for star formation and feedback that depend on halo properties such as halo mass, central overdensity, and virial temperature. In this paper, we address the convergence of individual halo properties, based on their number of particles N, focusing, in particular, on the mass of halos near the resolution limit of a simulation. While it has been established that the halo mass function is sampled on average down to N ~ 20-30 particles, we show that individual halo properties exhibit significant scatter, and some systematic biases, as one approaches the resolution limit. We carry out a series of cosmological simulations using the Gadget2 and Enzo codes with Np = 643 to Np = 10243 total particles, keeping the same large-scale structure in the simulation box. We consider boxes of small (l box = 8 Mpc h –1), medium (l box = 64 Mpc h –1), and large (l box = 512 Mpc h –1) size to probe different halo masses and formation redshifts. We cross-identify dark matter halos in boxes at different resolutions and measure the scatter in their properties. The uncertainty in the mass of single halos depends on the number of particles (scaling approximately as N –1/3), but the rarer the density peak, the more robust its identification. The virial radius of halos is very stable and can be measured without bias for halos with N 30. In contrast, the average density within a sphere containing 25% of the total halo mass is severely underestimated (by more than a factor 2) and the halo spin is moderately overestimated for N 100. If sub-grid physics is implemented upon a cosmological simulation, we recommend that rare halos (~3σ peaks) be resolved with N 100 particles and common halos (~1σ peaks) with N 400 particles to avoid excessive numerical noise and possible systematic biases in the results.

The β-Model Problem: The Incompatibility of X-Ray and Sunyaev-Zeldovich Effect Model Fitting for Galaxy Clusters

We have analyzed a large sample of numerically simulated clusters to demonstrate the adverse effects resulting from the use of X-ray-fitted β-model parameters with Sunyaev-Zeldovich effect (SZE) data. There is a fundamental incompatibility between β-model fits to X-ray surface brightness profiles and those done with SZE profiles. Since observational SZE radial profiles are in short supply, the X-ray parameters are often used in SZE analysis. We show that this leads to biased estimates of the integrated Compton y-parameter inside r500 calculated from clusters. We suggest a simple correction of the method, using a nonisothermal β-model modified by a universal temperature profile, which brings these calculated quantities into closer agreement with the true values.