Erwin T. Lau

The Mean and Scatter of the Velocity Dispersion-Optical Richness Relation for MaxBCG Galaxy Clusters

The distribution of galaxies in position and velocity around the centers of galaxy clusters encodes important information about cluster mass and structure. Using the maxBCG galaxy cluster catalog identified from imaging data obtained in the Sloan Digital Sky Survey, we study the BCG-galaxy velocity correlation function. By modeling its non-Gaussianity, we measure the mean and scatter in velocity dispersion at fixed richness. The mean velocity dispersion increases from 202 ± 10 km s-1 for small groups to more than 854 ± 102 km s-1 for large clusters. We show the scatter to be at most 40.5% ± 3.5%, declining to 14.9% ± 9.4% in the richest bins. We test our methods in the C4 cluster catalog, a spectroscopic cluster catalog produced from the Sloan Digital Sky Survey DR2 spectroscopic sample, and in mock galaxy catalogs constructed from N-body simulations. Our methods are robust, measuring the scatter to well within 1 σ of the true value, and the mean to within 10%, in the mock catalogs. By convolving the scatter in velocity dispersion at fixed richness with the observed richness space density function, we measure the velocity dispersion function of the maxBCG galaxy clusters. Although velocity dispersion and richness do not form a true mass-observable relation, the relationship between velocity dispersion and mass is theoretically well characterized and has low scatter. Thus, our results provide a key link between theory and observations up to the velocity bias between dark matter and galaxies.

HYDRODYNAMIC SIMULATION OF NON-THERMAL PRESSURE PROFILES OF GALAXY CLUSTERS

Cosmological constraints from X-ray and microwave observations of galaxy clusters are subjected to systematic uncertainties. Non-thermal pressure support due to internal gas motions in galaxy clusters is one of the major sources of astrophysical uncertainties. Using a mass-limited sample of galaxy clusters from a high-resolution hydrodynamical cosmological simulation, we characterize the non-thermal pressure fraction profile and study its dependence on redshift, mass, and mass accretion rate. We find that the non-thermal pressure fraction profile is universal across redshift when galaxy cluster radii are defined with respect to the mean matter density of the universe instead of the commonly used critical density. We also find that the non-thermal pressure is predominantly radial, and the gas velocity anisotropy profile exhibits strong universality when galaxy cluster radii are defined with respect to the mean matter density of the universe. However, we find that the non-thermal pressure fraction is strongly dependent on the mass accretion rate of the galaxy cluster. We provide fitting formulae for the universal non-thermal pressure fraction and velocity anisotropy profiles of gas in galaxy clusters, which should be useful in modeling astrophysical uncertainties pertinent to using galaxy clusters as cosmological probes.

Quantifying properties of ICM inhomogeneities

We present a new method to identify and characterize the structure of the intracluster medium (ICM) in simulated galaxy clusters. The method uses the median of gas properties, such as density and pressure, which we show to be very robust to the presence of gas inhomogeneities. In particular, we show that the radial proles of median gas properties in cosmological simulations of clusters are smooth and do not exhibit uctuations at locations of massive clumps in contrast to mean and mode properties. Analysis of simulations shows that distribution of gas properties in a given radial shell can be well described by a log-normal PDF and a tail. The former corresponds to a nearly hydrostatic bulk component, accounting for 99 per cent of the volume, while the tail corresponds to high density inhomogeneities. The clumps can thus be easily identied with the volume elements corresponding to the tail of the distribution. We show that this results in a simple and robust separation of the diuse and clumpy components of the ICM. The full width half maximum of the density distribution in simulated clusters is a growing function of radius and varies from 0.15 dex in cluster centre to 0.5 dex at 2r500 in relaxed clusters. The small scatter in the width between relaxed clusters suggests that the degree of inhomogeneity is a robust characteristic of the ICM. It broadly agrees with the amplitude of density perturbations found in the Coma cluster core. We discuss the origin of ICM density variations in spherical shells and show that less than 20 per cent of the width can be attributed to the triaxiality of the cluster gravitational potential. As a link to X-ray observations of real clusters we evaluated the ICM clumping factor, weighted with the temperature dependent X-ray emissivity, with and without high density inhomogeneities. We argue that these two cases represent upper and lower limits on the departure of the observed X-ray emissivity from the median value. We nd that the typical value of the clumping factor in the bulk component of relaxed clusters varies from 1:1 1:2 at r500 up to 1:3 1:4 at r200 , in broad agreement with recent observations.

SHAPES OF GAS, GRAVITATIONAL POTENTIAL, AND DARK MATTER IN ΛCDM CLUSTERS

We present analysis of the three-dimensional shape of intracluster gas in clusters formed in cosmological simulations of the Lambda CDM cosmology and compare it to the shape of dark matter distribution and the shape of the overall isopotential surfaces. We find that in simulations with radiative cooling, star formation, and stellar feedback (CSF), intracluster gas outside the cluster core (r >= 0.1r(500)) is more spherical compared to non-radiative (NR) simulations, while in the core the gas in the CSF runs is moretriaxial and has a distinctly oblate shape. The latter reflects the ongoing cooling of gas, which settles into a thick oblate ellipsoid as it loses thermal energy. The shape of the gas in the inner regions of clusters can therefore be a useful diagnostic of gas cooling. We find that gas traces the shape of the underlying potential rather well outside the core, as expected in hydrostatic equilibrium. At smaller radii, however, the gas and potential shapes differ significantly. In the CSF runs, the difference reflects the fact that gas is partly rotationally supported. Interestingly, we find that in NR simulations the difference between gas and potential shape at small radii is due to random gas motions, which make the gas distribution more spherical than the equipotential surfaces. Finally, we use mock Chandra X-ray maps to show that the differences in shapes observed in a three-dimensional distribution of gas are discernible in the ellipticity of X-ray isophotes. Contrasting the ellipticities measured in simulated clusters against observations can therefore constrain the amount of cooling in the intracluster medium and the presence of random gas motions in cluster cores.

The relation between gas density and velocity power spectra in galaxy clusters: High-resolution hydrodynamic simulations and the role of conduction

Exploring the power spectrum of fluctuations and velocities in the intracluster medium (ICM) can help us to probe the gas physics of galaxy clusters. Using high-resolution 3D plasma simulations, we study the statistics of the velocity field and its inti mate relation with the ICM thermodynamic perturbations. The normalization of the ICM spectrum (related to density, entropy, or pressure fl uctuations) is linearly tied to the level of large-scale motions, which e xcite both gravity and sound waves due to stratification. For low 3D Mach number M ∼ 0.25, gravity waves mainly drive entropy perturbations, traced by preferentially tangential turbu lence. For M > 0.5, sound waves start to significantly contribute, passing th e leading role to compressive pressure fluctuations, associated with isotropic turbulence (or a slight radial bias). Densit y and temperature fluctuations are then characterized by the dominant process: isobaric (low M), adiabatic (high M), or isothermal (strong conduction). Most clusters reside in the intermediate regime, showing a mixture of gravity and sound waves, hence drifting towards isotropic velocities. Remarkably, regardless of t he regime, the variance of density perturbations is comparable to the 1D Mach number, M1D ∼δρ/ρ. This linear relation allows to easily convert between gas motions and ICM perturbations (δρ/ρ 0.1 in massive clusters), allowing to calibrate the linear relation and to constrain relative perturbations down to just a few per cent .

nIFTy galaxy cluster simulations – I. Dark matter and non-radiative models

We have simulated the formation of a galaxy cluster in a Ʌ cold dark matter universe using 13 different codes modelling only gravity and non-radiative hydrodynamics (RAMSES, ART, AREPO, HYDRA and nine incarnations of GADGET). This range of codes includes particle-based, moving and fixed mesh codes as well as both Eulerian and Lagrangian fluid schemes. The various GADGET implementations span classic and modern smoothed particle hydrodynamics (SPH) schemes. The goal of this comparison is to assess the reliability of cosmological hydrodynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be non-radiative. We compare images of the cluster at z = 0, global properties such as mass and radial profiles of various dynamical and thermodynamical quantities. The underlying gravitational framework can be aligned very accurately for all the codes allowing a detailed investigation of the differences that develop due to the various gas physics implementations employed. As expected, the mesh-based codes RAMSES, ART and AREPO form extended entropy cores in the gas with rising central gas temperatures. Those codes employing classic SPH schemes show falling entropy profiles all the way into the very centre with correspondingly rising density profiles and central temperature inversions. We show that methods with modern SPH schemes that allow entropy mixing span the range between these two extremes and the latest SPH variants produce gas entropy profiles that are essentially indistinguishable from those obtained with grid-based methods.

EFFECTS OF BARYON DISSIPATION ON THE DARK MATTER VIRIAL SCALING RELATION

We investigate effects of baryon dissipation on the dark matter virial scaling relation between total mass and velocity dispersion and the velocity bias of galaxies in groups and clusters using self-consistent cosmological simulations. We show that the baryon dissipation increases the velocity dispersion of dark matter within the virial radius by 5% - 10%. The effect is mainly driven by the change in density and gravitational potential in inner regions of cluster, and it is larger in lower mass systems where gas cooling and star formation are more efficient. We also show that the galaxy velocity bias depends on how galaxies are selected. Galaxies selected based on their stellar mass exhibit no velocity bias, while galaxies selected based on their total mass show positive bias of ~10%, consistent with previous results based on collisionless dark matter- only simulations. We further find that observational estimates of galaxy velocity dispersion are unbiased with respect to the velocity dispersion of dark matter, provided galaxies are selected using their stellar masses and and their velocity dispersions are computed with more than twenty most massive galaxies. Velocity dispersions estimated with fewer galaxies, on the other hand, can lead to significant underestimate of dynamical masses. Results presented in this paper should be useful in interpretating high-redshift groups and clusters as well as cosmological constraints derived from upcoming optical cluster surveys.

Temperature structure of the intracluster medium from smoothed-particle hydrodynamics and adaptive-mesh refinement simulations

Analyses of cosmological hydrodynamic simulations of galaxy clusters suggest that X-ray masses can be underestimated by 10% to 30%. The largest bias originates by both violation of hydrostatic equilibrium and an additional temperature bias caused by inhomogeneities in the X-ray emitting intra-cluster medium (ICM). To elucidate on this large dispersion among theoretical predictions, we evaluate the degree of temperature structures in cluster sets simulated either with smoothed-particle-hydrodynamics (SPH) and adaptive-mesh-refinement (AMR) codes. We find that the SPH simulations produce larger temperature variations connected to the persistence of both substructures and their stripped cold gas. This difference is more evident in no-radiative simulations, while it is reduced in the presence of radiative cooling. We also find that the temperature variation in radiative cluster simulations is generally in agreement with the observed one in the central regions of clusters. Around R500 the temperature inhomogeneities of the SPH simulations can generate twice the typical hydrostatic-equilibrium mass bias of the AMR sample. We emphasize that a detailed understanding of the physical processes responsible for the complex thermal structure in ICM requires improved resolution and high sensitivity observations in order to extend the analysis to higher temperature systems and larger cluster-centric radii. Subject headings: galaxies: clusters: general ‐ galaxies: clusters: intracluster medium ‐ X-rays: galaxies: clusters ‐ methods: numerical

PREDICTING MERGER-INDUCED GAS MOTIONS IN ΛCDM GALAXY CLUSTERS

In the hierarchical structure formation model, clusters of galaxies form through a sequence of mergers and continuous mass accretion, which generate significant random gas motions especially in their outskirts where material is actively accreting. Non-thermal pressure provided by the internal gas motions affects the thermodynamic structure of the X-ray emitting intracluster plasma and introduces biases in the physical interpretation of X-ray and Sunyaev-Zeldovich effect observations. However, we know very little about the nature of gas motions in galaxy clusters. The ASTRO-H X-ray mission, scheduled to launch in 2015, will have a calorimeter capable of measuring gas motions in galaxy clusters at the level of 100 km s–1. In this work, we predict the level of merger-induced gas motions expected in the ΛCDM model using hydrodynamical simulations of galaxy cluster formation. We show that the gas velocity dispersion is larger in more massive clusters, but exhibits a large scatter. We show that systems with large gas motions are morphologically disturbed, while early forming, relaxed groups show a smaller level of gas motions. By analyzing mock ASTRO-H observations of simulated clusters, we show that such observations can accurately measure the gas velocity dispersion out to the outskirts of nearby relaxed galaxy clusters. ASTRO-H analysis of merging clusters, on the other hand, requires multi-component spectral fitting and enables unique studies of substructures in galaxy clusters by measuring both the peculiar velocities and the velocity dispersion of gas within individual sub-clusters.

On the cross-section of dark matter using substructure infall into galaxy clusters

We develop a statistical method to measure the interaction cross-section of dark matter, exploiting the continuous minor merger events in which small substructures fall into galaxy clusters. We find that by taking the ratio of the distances between the galaxies and dark matter, and galaxies and gas in accreting subhaloes, we form a quantity that can be statistically averaged over a large sample of systems whilst removing any inherent line-of-sight projections. To interpret this ratio as a cross-section of dark matter, we derive an analytical description of subhalo infall allowing us to constrain self-interaction models in which drag is an appropriate macroscopic treatment. We create mock observations from cosmological simulations of structure formation and find that collisionless dark matter becomes physically separated from X-ray gas by up to ∼20 h−1 kpc. Adding realistic levels of noise, we are able to predict achievable constraints from observational data. Current archival data should be able to detect a difference in the dynamical behaviour of dark matter and standard model particles at 6σ, and measure the total interaction cross-section σ/m with 68 per cent confidence limits of ±1 cm2 g−1. We note that this method is not restricted by the limited number of major merging events and is easily extended to large samples of clusters from future surveys which could potentially push statistical errors to <0.1 cm2 g−1.