K. Dolag

Substructures in hydrodynamical cluster simulations

The abundance and structure of dark matter subhaloes have been analysed extensively in recent studies of dark-matter-only simulations, but comparatively little is known about the impact of baryonic physics on halo substructures. We here extend the SUBFIND algorithm for substructure identification such that it can be reliably applied to dissipative hydrodynamical simulations that include star formation. This allows, in particular, the identification of galaxies as substructures in simulations of clusters of galaxies and a determination of their content of gravitationally bound stars, dark matter and hot and cold gas. Using a large set of cosmological cluster simulations, we present a detailed analysis of halo substructures in hydrodynamical simulations of galaxy clusters, focusing in particular on the influence both of radiative and non-radiative gas physics and of non-standard physics such as thermal conduction and feedback by galactic outflows. We also examine the impact of numerical nuisance parameters such as artificial viscosity parameterizations. We find that diffuse hot gas is efficiently stripped from subhaloes when they enter the highly pressurized cluster atmosphere. This has the effect of decreasing the subhalo mass function relative to a corresponding dark-matter-only simulation. These effects are mitigated in radiative runs, where baryons condense in the central subhalo regions and form compact stellar cores. However, in all cases, only a very small fraction, of the order of one per cent, of subhaloes within the cluster virial radii preserve a gravitationally bound hot gaseous atmosphere. The fraction of mass contributed by gas in subhaloes is found to increase with the cluster-centric distance. Interestingly, this trend extends well beyond the virial radii, thus showing that galaxies feel the environment of the pressurized cluster gas over fairly large distances. The compact stellar cores (i.e. galaxies) are generally more resistant against tidal disruption than pure dark matter subhaloes. Still, the fraction of star-dominated substructures within our simulated clusters is only ~10 per cent. We expect that the finite resolution in our simulations makes the galaxies overly susceptible to tidal disruption, hence the above fraction of star-dominated galaxies should represent a lower limit for the actual fraction of galaxies surviving the disruption of their host dark matter subhalo.

X-ray properties of galaxy clusters and groups from a cosmological hydrodynamical simulation

We present results on the X-ray properties of clusters and groups of galaxies, extracted from a large cosmological hydrodynamical simulation. We used the TREE+SPH code GADGET to simulate a concordance A cold dark matter cosmological model within a box of 192 h -1 Mpc on a side, 480 3 dark matter particles and as many gas particles. The simulation includes radiative cooling assuming zero metallicity, star formation and supernova feedback. The very high dynamic range of the simulation allows us to cover a fairly large interval of cluster temperatures. We compute X-ray observables of the intracluster medium (ICM) for simulated groups and clusters and analyse their statistical properties. The simulated mass-temperature relation is consistent with observations once we mimic the procedure for mass estimates applied to real clusters. Also, with the adopted choices of Ω m = 0.3 and σ 8 = 0.8 for matter density and power spectrum normalization, respectively, the resulting X-ray temperature functton agrees with the most recent observational determinations. The luminosity-temperature relation also agrees with observations for clusters with T ≥ 2 keV. At the scale of groups, T ≥ 1 keV, we find no change of slope in this relation. The entropy in central cluster regions is higher than predicted by gravitational heating alone, the excess being almost the same for clusters and groups. We also find that the simulated clusters appear to have suffered some overcooling. We find f * ≃ 0.2 for the fraction of baryons in stars within clusters, thus approximately twice as large as the value observed. Interestingly, temperature profiles of simulated clusters are found to increase steadily toward cluster centres. They decrease in the outer regions, much like observational data do at r ≥ 0.2r vir , while not showing an isothermal regime followed by a smooth temperature decline in the innermost regions. Our results thus demonstrate the need for yet more efficient sources of energy feedback and/or the need to consider additional physical process which may be able to further suppress the gas density at the scale of poor clusters and groups, and, at the same time, to regulate the cooling of the ICM in central regions.

Turbulent gas motions in galaxy cluster simulations: the role of smoothed particle hydrodynamics viscosity

Smoothed particle hydrodynamics (SPH) employs an artificial viscosity to properly capture hydrodynamic shock waves. In its original formulation, the resulting numerical viscosity is large enough to suppress structure in the velocity field on scales well above the nominal resolution limit, and to damp the generation of turbulence by fluid instabilities. This could artificially suppress random gas motions in the intracluster medium (ICM), which are driven by infalling structures during the hierarchical structure formation process. We show that this is indeed the case by analysing results obtained with an SPH formulation where an individual, time-variable viscosity is used for each particle, following a suggestion by Morris & Monaghan. Using test calculations involving strong shocks, we demonstrate that this scheme captures shocks as well as the original formulation of SPH, but, in regions away from shocks, the numerical viscosity is much smaller. In a set of nine high-resolution simulations of cosmological galaxy cluster formation, we find that this low-viscosity formulation of SPH produces substantially higher levels of turbulent gas motions in the ICM, reaching a kinetic energy content in random gas motions (measured within a 1-Mpc cube) of up to 5‐30 per cent of the thermal energy content, depending on cluster mass. This also has significant effects on radial gas profiles and bulk cluster properties. We find a central flattening of the entropy profile and a reduction of the central gas density in the low-viscosity scheme. As a consequence, the bolometric X-ray luminosity is decreased by about a factor of 2. However, the cluster temperature profile remains essentially unchanged. Interestingly, this tends to reduce the differences seen in SPH and adaptive mesh refinement simulations of cluster formation. Finally, invoking a model for particle acceleration by magnetohydrodynamics waves driven by turbulence, we find that efficient electron acceleration and thus diffuse radio emission can be powered in the clusters simulated with the low-viscosity scheme provided that more than 5‐10 per cent of the turbulent energy density is associated with fast magneto-sonic modes.

Numerical study of halo concentrations in dark-energy cosmologies

We study the concentration parameters, their mass dependence and redshift evolution, of dark-matter halos in different dark-energy cosmologies with constant and time-variable equation of state, and compare them with standard ACDM and OCDM models. We find that previously proposed algorithms for predicting halo concentrations can be well adapted to dark-energy models. When centred on the analytically expected values, halo concentrations show a log-normal distribution with a uniform standard deviation of ∼0.2. The dependence of averaged halo concentrations on mass and redshift permits a simple fit of the form (1 + z) c = c 0 (M/M 0 ) α , with α -0.1 throughout. We find that the cluster concentration depends on the dark energy equation of state at the cluster formation redshift z coll through the linear growth factor D + (z coll ). As a simple correction accounting for dark-energy cosmologies, we propose scaling c 0 from ACDM with the ratio of linear growth factors, c 0 → c 0 D + (Z coll )/D +.ACDM (z coll ).

Constrained simulations of the magnetic field in the local Universe and the propagation of ultrahigh energy cosmic rays

We use simulations of large-scale structure formation to study the build-up of magnetic fields (MFs) in the intergalactic medium. Our basic assumption is that cosmological MFs grow in a magnetohydrodynamical (MHD) amplification process driven by structure formation out of a magnetic seed field present at high redshift. This approach is motivated by previous simulations of the MFs in galaxy clusters which, under the same hypothesis that we adopt here, succeeded in reproducing Faraday rotation measurements (RMs) in clusters of galaxies. OurCDM initial conditions for the dark matter density fluctuations have been statistically constrained by the observed large-scale density field within a sphere of 110 Mpc around the Milky Way, based on the IRAS 1.2-Jy all-sky redshift survey. As a result, the positions and masses of prominent galaxy clusters in our simulation coincide closely with their real counterparts in the Local Universe. We find excellent agreement between RMs of our simulated galaxy clusters and observational data. The improved numerical resolution of our simulations compared to previous work also allows us to study the MF in large-scale filaments, sheets and voids. By tracing the propagation of ultra high energy (UHE) protons in the simulated MF we construct full-sky maps of expected deflection angles of protons with arrival energies E = 10 20 eV and 4 × 10 19 eV, respectively. Accounting only for the structures within 110 Mpc, we find that strong deflections are only produced if UHE protons cross galaxy clusters. The total area on the sky covered by these structures is however very small. Over still larger distances, multiple crossings of sheets and filaments may give rise to noticeable deflections over a significant fraction of the sky; the exact amount and angular distribution depends on the model adopted for the magnetic seed field. Based on our results we argue that over a large fraction of the sky the deflections are likely to remain smaller than the present experimental angular sensitivity. Therefore, we conclude that forthcoming air shower experiments should be able to locate sources of UHE protons and shed more light on the nature of cosmological MFs.

Magnetic fields and Faraday rotation in clusters of galaxies

We present a numerical approach to investigate the relationship between magnetic fields and Faraday rotation effects in clusters of galaxies. We can infer the structure and strength of intra-cluster magnetic fields by comparing our simulations with the observed polarization properties of extended cluster radio sources such as radio galaxies and halos. We find the observations require a magnetic field which fluctuates over a wide range of spatial scales (at least one order of magnitude). If several polarized radio sources are located at different projected positions in a galaxy cluster, as is the case for A119, detailed Faraday rotation images allow us to constrain both the magnetic field strength and the slope of the power spectrum. Our results show that the standard analytic expressions applied in the literature overestimate the cluster magnetic field strengths by a factor of ∼2. We investigate the possible effects of our models on beam depolarization of radio sources whose radiation traverses the magnetized intracluster medium. Finally, we point out that radio halos may provide important information about the spatial power spectrum of the magnetic field fluctuations on large scales. In particular, different values of the index of the power spectrum produce very different total intensity and polarization brightness distributions.

The diffuse light in simulations of galaxy clusters

We study the properties of the diffuse light in galaxy clusters forming in a large hydrodynamical cosmological simulation of the Λ cold dark matter cosmology. The simulation includes a model for radiative cooling, star formation in dense cold gas, and feedback by Type II supernova explosions. We select clusters having mass M > 1014 h-1 M☉ and study the spatial distribution of their star particles. While most stellar light is concentrated in gravitationally bound galaxies orbiting in the cluster potential, we find evidence for a substantial diffuse component, which may account for the extended halos of light observed around central cD galaxies. We find that more massive simulated clusters have a larger fraction of stars in the diffuse light than the less massive ones. The intracluster light is more centrally concentrated than the galaxy light, and the stars in the diffuse component are on average older than the stars in cluster galaxies, supporting the view that the diffuse light is not a random sampling of the stellar population in the cluster galaxies. We thus expect that at least ~10% of the stars in a cluster may be distributed as intracluster light, largely hidden thus far because of its very low surface brightness.

An MHD gadget for cosmological simulations

Various radio observations have shown that the hot atmospheres of galaxy clusters are magnetized. However, our understanding of the origin of these magnetic fields, their implications on structure formation and their interplay with the dynamics of the cluster atmosphere, especially in the centers of galaxy clusters, is still very limit ed. In preparation for the upcoming new generation of radio telescopes (like EVLA, LWA, LOFAR and SKA), a huge effort is being made to learn more about cosmological magnetic fields f rom the observational perspective. Here we present the implementation of magneto-hydrodynamics in the cosmological SPH code GADGET (Springel et al. 2001; Springel 2005). We discuss the details of the implementation and various schemes to suppress numerical instabilities as well as regularization schemes, in the context of cosmological simulations. The performance of the SPH-MHD code is demonstrated in various one and two dimensional test problems, which we performed with a fully, three dimensional setup to test the code under reali stic circumstances. Comparing solutions obtained using ATHENA (Stone et al. 2008), we find exc ellent agreement with our SPH-MHD implementation. Finally we apply our SPH-MHD implementation to galaxy cluster formation within a large, cosmological box. Performing a resolution study we demonstrate the robustness of the predicted shape of the magnetic field pr ofiles in galaxy clusters, which is in good agreement with previous studies.

Cosmological simulations of black hole growth: AGN luminosities and downsizing

In this study, we present a detailed, statistical analysis of black hole growth and the evolution of active galactic nuclei (AGN) using cosmological hydrodynamic simulations run down to z = 0. The simulations self-consistently follow radiative cooling, star formation, metal enrichment, black hole growth and associated feedback processes from both supernovae typeII/Ia and AGN. We consider two simulation runs, one with a large co-moving volume of (128 Mpc/h) 3 and one with a smaller volume of (48 Mpc/h) 3 but with a by a factor of almost 20 higher mass resolution. We compare the predicted statistical properties of AGN with results from large observational surveys. Consistently with previous results, our simulations are in reasonably good agreement with black hole properties of the local Universe. Furthermore, our simulations can successfully reproduce the evolution of the bolometric AGN luminosity function for both the low-luminosity and the high-luminosity end up to z = 2.5. In particular, the latter is for the first time accessible thanks to the large simulated volume in our larger run. In addition, the smaller but higher resolution run is able to match the observational data of the low bolometric luminosity end up to z = 4 5. We also perform a direct comparison with the observed soft and hard X-ray luminosity functions of AGN, including an empirical correction for a torus-level obscuration, and find a similarly good agreement. These results show that our simulations can self-consistently predict the observed “downsizing” trend in the AGN number density evolution, i.e. the number densities of luminous AGN peak at higher redshifts than those of faint AGN. Implications of the downsizing behaviour on active black holes, their masses and Eddington-ratios are discussed. Overall, the downsizing behaviour in the AGN number density as a function of redshift can be attributed to a combination of the gas density evolution in the resolved vicinity of a (massive) black hole (which is depleted with evolving time mainly as a consequence of the radio-mode feedback) and to the decreasing mean relative velocities between the (low mass) black holes and the surrounding gas with decreasing redshift.

Thermal conduction in simulated galaxy clusters

We study the formation of clusters of galaxies using high-resolution hydrodynamic cosmological simulations that include the effect of thermal conduction with an effective isotropic conductivity of the classical Spitzer 1 3 value. We find that, for both a hot ( keV) and several cold ( keV) galaxy clusters, the baryonic T 12 T 2 LL XX fraction converted into stars does not change significantly when thermal conduction is included. However, the temperature profiles are modified, particularly in our simulated hot system, where an extended isothermal core is readily formed. As a consequence of heat flowing from the inner regions of the cluster both to its outer parts and into its innermost resolved regions, the entropy profile is altered as well. This effect is almost negligible for the cold cluster, as expected based on the strong temperature dependence of the conductivity. Our results demonstrate that while thermal conduction can have a significant influence on the properties of the intracluster medium (ICM) of rich clusters, it appears unlikely to provide by itself a solution for the overcooling problem in clusters or to explain the current discrepancies between the observed and simulated properties of the ICM. Subject headings: conduction — cosmology: theory — galaxies: clusters: general — methods: numerical On-line material: color figure