Hydrodynamical Simulations of Galaxy Clusters

In my contribution I discuss the relevance that hydrodynamical simulation of clusters can play to understand the ICM physics and to calibrate mass estimates from X-ray observable quantities. Using hydrodynamical simulations, which cover quite a large dynamical range and include a fairly advanced treatment of the gas physics (cooling, star formation and SN feedback), I show that scaling relations among X-ray observable quantities can be reproduced quite well. At the sametime, these simulations fail at accounting for several observational quantities, which are related to the cooling structure of the ICM: the fraction of stars, the temperature profiles and the gas entropy in central cluster regions. This calls for the need of introducing in simulations suitable physical mechanisms which should regulate the cooling structure of the ICM.     

The Sunyaev–Zel'dovich temperature of the intracluster medium

The relativistic Sunyaev–Zel'dovich (SZ) effect offers a method, independent of X-ray, for measuring the temperature of the intracluster medium (ICM) in the hottest systems. Here, using N -body/hydrodynamic simulations of three galaxy clusters, we compare the two quantities for a non-radiative ICM, and for one that is subject both to radiative cooling and to strong energy feedback from galaxies. Our study has yielded two interesting results. First, in all cases, the SZ temperature is hotter than the X-ray temperature and is within 10 per cent of the virial temperature of the cluster. Secondly, the mean SZ temperature is less affected by cooling and feedback than the X-ray temperature. Both these results can be explained by the SZ temperature being less sensitive to the distribution of cool gas associated with cluster substructure. A comparison of the SZ and X-ray temperatures (measured for a sample of hot clusters) would therefore yield interesting constraints on the thermodynamic structure of the intracluster gas.     

Sunyaev–Zel'dovich cluster survey simulations for Planck

We examine the ability of the future Planck mission to provide a catalogue of galaxy clusters observed via their Sunyaev–Zel'dovich (SZ) distortion in the cosmic microwave background (CMB). For this purpose we produce full-sky SZ maps based on N -body simulations and scaling relations between cluster properties for several cosmological models. We extrapolate the N -body simulations by a mass function to high redshifts in order to obtain a realistic SZ background. The simulated Planck observations include, besides the thermal and kinematic SZ effects, contributions from the primordial CMB, extragalactic point sources as well as Galactic dust, free–free and synchrotron emission. A harmonic-space maximum-entropy method is used to separate the SZ signal from contaminating components in combination with a cluster detection algorithm based on thresholding and flux integration to identify clusters and to obtain their fluxes. We estimate a survey sensitivity limit (depending on the quality of the recovered cluster flux) and provide cluster survey completeness and purity estimates. We find that, given our modelling and detection algorithm, Planck will reliably detect at least several thousands of clusters over the full sky. The exact number depends on the particular cosmological model (up to 10 000 cluster detections in a concordance ΛCDM model with  σ₈= 0.9  ). We show that the Galaxy does not significantly affect the cluster detection. Furthermore, the dependence of the thermal SZ power spectrum on the matter variance on scales of  8 h ⁻¹  Mpc and the quality of its reconstruction by the employed method are investigated. Our simulations suggest that the Planck cluster sample will not only be useful as a basis for follow-up observations, but also will have the ability to provide constraints on cosmological parameters.     

Morphology of flows and buoyant bubbles in the Virgo cluster

There is growing evidence that the active galactic nuclei (AGN) associated with the central elliptical galaxy in clusters of galaxies are playing an important role in the evolution of the intracluster medium (ICM) and clusters themselves. We use high-resolution three-dimensional simulations to study the interaction of the cavities created by AGN outflows (bubbles) with the ambient ICM. The gravitational potential of the cluster is modelled using the observed temperature and density profiles of the Virgo cluster. We demonstrate the importance of the hydrodynamical Kutta–Zhukovsky forces associated with the vortex ring structure of the bubbles, and discuss possible effects of diffusive processes on their evolution.     

An SZ temperature decrement–X-ray luminosity relation for galaxy clusters

We present the observed relation between Δ T _SZ, the cosmic microwave background (CMB) temperature decrement due to the Sunyaev–Zeldovich (SZ) effect, and L , the X-ray luminosity of galaxy clusters. We discuss this relation in terms of the cluster properties, and show that the slope of the observed Δ T _SZ– L relation is in agreement with both the L – T _e relation based on numerical simulations and X-ray emission observations, and the M _gas– L relation based on observation. The slope of the Δ T _SZ– L relation is also consistent with the M _tot– L relation, where M _tot is the cluster total mass based on gravitational lensing observations. This agreement may be taken to imply a constant gas mass fraction within galaxy clusters, however, there are large uncertainties, dominated by observational errors, associated with these relations. Using the Δ T _SZ– L relation and the cluster X-ray luminosity function, we evaluate the local cluster contribution to arcmin-scale cosmic microwave background anisotropies. The Compton distortion y -parameter produced by galaxy clusters through the SZ effect is roughly two orders of magnitude lower than the current upper limit based on FIRAS observations.     

The impact of dust on the scaling properties of galaxy clusters

We investigate the effect of dust on the scaling properties of galaxy clusters based on hydrodynamic N -body simulations of structure formation. We have simulated five dust models plus radiative cooling and adiabatic models using the same initial conditions for all runs. The numerical implementation of dust was based on the analytical computations of Montier & Giard. We set up dust simulations to cover different combinations of dust parameters that make evident the effects of size and abundance of dust grains. Comparing our radiative plus dust cooling runs with a purely radiative cooling simulation, we find that dust has an impact on cluster scaling relations. It mainly affects the normalization of the scalings (and their evolution), whereas it introduces no significant differences in their slopes. The strength of the effect critically depends on the dust abundance and grain size parameters as well as on the cluster scaling. Indeed, cooling due to dust is effective in the cluster regime and has a stronger effect on the 'baryon driven' statistical properties of clusters such as   L _X– M , Y – M , S – M   scaling relations. Major differences, relative to the radiative cooling model, are as high as 25 per cent for the   L _X– M   normalization, and about 10 per cent for the Y – M and S – M normalizations at redshift zero. On the other hand, we find that dust has almost no impact on the 'dark matter driven'   T _mw– M   scaling relation. The effects are found to be dependent in equal parts on both dust abundances and grain size distributions for the scalings investigated in this paper. Higher dust abundances and smaller grain sizes cause larger departures from the radiative cooling (i.e. with no dust) model.     

Are 'Bondi–Hoyle wakes' detectable in clusters of galaxies?

In clusters of galaxies, the reaction of the intracluster medium (ICM) to the motion of the co-existing galaxies in the cluster triggers the formation of unique features, which trace their position and motion. Galactic wakes, for example, are an apparent result of the ICM/galaxy interactions, and they constitute an important tool for deciphering the motion of the cluster galaxies.
In this paper we investigate whether Bondi–Hoyle accretion can create galactic wakes by focusing the ICM behind moving galaxies. The solution of the equations that describe this physical problem provides us with observable quantities along the wake at any time of its lifetime. We also investigate which are the best environmental conditions for the detectability of such structures in the X-ray images of clusters of galaxies.
We find that significant Bondi–Hoyle wakes can only be formed in low-temperature clusters, and that they are more pronounced behind slow-moving, relatively massive galaxies. The scalelength of these elongated structures is not very large: in the most favourable conditions a Bondi–Hoyle wake in a cluster at the redshift of z =0.05 is 12 arcsec long. However, the X-ray emission of the wake is noticeably strong: the X-ray flux can reach ∼30 times the flux of the surrounding medium. Such features will be easily detectable in the X-ray images of nearby, relatively poor clusters of galaxies by the Chandra and XMM-Newton satellites.     

Numerical Simulations of the Interaction of Jets with the Intracluster Medium

We study, by numerical simulations, the propagation of an axisymmetric supersonic jet in an isothermal King atmosphere and we analyse the evolution of the resulting X-ray properties and their dependence on the jet physical parameters. We show the existence of two distinct regimes of interaction, with strong and weak shocks. In the first case shells of enhanced X-ray emission are to be expected, whereas in the second case we expect deficit of X-ray emission coincident with the cocoon. Analysing the results of our simulations we find that the jet kinetic power is the main parameter controlling the transition between the two regimes. We also discuss, in the same scheme, the ICM heating induced by the jet propagation, considering its effects on the observed relations between the cluster X-ray luminosity and temperature and between cluster entropy and temperature.     

Adiabatic scaling relations of galaxy clusters

The aim of this work is to show that, contrary to popular belief, galaxy clusters are not expected to be self-similar, even when the only energy sources available are gravity and shock-wave heating. In particular, we investigate the scaling relations between mass, luminosity and temperature of galaxy groups and clusters in the absence of radiative processes. Theoretical expectations are derived from a polytropic model of the intracluster medium and compared with the results of high-resolution adiabatic gasdynamical simulations. It is shown that, in addition to the well-known relation between the mass and concentration of the dark matter halo, the effective polytropic index of the gas also varies systematically with cluster mass, and therefore neither the dark matter nor the gas profiles are exactly self-similar. It is remarkable, though, that the effects of concentration and polytropic index tend to cancel each other, leading to scaling relations whose logarithmic slopes roughly match the predictions of the most-basic self-similar models. We provide a phenomenological fit to the relation between polytropic index and concentration, as well as a self-consistent scheme to derive the non-linear scaling relations expected for any cosmology and the best-fitting normalizations of the M – T , L – T and F – T relations appropriate for a Λ cold dark matter universe. The predicted scaling relations reproduce observational data reasonably well for massive clusters, where the effects of cooling and star formation are expected to play a minor role.     

Gamma-ray probe of cosmic ray pressure in galaxy clusters and cosmological implications

Cosmic rays produced in cluster accretion and merger shocks provide pressure to the intracluster medium (ICM) and affect the mass estimates of galaxy clusters. Although direct evidence for cosmic ray ions in the ICM is still lacking, they produce γ-ray emission through the decay of neutral pions produced in their collisions with ICM nucleons. We investigate the capability of the Gamma-ray Large Area Space Telescope ( GLAST ) and imaging atmospheric Čerenkov telescopes (IACTs) for constraining the cosmic ray pressure contribution to the ICM. We show that GLAST can be used to place stringent upper limits, a few per cent for individual nearby rich clusters, on the ratio of pressures of the cosmic rays and thermal gas. We further show that it is possible to place tight (≲10 per cent) constraints for distant  ( z ≲ 0.25)  clusters in the case of hard spectrum, by stacking signals from samples of known clusters. The GLAST limits could be made more precise with the constraint on the cosmic ray spectrum potentially provided by IACTs. Future γ-ray observations of clusters can constrain the evolution of cosmic ray energy density, which would have important implications for cosmological tests with upcoming X-ray and Sunyaev–Zel'dovich effect cluster surveys.     

Turbulence in clusters of galaxies and X-ray line profiles

Large-scale bulk motions and hydrodynamic turbulence in the intergalactic gas that fills clusters of galaxies significantly broaden X-ray emission lines. For lines of heavy ions (primarily helium-like and hydrogen-like iron ions), the hydrodynamic broadening is appreciably larger than the thermal broadening. Since clusters of galaxies have a negligible optical depth for resonant scattering in the forbidden and intercombination lines of these ions, these lines are not additionally broadened. At the same time, they are very intense, which allows deviations of the spectrum from the Gaussian spectrum in the line wings to be investigated. The line shape proves to be an important indicator of bulk hydrodynamic processes. Doppler probing of turbulence becomes possible, because the cryogenic detectors of the X-ray observatories now ready for launch and being planned will have a high energy resolution (from 5 eV for ASTRO-E2 to 1–2 eV for Constellation-X and XEUS). We use the spectral representation of a Kolmogorov cascade in the inertial range to calculate the characteristic shapes of radiation lines. Significant deviations in the line profiles from the Gaussian profile (shape asymmetry, additional peaks, sharp breaks in the exponential tails) are expected for large-scale turbulence. The kinematic SZ effect and the X-ray line profiles carry different information about the hydrodynamic velocity distribution in clusters of galaxies and complement each other, allowing the redshift, the peculiar velocity of the cluster, and the bulk velocity dispersion to be separated.     

Sound waves excitation by jet-inflated bubbles in clusters of galaxies

We show that repeated sound waves in the intracluster medium (ICM) can be excited by a single inflation episode of an opposite bubble pair. To reproduce this behaviour in numerical simulations, the bubbles should be inflated by jets, rather than being injected artificially as already full-blown bubbles. The multiple sound waves are excited by the motion of the bubble–ICM boundary that is caused by vortices inside the inflated bubbles and the backflow ('cocoon') of the ICM around the bubble. These sound waves form a structure that can account for the ripples observed in the Perseus cooling flow cluster. We inflate the bubbles using slow massive jets either with a very wide opening angle or that are narrow and precessing. The wide jets (or collimated fast winds) are slow in the sense that they are highly subrelativistic,   v _j∼ 0.01 c – 0.1 c   , and they are massive in the sense that the pair of bubbles carries back to the ICM a large fraction of the cooling mass, i.e.  ∼1–50 M_⊙ yr⁻¹  . We use a two-dimensional axisymmetric (referred to as 2.5D) hydrodynamical numerical code ( vh-1 ).     

Scalability of supernova remnant simulations

The simulation or solution of the supernova remnant evolution may be scaled from one interstellar environment to another. We systematically examine this scalability, the use of which is so far still very limited in astrophysical literature. We show how the scalability is affected by various constraints imposed by physical processes and initial conditions, and demonstrate the use of the scaling as a powerful tool to explore the interdependence among relevant parameters, based on a minimum set of simulations. In particular, we devise a scaling scheme that can be used to adaptively generate numerous seed remnants and plant them into 3D hydrodynamic simulations of the supernova-dominated interstellar medium.     

Surveying the sky with the Arcminute MicroKelvin Imager: expected constraints on galaxy cluster evolution and cosmology

We discuss prospects for cluster detection via the Sunyaev–Zel'dovich (SZ) effect in a blank field survey with the interferometer array, the Arcminute MicroKelvin Imager (AMI). Clusters of galaxies selected in the SZ effect probe cosmology and structure formation with little observational bias, because the effect measures integrated gas pressure directly, and does so independently of cluster redshift.
We use hydrodynamical simulations in combination with the Press–Schechter expression to simulate SZ cluster sky maps. These are used with simulations of the observation process to gauge the expected SZ cluster counts. Even with a very conservative choice of parameters we find that AMI will discover at least several tens of clusters every year with     the numbers depend on factors such as the mean matter density, the density fluctuation power spectrum and cluster gas evolution. The AMI survey itself can distinguish between these to some degree, and parameter degeneracies are largely eliminated given optical and X-ray follow-up of these clusters; this will also permit direct investigation of cluster physics and what drives the evolution.     

Hydrodynamical simulations of cluster formation with central AGN heating

We analyse a hydrodynamical simulation model for the recurrent heating of the central intra-cluster medium (ICM) by active galactic nuclei (AGN). Besides the self-gravity of the dark matter and gas components, our approach includes the radiative cooling and photoheating of the gas, as well as a subresolution multiphase model for star formation and supernova feedback. Additionally, we incorporate a periodic heating mechanism in the form of hot, buoyant bubbles, injected into the intragalactic medium (IGM) during the active phases of the accreting central AGN. We use simulations of isolated cluster haloes of different masses to study the bubble dynamics and heat transport into the IGM. We also apply our model to self-consistent cosmological simulations of the formation of galaxy clusters with a range of masses. Our numerical schemes explore a variety of different assumptions for the spatial configuration of AGN-driven bubbles, for their duty cycles and for the energy injection mechanism, in order to obtain better constraints on the underlying physical picture. We argue that AGN heating can substantially affect the properties of both the stellar and gaseous components of clusters of galaxies. Most importantly, it alters the properties of the central dominant (cD) galaxy by reducing the mass deposition rate of freshly cooled gas out of the ICM, thereby offering an energetically plausible solution to the cooling-flow problem. At the same time, this leads to reduced or eliminated star formation in the central cD galaxy, giving it red stellar colours as observed.     

A study of the Sunyaev–Zel'dovich increment using archival SCUBA data

In a search for evidence of the short wavelength increment in the Sunyaev–Zel'dovich (SZ) effect, we have analysed archival galaxy cluster data from the Submillimetre Common User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope, resulting in the most complete pointed survey of clusters at 850 μm to date. SCUBA's 850-μm passband overlaps the peak of the SZ increment. The sample consists of 44 galaxy clusters in the range 0 < z < 1.3. Maps of each of the clusters have been made and sources have been extracted; as an ancillary product, we generate the most thorough galaxy cluster point source list yet from SCUBA. 17 of these clusters are free of obvious active galactic nuclei (AGN) and have data deep enough to provide interesting measurements of the expected SZ signal. Specialized analysis techniques are employed to extract the SZ effect signal from these SCUBA data, including using SCUBA's short wavelength band as an atmospheric monitor and fitting the long wavelength channel to a model of the spatial distribution of each cluster's SZ effect. By explicitly excising the exact cluster centre from our analysis, we demonstrate that emission from galaxies within the cluster does not contaminate our measurement. The SZ amplitudes from our measurements are consistently higher than the amplitudes inferred from low-frequency measurements of the SZ decrement.