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.     

Apparent and actual galaxy cluster temperatures

The redshift evolution of the galaxy cluster temperature function is a powerful probe of cosmology. However, its determination requires the measurement of redshifts for all clusters in a catalogue, which is likely to prove challenging for large catalogues expected from XMM-Newton , which may contain of the order of 2000 clusters with measurable temperatures, distributed around the sky. In this paper we study the apparent cluster temperature, which can be obtained without cluster redshifts. We show that the apparent temperature function itself is of limited use in constraining cosmology, and so concentrate our focus on studying how apparent temperatures can be combined with other X-ray information to constrain the cluster redshift. We also briefly study the circumstances under which the non-thermal spectral features can provide redshift information.     

A new method to derive star formation histories of galaxies from their star cluster distributions

Star formation happens in a clustered way which is why the star cluster population of a particular galaxy is closely related to the star formation history of this galaxy. From the probabilistic nature of a mass function follows that the mass of the most massive cluster of a complete population, M _max, has a distribution with the total mass of the population as a parameter. The total mass of the population is connected to the star formation rate (SFR) by the length of a formation epoch.
Since due to evolutionary effects only massive star clusters are observable up to high ages, it is convenient to use this M _max(SFR) relation for the reconstruction of a star formation history. The age distribution of the most massive clusters can therefore be used to constrain the star formation history of a galaxy. The method, including an assessment of the inherent uncertainties, is introduced with this contribution, while following papers will apply this method to a number of galaxies.     

Coulomb interactions in the intracluster medium

In this paper we discuss the effect of Coulomb collisions on the temperature profiles of the intracluster medium in clusters of galaxies, motivated by recent reports of negative temperature gradients in some clusters by Markevitch et al. The time-scale for electrons and protons to reach temperature equilibrium can exceed a few × 10⁹ years beyond radii of a megaparsec, if the intracluster gas is assumed to be at the usual cluster virial temperature. If a cluster merger has occurred within that time causing the protons, but not the electrons, to be rapidly heated then a small negative temperature gradient can result. This gradient is larger in clusters with higher temperatures and steeper density profiles.   Applying these considerations to the cluster of galaxies A2163, we conclude that, more plausibly, the observed gradient is due to a lack of hydrostatic equilibrium following a merger.     

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.     

Radio signature of cosmological structure formation shocks

In the course of the formation of cosmological structures, large shock waves are generated in the intracluster medium (ICM). In analogy to processes in supernova remnants, these shock waves may generate a significant population of relativistic electrons which, in turn, produce observable synchrotron emission. The extended radio relics found at the periphery of several clusters and possibly also a fraction of radio halo emission may have this origin. Here, we derive an analytic expression for (i) the total radio power in the downstream region of a cosmological shock wave, and (ii) the width of the radio-emitting region. These expressions predict a spectral slope close to −1 for strong shocks. Moderate shocks, such as those produced in mergers between clusters of galaxies, lead to a somewhat steeper spectrum. Moreover, we predict an upper limit for the radio power of cosmological shocks. Comparing our results to the radio relics in Abell 115, 2256 and 3667, we conclude that the magnetic field in these relics is typically at a level of 0.1 μG. Magnetic fields in the ICM are presumably generated by the shocks themselves; this allows us to calculate the radio emission as a function of the cluster temperature. The resulting emissions agree very well with the radio power–temperature relation found for cluster haloes. Finally, we show that cosmic accretion shocks generate less radio emission than merger shock waves. The latter may, however, be detected with upcoming radio telescopes.     

Deconvolution of ASCA X-ray data – II. Radial temperature and metallicity profiles for 106 galaxy clusters

In Paper I we presented a methodology to recover the spatial variations of properties of the intracluster gas from ASCA X-ray satellite observations of galaxy clusters. We verified the correctness of this procedure by applying it to simulated cluster data sets that we had subjected to the various contaminants common in ASCA data. In this paper we present the results that we obtain when we apply this method to real galaxy cluster observations. We determine broad-band temperature and cooling-flow mass-deposition rates for the 106 clusters in our sample, and obtain temperature, abundance and emissivity profiles (i.e., at least two annular bins) for 98 of these clusters. We find that 90 per cent of these temperature profiles are consistent with isothermality at the 3 σ confidence level. This conflicts with the prevalence of steeply declining cluster temperature profiles found by Markevitch et al. from a sample of 30 clusters.     

Tidal tails of star clusters

Based on recent findings of a formation mechanism of substructure in tidal tails by Küpper et al., we investigate a more comprehensive set of N -body models of star clusters on orbits about a Milky Way like potential. We find that the predicted epicyclic overdensities arise in any tidal tail no matter which orbit the cluster follows as long as the cluster lives long enough for the overdensities to build up.
The distance of the overdensities along the tidal tail from the cluster centre depends for circular orbits only on the mass of the cluster and the strength of the tidal field, and therefore decreases monotonically with time, while for eccentric orbits the orbital motion influences the distance, causing a periodic compression and stretching of the tails and making the distance oscillate with time. We provide an approximation for estimating the distance of the overdensities in this case.
We describe an additional type of overdensity which arises in extended tidal tails of clusters on eccentric orbits, when the acceleration of the tidal field on the stellar stream is no longer homogeneous. Moreover, we conclude that a pericentre passage or a disc shock is not the direct origin of an overdensity within a tidal tail. Escape due to such tidal perturbations does not take place immediately after the perturbation but is rather delayed and spread over the orbit of the cluster. All observable overdensities are therefore of the mentioned two types. In particular, we note that substructured tidal tails do not imply the existence of dark matter substructures in the haloes of galaxies.     

Sunyaev–Zel'dovich profiles and scaling relations: modelling effects and observational biases

We use high-resolution hydrodynamic resimulations to investigate the properties of the thermal Sunyaev–Zel'dovich (SZ) effect from galaxy clusters. We compare results obtained using different physical models for the intracluster medium (ICM), and show how they modify the SZ emission in terms of cluster profiles and scaling relations. We also produce realistic mock observations to verify whether the results from hydrodynamic simulations can be confirmed. We find that SZ profiles depend marginally on the modelled physical processes, while they exhibit a strong dependence on cluster mass. The central and total SZ emission strongly correlates with the cluster X-ray luminosity and temperature. The logarithmic slopes of these scaling relations differ from the self-similar predictions by less than 0.2; the normalization of the relations is lower for simulations including radiative cooling. The observational test suggests that SZ cluster profiles are unlikely to be able to probe the ICM physics. The total SZ decrement appears to be an observable much more robust than the central intensity, and we suggest using the former to investigate scaling relations.     

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.     

The prevalence of cooling cores in clusters of galaxies at z≈ 0.15–0.4

We present a Chandra study of 38 X-ray-luminous clusters of galaxies in the ROSAT Brightest Cluster Sample (BCS) that lie at moderate redshifts  ( z ≈ 0.15–0.4)  . Based primarily on power ratios and temperature maps, we find that the majority of clusters at moderate redshift generally have smooth, relaxed morphologies with some evidence for mild substructure perhaps indicative of recent minor merger activity. Using spatially resolved spectral analyses, we find that cool cores appear still to be common at moderate redshift. At a radius of 50 kpc, we find that at least 55 per cent of the clusters in our sample exhibit signs of mild cooling  ( t _cool < 10 Gyr)  , while in the central bin at least 34 per cent demonstrate signs of strong cooling  ( t _cool < 2 Gyr)  . These percentages are nearly identical to those found for luminous, low-redshift clusters of galaxies, indicating that there appears to be little evolution in cluster cores since   z ≈ 0.4  and suggesting that heating and cooling mechanisms may already have stabilized by this epoch. Comparing the central cooling times to catalogues of central Hα emission in BCS clusters, we find a strong correspondence between the detection of Hα and central cooling time. We also confirm a strong correlation between the central cooling time and cluster power ratios, indicating that crude morphological measures can be used as a proxy for more rigorous analysis in the face of limited signal-to-noise ratio data. Finally, we find that the central temperatures for our sample typically drop by no more than a factor of ∼3–4 from the peak cluster temperatures, similar to those of many nearby clusters.     

Can simulations reproduce the observed temperature–mass relation for clusters of galaxies?

It has become increasingly apparent that traditional hydrodynamical simulations of galaxy clusters are unable to reproduce the observed properties of galaxy clusters, in particular overpredicting the mass corresponding to a given cluster temperature. Such overestimation may lead to systematic errors in results using galaxy clusters as cosmological probes, such as constraints on the density perturbation normalization σ ₈. In this paper we demonstrate that inclusion of additional gas physics, namely radiative cooling and a possible pre-heating of gas prior to cluster formation, is able to bring the temperature–mass relation in the innermost parts of clusters into good agreement with recent determinations by Allen, Schmidt & Fabian using Chandra data.     

V407 Vul: a direct impact accretor

Chandra and XMM-Newton observations have confirmed the presence of large temperature gradients within the cores of many relaxed clusters of galaxies. Here we investigate whether thermal conduction operating over those gradients can supply sufficient heat to offset radiative cooling. Narayan & Medredev and Gruzinov have noted, using published results on cluster temperatures, that conduction within a factor of a few of the Spitzer rate is sufficient to balance bremsstrahlung cooling. From a detailed study of the temperature and emission measure profiles of Abell 2199 and Abell 1835, we find that the heat flux required by conduction is consistent with or below the rate predicted by Spitzer in the outer regions of the core. Conduction may therefore explain the lack of observational evidence for large mass cooling rates inferred from arguments based simply on radiative cooling, provided that conductivity is suppressed by no more than a factor of 3 below the full Spitzer rate. To stem cooling in the central 20 kpc however, would necessitate conductivity values of at least a factor of 2 larger than the Spitzer values, which we consider implausible. This may provide an explanation for the observed star formation and optical nebulosities in cluster cores. The solution is likely to be time-dependent. We briefly discuss the possible origin of the cooler gas and the implications for massive galaxies.     

The connection between globular cluster systems and the host galaxies

A large number of early-type galaxies are now known to possess blue and red subpopulations of globular clusters. We have compiled a data base of 28 such galaxies exhibiting bimodal globular cluster colour distributions. After converting to a common V – I colour system, we investigate correlations between the mean colour of the blue and red subpopulations with galaxy velocity dispersion. We support previous claims that the mean colours of the blue globular clusters are unrelated to their host galaxy. They must have formed rather independently of the galaxy potential they now inhabit. The mean blue colour is similar to that for halo globular clusters in our Galaxy and M31. The red globular clusters, on the other hand, reveal a strong correlation with galaxy velocity dispersion. Furthermore, in well-studied galaxies the red subpopulation has similar, and possibly identical, colours to the galaxy halo stars. Our results indicate an intimate link between the red globular clusters and the host galaxy; they share a common formation history. A natural explanation for these trends would be the formation of the red globular clusters during galaxy collapse.     

Interactions of radio galaxies and the intracluster medium in Abell 160 and Abell 2462

We present Chandra and Very Large Array observations of two galaxy clusters, Abell 160 and Abell 2462, whose brightest cluster galaxies (BCGs) host wide angle tailed radio galaxies (WATs). We search for evidence of interactions between the radio emission and the hot, X-ray emitting gas, and we test various jet termination models. We find that both clusters have cool BCGs at the cluster centre, and that the scale of these cores (∼30–40 kpc for both sources) is of approximately the same scale as the length of the radio jets. For both sources, the jet flaring point is coincident with a steepening in the host cluster's temperature gradient, and similar results are found for 3C 465 and Hydra A. However, none of the published models of WAT formation offers a satisfactory explanation as to why this may be the case. Therefore, it is unclear what causes the sudden transition between the jet and the plume. Without accurate modelling, we cannot ascertain whether the steepening of the temperature gradient is the main cause of the transition, or merely a tracer of an underlying process.     

Clusters of galaxies with modified Newtonian dynamics

I consider X-ray emitting clusters of galaxies in the context of modified Newtonian dynamics (MOND). Self-gravitating isothermal gas spheres are not good representations of rich clusters; the X-ray luminosity at a given temperature is typically an order of magnitude larger than observed, and the predicted X-ray surface brightness distribution is not well-matched by the standard 'β-model' fits to the observations. Pure gas spheres with a density distribution described by a β-model also fail because, with MOND, these objects are far from isothermal and again overluminous. These problems may be resolved by adding an additional dark mass component in the central regions, here modelled by a constant density sphere contained within two core radii and having a mass typically of one to two times the total cluster mass in the gas. With this additional component, the observed luminosity–temperature relation for clusters of galaxies is reproduced, and the typical mass discrepancy in actual clusters is three to four times smaller than implied by Newtonian dynamics. Thus, while MOND significantly reduces the mass of the dark component in clusters it does not remove it completely. I speculate on the nature of the dark component and argue that neutrinos, with mass near the experimental upper limit are a possible candidate.     

X-ray colour maps of the cores of galaxy clusters

We present an analysis of X-ray colour maps of the cores of clusters of galaxies, formed from the ratios of counts in different X-ray bands. Our technique groups pixels lying between contours in an adaptively smoothed image of a cluster. We select the contour levels to minimize the uncertainties in the colour ratios, whilst preserving the structure of the object. We extend the work of Allen & Fabian by investigating the spatial distributions of cooling gas and absorbing material in cluster cores. Their sample is almost doubled: we analyse archive ROSAT Position Sensitive Proportional Counter (PSPC) data for 33 clusters from the sample of the 55 brightest X-ray clusters in the sky. Many of our clusters contain strong cooling flows. We present colour maps of a sample of the clusters, in addition to adaptively smoothed images in different bands. Most of the cooling flow clusters display little substructure, unlike several of the non-cooling-flow clusters.
We fitted an isothermal plasma model with galactic absorption and constant metallicity to the mid-over-high energy colours in our clusters. Those clusters with known strong cooling flows have inner contours which fit a significantly lower temperature than the outer contours. Clusters in the sample without strong cooling flows show no significant temperature variation. The inclusion of a metallicity gradient alone was not sufficient to explain the observations. A cooling flow component plus a constant temperature phase did account for the colour profiles in clusters with known strong cooling flow components. We also had to increase the levels of absorbing material to fit the low-over-high colours at the cluster centres. Our results provide more evidence that cooling flows accumulate absorbing material. No evidence for increased absorption was found for the non-cooling-flow clusters.     

Constraining the Mass Distribution of Cluster Galaxies by Weak Lensing

Analysing the weak lensing distortions of the images of faint background galaxies provides a means to constrain the average mass distribution of cluster galaxies and potentially to test the extent of their dark matter haloes as a function of the density of their environment. The observable image distortions are a consequence of the interplay between the effects of a global cluster mass distribution and the perturbations resulting from individual cluster galaxies. Starting from a reconstruction of the cluster mass distribution with conventional techniques, we apply a maximum likelihood method to infer the average properties of an ensemble of cluster galaxies. From simulations this approach is found to be reliable as long as the galaxies including their dark matter haloes only contribute a small fraction to the total mass of the system. If their haloes are extended, the galaxies contain a substantial mass fraction. In this case our method is still applicable in the outer regions of clusters, where the surface mass density is low, but yields biased estimates of the parameters describing the mass profiles of the cluster galaxies in the central part of the cluster. In that case it will be necessary to resort to more sophisticated strategies by modelling cluster galaxies and an underlying global mass distribution simultaneously. We conclude that galaxy–galaxy lensing in clusters provides a unique means to probe the presence and extent of dark haloes of cluster galaxies.