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.     

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.     

Bubbles, feedback and the intracluster medium: three-dimensional hydrodynamic simulations

We use a three-dimensional hydrodynamical code to simulate the effect of energy injection on cooling flows in the intracluster medium. Specifically, we compare a simulation of a 10¹⁵-M_⊙ cluster with radiative cooling only with a second simulation in which thermal energy is injected 31 kpc off-centre, over 64 kpc³ at a rate of     for 50 Myr. The heat injection forms a hot, low-density bubble which quickly rises, dragging behind it material from the cluster core. The rising bubble pushes with it a shell of gas which expands and cools. We find the appearance of the bubble in X-ray temperature and luminosity to be in good qualitative agreement with recent Chandra observations of cluster cores. Toward the end of the simulation, at 600 Myr, the displaced gas begins to fall back toward the core, and the subsequent turbulence is very efficient at mixing the low- and high-entropy gas. The result is that the cooling flow is disrupted for up to ∼ 50 Myr after the injection of energy ceases. Thus this mechanism provides a very efficient method for regulating cooling flows, if the injection events occur with a 1:1 duty cycle.     

Morphological redshift estimates for galaxy clusters in a Sunyaev–Zel'dovich effect survey

We develop a new method to estimate the redshift of galaxy clusters through resolved images of the Sunyaev–Zel'dovich effect (SZE). Our method is based on morphological observables which can be measured by actual and future SZE experiments. We test the method with a set of high-resolution hydrodynamical simulations of galaxy clusters at different redshifts. Our method combines the observables in a principal component analysis. After calibrating the method with an independent redshift estimation for some of the clusters, we show – using a Bayesian approach – how the method can give an estimate of the redshift of the galaxy clusters. Although the error bars given by the morphological redshift estimation are large, it should be useful for future SZE surveys where thousands of clusters are expected to be detected; a first preselection of the high-redshift candidates could be done using our proposed morphological redshift estimator. Although not considered in this work, our method should also be useful to give an estimate of the redshift of clusters in X-ray and optical surveys.     

Detecting Sunyaev–Zel'dovich clusters with Planck– II. Foreground components and optimized filtering schemes

The Planck mission is the most sensitive all-sky cosmic microwave background (CMB) experiment currently planned. The High-Frequency Instrument (HFI) will be especially suited for observing clusters of galaxies by their thermal Sunyaev–Zel'dovich (SZ) effect. In order to assess Planck 's SZ capabilities in the presence of spurious signals, a simulation is presented that combines maps of the thermal and kinetic SZ effects with a realization of the CMB, in addition to Galactic foregrounds (synchrotron emission, free–free emission, thermal emission from dust, CO-line radiation) as well as the submillimetric emission from celestial bodies of our Solar system. Additionally, observational issues such as the finite angular resolution and spatially non-uniform instrumental noise of Planck 's sky maps are taken into account, yielding a set of all-sky flux maps, the autocorrelation and cross-correlation properties of which are examined in detail. In the second part of the paper, filtering schemes based on scale-adaptive and matched filtering are extended to spherical data sets, that enable the amplification of the weak SZ signal in the presence of all contaminations stated above. The theory of scale-adaptive and matched filtering in the framework of spherical maps is developed, the resulting filter kernel shapes are discussed and their functionality is verified.     

Hydrodynamical simulations of the Sunyaev–Zel'dovich effect

With detections of the Sunyaev–Zel'dovich (SZ) effect induced by galaxy clusters becoming routine, it is crucial to establish accurate theoretical predictions. We use a hydrodynamical N -body code to generate simulated maps, of size 1 deg², of the thermal SZ effect. This is done for three different cosmologies: the currently favoured low-density model with a cosmological constant, a critical-density model and a low-density open model. We stack simulation boxes corresponding to different redshifts in order to include contributions to the Compton y -parameter out to the highest necessary redshifts. Our main results are as follows.
(i) The mean y -distortion is around 4×10⁻⁶ for low-density cosmologies, and 1×10⁻⁶ for critical density. These are below current limits, but not by a wide margin in the former case.
(ii) In low-density cosmologies, the mean y -distortion is contributed across a broad range of redshifts, with the bulk coming from z ≲2 and a tail out to z ∼5. For critical-density models, most of the contribution comes from z <1.
(iii) The number of SZ sources above a given y depends strongly on instrument resolution. For a 1-arcmin beam, there are around 0.1 sources per deg² with y >10⁻⁵ in a critical-density Universe, and around 8 such sources per deg² in low-density models. Low-density models with and without a cosmological constant give very similar results.
(iv) We estimate that the Planck satellite will be able to see of order 25 000 SZ sources if the Universe has a low density, or around 10 000 if it has critical density.     

The Sunyaev–Zel'dovich effect as a cosmological discriminator

We show how future measurements of the Sunyaev–Zel'dovich effect (SZE) can be used to constrain the cosmological parameters. We combine the SZ information expected from the Planck full-sky survey, N ( S ), where no redshift information is included, with the N ( z ) obtained from an optically identified SZ-selected survey covering less than 1 per cent of the sky. We demonstrate how with a small subsample (≈300 clusters) of the whole SZ catalogue observed optically it is possible to reduce the degeneracy among the cosmological parameters drastically. We have studied the requirements for performing the optical follow-up and we show the feasibility of such a project. Finally, we have compared the cluster expectations for Planck with those expected for Newton–XMM during their lifetimes. It is shown that, owing to its larger sky coverage, Planck will detect a factor of ∼5 times more clusters than Newton–XMM and also provide a larger redshift coverage.