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.     

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.     

Hydrodynamical simulations of the Sunyaev–Zel'dovich effect: the kinetic effect

We use hydrodynamical N -body simulations to study the kinetic Sunyaev–Zel'dovich effect. We construct sets of maps, one square degree in size, in three different cosmological models. We confirm earlier calculations that on the scales studied the kinetic effect is much smaller than the thermal (except close to the thermal null point), with an rms dispersion smaller by about a factor of 5 in the Rayleigh–Jeans region. We study the redshift dependence of the rms distortion and the pixel distribution at the present epoch. We compute the angular power spectra of the maps, including their redshift dependence, and compare them with the thermal Sunyaev–Zel'dovich effect and with the expected cosmic microwave background anisotropy spectrum as well as with determinations by other authors. We correlate the kinetic effect with the thermal effect both pixel-by-pixel and for identified thermal sources in the maps to assess the extent to which the kinetic effect is enhanced in locations of strong thermal signal.     

Gravitational lensing and the Sunyaev–Zel'dovich effect in the millimetre/submillimetre waveband

The intensity of the cosmic microwave background radiation in the fields of clusters of galaxies is modified by inverse Compton scattering in the hot intracluster gas — the Sunyaev–Zel'dovich (SZ) effect. The effect is expected to be most pronounced at a frequency of about 350 GHz (a wavelength of about 800 μm), and has been detected in the centimetre and millimetre wavebands. In the millimetre/submillimetre waveband, the gravitationally lensed images of distant dusty star-forming galaxies in the background of the cluster are predicted to dominate the appearance of clusters on scales of several arcsec, and could confuse observations of the SZ effect at frequencies greater than about 200 GHz (wavelengths shorter than about 1.5 mm). Recent observations by Smail, Ivison &38; Blain confirm that a significant population of confusing sources is present in this waveband. Previous estimates of source confusion in observations of the millimetre/submillimetre-wave SZ effect did not include the effects of lensing by the cluster, and so the accuracy of such measurements could be lower than expected. Source subtraction may be required in order to measure the SZ effect accurately, and a careful analysis of the results of an ensemble of SZ measurements could be used to impose limits to the form of evolution of distant dusty star-forming galaxies.     

Bayesian joint analysis of cluster weak lensing and Sunyaev–Zel'dovich effect data

As the quality of the available galaxy cluster data improves, the models fitted to these data might be expected to become increasingly complex. Here we present the Bayesian approach to the problem of cluster data modelling: starting from simple, physically motivated parametrized functions to describe the cluster's gas density, gravitational potential and temperature, we explore the high-dimensional parameter spaces with a Markov-Chain Monte Carlo sampler, and compute the Bayesian evidence in order to make probabilistic statements about the models tested. In this way sufficiently good data will enable the models to be distinguished, enhancing our astrophysical understanding; in any case the models may be marginalized over in the correct way when estimating global, perhaps cosmological, parameters. In this work we apply this methodology to two sets of simulated interferometric Sunyaev–Zel'dovich effect and gravitational weak lensing data, corresponding to current and next-generation telescopes. We calculate the expected precision on the measurement of the cluster gas fraction from such experiments, and investigate the effect of the primordial cosmic microwave background (CMB) fluctuations on their accuracy. We find that data from instruments such as the Arcminute Microkelvin Imager (AMI), when combined with wide-field ground-based weak lensing data, should allow both cluster model selection and estimation of gas fractions to a precision of better than 30 per cent for a given cluster.     

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.     

Bayesian modelling of clusters of galaxies from multifrequency-pointed Sunyaev–Zel'dovich observations

We present a Bayesian approach to modelling galaxy clusters using multi-frequency pointed observations from telescopes that exploit the Sunyaev–Zel'dovich effect. We use the recently developed multinest technique to explore the high-dimensional parameter spaces and also to calculate the Bayesian evidence. This permits robust parameter estimation as well as model comparison. Tests on simulated Arcminute Microkelvin Imager observations of a cluster, in the presence of primary CMB signal, radio point sources (detected as well as an unresolved background) and receiver noise, show that our algorithm is able to analyse jointly the data from six frequency channels, sample the posterior space of the model and calculate the Bayesian evidence very efficiently on a single processor. We also illustrate the robustness of our detection process by applying it to a field with radio sources and primordial CMB but no cluster, and show that indeed no cluster is identified. The extension of our methodology to the detection and modelling of multiple clusters in multi-frequency SZ survey data will be described in a future work.     

Statistics of the Sunyaev–Zel'dovich effect power spectrum

Using large numbers of simulations of the microwave sky, incorporating the cosmic microwave background (CMB) and the Sunyaev–Zel'dovich (SZ) effect due to clusters, we investigate the statistics of the power spectrum at microwave frequencies between spherical multipoles of 1000 and 10 000. From these virtual sky maps, we find that the spectrum of the SZ effect has a larger standard deviation by a factor of 3 than would be expected from purely Gaussian realizations, and has a distribution that is significantly skewed towards higher values, especially when small map sizes are used. The standard deviation is also increased by around 10 per cent compared to the trispectrum calculation due to the clustering of galaxy clusters. We also consider the effects of including residual point sources and uncertainties in the gas physics. This has implications for the excess power measured in the CMB power spectrum by the Cosmic Background Imager (CBI) and Berkeley–Illinois–Maryland Association (BIMA) experiments. Our results indicate that the observed excess could be explained using a lower value of σ₈ than previously suggested, however the effect is not enough to match  σ₈= 0.825  . The uncertainties in the gas physics could also play a substantial role. We have made our maps of the SZ effect available online.     

Relativistic corrections to the multiple scattering effect on the Sunyaev–Zel'dovich effect in the isotropic approximation

We extend the formalism for the calculation of the relativistic corrections to the Sunyaev–Zel'dovich effect for clusters of galaxies and include the multiple scattering effects in the isotropic approximation. We present the results of the calculations by the Fokker–Planck expansion method as well as by the direct numerical integration of the collision term of the Boltzmann equation. The multiple scattering contribution is found to be very small compared with the single scattering contribution. For high-temperature galaxy clusters of     the ratio of both the contributions is −0.2 per cent in the Wien region. In the Rayleigh–Jeans region the ratio is −0.03 per cent. Therefore the multiple scattering contribution is safely neglected for the observed galaxy clusters.     

Sunyaev–Zel'dovich effect from quasar-driven blast waves

Quasar-driven winds are currently the best candidates for accounting for the pre-heating of the intergalactic medium in clusters. Such winds, occurring during early phases of the evolution of spheroidal galaxies, shock-heat the interstellar gas, thus inducing a detectable Sunyaev–Zel'dovich effect. We estimate the amplitude and the angular scale of such an effect as well as its counts as a function of the Comptonization parameter y . The contamination arising from radio emission by the quasar itself is also discussed. The corresponding mean Compton distortion of the cosmic microwave background spectrum is found to be well below the COBE /FIRAS upper limit.     

Biases on the cosmological parameters and thermal Sunyaev–Zel'dovich residuals

We examine the biases induced on cosmological parameters when the presence of secondary anisotropies is not taken into account in cosmic microwave background analyses. We first develop an exact analytical expression for computing the biases on parameters when any additive signal is neglected in the analysis. We then apply it in the context of the forthcoming Planck experiment. For illustration, we investigate the effect of the sole residual thermal Sunyaev–Zel'dovich signal that remains after cluster extraction. We find, in particular, that analyses neglecting the presence of this contribution introduce on the cosmological parameters n _s and τ biases, at least ∼6.5 and 2.9 times their 1σ confidence intervals. The Ω_b parameter is also biased to a lesser extent.     

H 0 from an orientation-unbiased sample of Sunyaev–Zel'dovich and X-ray clusters

We have observed the Sunyaev–Zel'dovich (SZ) effect in a sample of five moderate-redshift clusters with the Ryle Telescope, and used them in conjunction with X-ray imaging and spectral data from ROSAT and ASCA to measure the Hubble constant. This sample was chosen with a strict X-ray flux limit using both the Bright Cluster Sample and the Northern ROSAT All-Sky Survey (RASS) cluster catalogues to be well above the surface brightness limit of the RASS, and hence to be unbiased with respect to the orientation of the cluster. This controls a major potential systematic effect in the SZ/X-ray method of measuring H ₀. Taking the weighted geometric mean of the results and including the main sources of error, namely the noise in the SZ measurement, the uncertainty in the X-ray temperatures and the unknown ellipticity and substructure of the clusters, we find   H ₀= 59⁺¹⁰₋₉ (random)⁺⁸₋₇(systematic) km s⁻¹ Mpc⁻¹  assuming a standard cold dark matter model with  Ω_M= 1.0, Ω_Λ= 0.0  or   H ₀= 66⁺¹¹₋₁₀ ⁺⁹₋₈ km  s⁻¹ Mpc⁻¹  if  Ω_M= 0.3, Ω_Λ= 0.7  .     

Optimizing the yield of Sunyaev–Zel'dovich cluster surveys

We consider the optimum depth of a cluster survey selected using the Sunyaev–Zel'dovich effect. By using simple models for the evolution of the cluster mass function and detailed modelling for a variety of observational techniques, we show that the optimum survey yield is achieved when the average size of the clusters selected is close to the size of the telescope beam. For a total power measurement, we compute the optimum noise threshold per beam as a function of the beam size and then discuss how our results can be used in more general situations. As a by-product we gain some insight into what is the most advantageous instrumental set-up. In the case of beam switching observations one is not severely limited if one manages to set the noise threshold close to the point which corresponds to the optimum yield. Considering a variety of alternative scenarios, we discuss how robust our conclusions are to modifications in the cluster model and cosmological parameters. The precise optimum is particularly sensitive to the amplitude of fluctuations and the profile of the gas in the cluster.