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.     

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.     

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.     

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.     

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.     

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.     

Sunyaev–Zel'dovich distortion from early galactic winds

We consider the distortion in the cosmic microwave background (CMB) resulting from galactic winds at high redshift. Winds outflowing from galaxies have been hypothesized to be possible sources of metals in the intergalactic medium, which is known to have been enriched to 10^−2.5 Z_⊙ at z ∼3. We model these winds as functions of mass of the parent galaxy and redshift, assuming that they activate at a common initial redshift, z _in, and calculate the mean y -distortion and the angular power spectrum of the distortion in the CMB. We find that the thermal Sunyaev–Zel'dovich (SZ) effect resulting from the winds is consistent with previous estimates. The distortion arising from the kinetic SZ (kSZ) effect is, however, found to be more important than the thermal SZ (tSZ) effect. We find that the distortion resulting from galactic winds is an important contribution to the power spectrum of distortion at very small angular scales ( l ∼10⁴). We also find that the power spectrum resulting from clustering dominates the Poisson power spectrum for l ≤(4–5)×10⁵. We show explicitly how the combined power spectrum from wind dominates over that of clusters at 217 GHz, relevant for PLANCK . We also show how these constraints change when the efficiency of the winds is varied.     

Constraints on structure formation models from the Sunyaev–Zel'dovich effect

In the context of cold dark matter (CDM) cosmological models, we have simulated images of the brightness temperature fluctuations in the cosmic microwave background (CMB) sky owing to the Sunyaev–Zel'dovich (S–Z) effect in a cosmological distribution of clusters. We compare the image statistics with recent ATCA limits on arcmin-scale CMB anisotropy. The S–Z effect produces a generically non-Gaussian field and we compute the variance in the simulated temperature-anisotropy images, after convolution with the ATCA beam pattern, for different cosmological models. All the models are normalized to the 4-yr COBE data. We find an increase in the simulated-sky temperature variance with increase in the cosmological density parameter Ω₀. A comparison with the upper limits on the sky variance set by the ATCA appears to rule out our closed-universe model: low-Ω₀ open-universe models are preferred. The result is independent of any present day observations of σ ₈.     

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.     

Measurement of the Sunyaev–Zel'dovich increment in massive galaxy clusters

We have detected the Sunyaev–Zel'dovich (SZ) increment at 850 μm in two galaxy clusters (Cl 0016+16 and MS 1054.4−0321) using the Submillimetre Common User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope. Fits to the isothermal β model yield a central Compton y parameter of  (2.2 ± 0.7) × 10⁻⁴  and a central 850-μm flux of  Δ I ₀= 2.2 ± 0.7 mJy beam⁻¹  in Cl 0016. This can be combined with decrement measurements to infer   y = (2.38 ±^0.36_0.34) × 10⁻⁴  and   v _pec= 400±¹⁹⁰⁰₁₄₀₀ km s⁻¹  . In MS 1054 we find a peak 850-μm flux of  Δ I ₀= 2.0 ± 1.0 mJy beam⁻¹  and   y = (2.0 ± 1.0) × 10⁻⁴  . To be successful such measurements require large chop throws and non-standard data analysis techniques. In particular, the 450-μm data are used to remove atmospheric variations in the 850-μm data. An explicit annular model is fit to the SCUBA difference data in order to extract the radial profile, and separately fit to the model differences to minimize the effect of correlations induced by our scanning strategy. We have demonstrated that with sufficient care, SCUBA can be used to measure the SZ increment in massive, compact galaxy clusters.     

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.