Approximation by q-Szasz operators

his paper deals with approximating properties of the newly defined $q$-generalization of the Sz\'{a}sz operators in the case $q>1$. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem are given. In particular, it is proved that the rate of approximation by the $q$-Sz\'{a}sz operators ($q>1$) is of order $q^{-n}$ versus $1/n$ for the classical Sz\'{a}sz--Mirakjan operators

The hybrid SZ power spectrum: Combining cluster counts and SZ fluctuations to probe gas physics

Sunyaev-Zeldovich (SZ) effect from a cosmological distribution of clusters carry information on the underlying cosmology as well as the cluster gas physics. In order to study either cosmology or clusters one needs to break the degeneracies between the two. We present a toy model showing how complementary informations from SZ power spectrum and the SZ flux counts, both obtained from upcoming SZ cluster surveys, can be used to mitigate the strong cosmological influence (especially that of sigma_8) on the SZ fluctuations. Once the strong dependence of the cluster SZ power spectrum on sigma_8 is diluted, the cluster power spectrum can be used as a tool in studying cluster gas structure and evolution. The method relies on the ability to write the Poisson contribution to the SZ power spectrum in terms the observed SZ flux counts. We test the toy model by applying the idea to simulations of SZ surveys.Comment: 12 pages. 11 plots. MNRAS submitte

Non-Gaussian Aspects of Thermal and Kinetic Sunyaev-Zel'dovich Effects

We discuss non-Gaussian effects associated with the local large-scale structure contributions to the Cosmic Microwave Background (CMB) anisotropies through the thermal Sunyaev-Zel'dovich (SZ) effect. The non-Gaussianities associated with the SZ effect arise from the existence of a significant four-point correlation function in large scale pressure fluctuations. Using the full covariance matrix of the SZ thermal power spectrum, we study astrophysical uses of the SZ effect and discuss the extent to which gas properties can be derived from a measurement of the SZ power spectrum. With the SZ thermal effect separated in temperature fluctuations using its frequency information, the kinetic SZ effect is expected to dominate the CMB temperature fluctuations at small angular scales. The presence of the SZ kinetic effect can be determined through a cross-correlation between the SZ thermal and a CMB map at small scales. We suggest a statistic that can be used to study the correlation between pressure traced by the SZ thermal effect and the baryons traced by the SZ kinetic effect involving the cross-power spectrum constructed through squared temperatures instead of the usual temperature itself. Through a signal-to-noise calculation, we show that future small angular scale multi-frequency CMB experiments, sensitive to multipoles of a few thousand, will be able to measure the cross-correlation of SZ thermal and SZ kinetic effect through a temperature squared power spectrum (abridged).Comment: 27 PRD Pages, 15 figures; Submitted to Phys. Rev.

HeCS-SZ: The Hectospec Survey of Sunyaev-Zeldovich Selected Clusters

We estimate cluster masses and velocity dispersions for 123 clusters from optical spectroscopy to compare the Sunyaev-Zeldovich (SZ) mass proxy and dynamical masses. Our new survey, HeCS-SZ (Hectospec Cluster Survey of SZ-selected clusters), includes 7,721 new or remeasured redshifts from MMT/Hectospec observations of 24 SZ-selected clusters at redshifts $z$=0.05-0.20 and not in previous surveys. We supplement the Hectospec data with spectra from the Sloan Digital Sky Survey (SDSS) and cluster data from the Cluster Infall Regions in SDSS (CIRS) project and the Hectospec Cluster Survey (HeCS), our Hectospec survey of clusters selected by X-ray flux. We measure the scaling relation between velocity dispersion and SZ mass estimates from the integrated Compton parameter for an SZ complete sample of 83 clusters. The observed relation agrees very well with a simple virial scaling from mass (based on SZ) to velocity dispersion. The SZ mass estimates (calibrated with hydrostatic X-ray mass estimates) are not significantly biased. Further, the velocity dispersion of cluster galaxies is consistent with the expected velocity dispersion of dark matter particles, indicating that galaxies are good dynamical tracers (i.e., velocity bias is small). Significant mass bias in SZ mass estimates could relieve tension between cosmological results from Planck SZ cluster counts and Planck CMB data. However, the excellent agreement between our measured velocity dispersions and those predicted from a virial scaling relation suggests that any SZ mass bias is too small to reconcile SZ and CMB results. In principle, SZ mass bias and velocity bias of galaxies could conspire to yield good agreement, but the required velocity bias is $\sigma_{galaxy}\approx 0.77\sigma_{DM}$, outside the range of plausible models of velocity bias in the literature.Comment: submitted to ApJ, 13 pages, 14 figures, 123 cluster

Sunyaev-Zeldovich effect in WMAP and its effect on cosmological parameters

We use multi-frequency information in first year WMAP data to search for the Sunyaev-Zeldovich (SZ) effect. WMAP has sufficiently broad frequency coverage to constrain SZ without the addition of higher frequency data: the SZ power spectrum amplitude is expected to increase 50% from W to Q frequency band. This, in combination with the low noise in WMAP, allows us to strongly constrain the SZ contribution. We derive an optimal frequency combination of WMAP cross-spectra to extract SZ in the presence of noise, CMB, and radio point sources, which are marginalized over. We find that the SZ contribution is less than 2% (95% c.l.) at the first acoustic peak in W band. Under the assumption that the removed radio point sources are not correlated with SZ this limit implies sigma_8<1.07 at 95% c.l. We investigate the effect on the cosmological parameters of allowing an SZ component. We run Monte Carlo Markov Chains with and without an SZ component and find that the addition of SZ does not affect any of the cosmological conclusions. We conclude that SZ does not contaminate the WMAP CMB or change cosmological parameters, refuting the recent claims that they may be corrupted.Comment: 10 pages, 5 figures, 2 tables. Submitted to Phys. Rev.

A Measurement of Secondary Cosmic Microwave Background Anisotropies with Two Years of South Pole Telescope Observations

We present the first three-frequency South Pole Telescope (SPT) cosmic microwave background (CMB) power spectra. The band powers presented here cover angular scales 2000 < ℓ < 9400 in frequency bands centered at 95, 150, and 220 GHz. At these frequencies and angular scales, a combination of the primary CMB anisotropy, thermal and kinetic Sunyaev-Zel'dovich (SZ) effects, radio galaxies, and cosmic infrared background (CIB) contributes to the signal. We combine Planck/HFI and SPT data at 220 GHz to constrain the amplitude and shape of the CIB power spectrum and find strong evidence for nonlinear clustering. We explore the SZ results using a variety of cosmological models for the CMB and CIB anisotropies and find them to be robust with one exception: allowing for spatial correlations between the thermal SZ effect and CIB significantly degrades the SZ constraints. Neglecting this potential correlation, we find the thermal SZ power at 150 GHz and ℓ = 3000 to be 3.65 ± 0.69 μK^2, and set an upper limit on the kinetic SZ power to be less than 2.8 μK^2 at 95% confidence. When a correlation between the thermal SZ and CIB is allowed, we constrain a linear combination of thermal and kinetic SZ power: D^(tSZ)_(3000) + 0.5D^(kSZ)_(3000) = 4.60 ± 0.63 μK^2, consistent with earlier measurements. We use the measured thermal SZ power and an analytic, thermal SZ model calibrated with simulations to determine σ_8 = 0.807 ± 0.016. Modeling uncertainties involving the astrophysics of the intracluster medium rather than the statistical uncertainty in the measured band powers are the dominant source of uncertainty on σ_8. We also place an upper limit on the kinetic SZ power produced by patchy reionization; a companion paper uses these limits to constrain the reionization history of the universe

X-Ray Properties of the First Sunyaev-Zel'dovich Effect Selected Galaxy Cluster Sample from the South Pole Telescope

We present results of X-ray observations of a sample of 15 clusters selected via their imprint on the cosmic microwave background from the thermal Sunyaev-Zel'dovich (SZ) effect. These clusters are a subset of the first SZ-selected cluster catalog, obtained from observations of 178 deg^2 of sky surveyed by the South Pole Telescope (SPT). Using X-ray observations with Chandra and XMM-Newton, we estimate the temperature, T_X, and mass, M_g, of the intracluster medium within r_500 for each cluster. From these, we calculate Y_X = M_(g)T_X and estimate the total cluster mass using an M_(500)-Y_X scaling relation measured from previous X-ray studies. The integrated Comptonization, Y SZ, is derived from the SZ measurements, using additional information from the X-ray-measured gas density profiles and a universal temperature profile. We calculate scaling relations between the X-ray and SZ observables and find results generally consistent with other measurements and the expectations from simple self-similar behavior. Specifically, we fit a Y_(SZ)-Y_X relation and find a normalization of 0.82 ± 0.07, marginally consistent with the predicted ratio of Y_(SZ)/Y_X = 0.91 ± 0.01 that would be expected from the density and temperature models used in this work. Using the Y_X-derived mass estimates, we fit a Y_(SZ)-M_500 relation and find a slope consistent with the self-similar expectation of Y_(SZ) ∝ M^(5/3) with a normalization consistent with predictions from other X-ray studies. We find that the SZ mass estimates, derived from cosmological simulations of the SPT survey, are lower by a factor of 0.78 ± 0.06 relative to the X-ray mass estimates. This offset is at a level of 1.3σ when considering the ~15% systematic uncertainty for the simulation-based SZ masses. Overall, the X-ray measurements confirm that the scaling relations of the SZ-selected clusters are consistent with the properties of other X-ray-selected samples of massive clusters, even allowing for the broad redshift range (0.29 < z < 1.08) of the sample

Cross-correlating the Thermal Sunyaev-Zel'dovich Effect and the Distribution of Galaxy Clusters

We present the analytical formulas, derived based on the halo model, to compute the cross-correlation between the thermal Sunyaev-Zel'dovich (SZ) effect and the distribution of galaxy clusters. By binning the clusters according to their redshifts and masses, this cross-correlation, the so-called stacked SZ signal, reveals the average SZ profile around the clusters. The stacked SZ signal is obtainable from a joint analysis of an arcminute-resolution cosmic microwave background (CMB) experiment and an overlapping optical survey, which allows for detection of the SZ signals for clusters whose masses are below the individual cluster detection threshold. We derive the error covariance matrix for measuring the stacked SZ signal, and then forecast for its detection from ongoing and forthcoming combined CMB-optical surveys. We find that, over a wide range of mass and redshift, the stacked SZ signal can be detected with a significant signal to noise ratio (total S/N \gsim 10), whose value peaks for the clusters with intermediate masses and redshifts. Our calculation also shows that the stacking method allows for probing the clusters' SZ profiles over a wide range of scales, even out to projected radii as large as the virial radius, thereby providing a promising way to study gas physics at the outskirts of galaxy clusters.Comment: 11 pages, 6 figures, 3 tables, minor revisions reflect PRD published versio