Estimating Power Spectrum of Sunyaev‐Zeldovich Effect from the Cross‐Correlation between theWilkinson Microwave Anistropy Probeand the Two Micron All Sky Survey

Abstract

We estimate the power spectrum of the Sunyaev-Zel'dovich (SZ) effect-induced temperature fluctuations on subdegree scales by using the cross-correlation between the three-year WMAP maps and the 2MASS galaxy distribution. We produced the SZ effect maps by hydrodynamic simulation samples of the ΛCDM model and show that the SZ effect temperature fluctuations are highly non-Gaussian. The PDF of the temperature fluctuations has a long tail. More than 70% of the power of the SZ effect temperature fluctuations is attributed to the top ~1% wavelet modes (long-tail events). On the other hand, the CMB temperature fluctuations basically are Gaussian. Although the mean power of CMB temperature fluctuations on subdegree scales is much higher than that of the SZ effect map, the SZ effect temperature fluctuations associated with top 2MASS clusters is comparable to the power of CMB temperature fluctuations on the same scales. Thus, from noisy WMAP maps, one can have a proper estimation of the SZ effect power at the positions of the top 2MASS clusters. The power spectrum given by these top wavelet modes is useful for constraining the density fluctuation amplitude parameter σ8. We find that the power spectrum of these top wavelet modes of the SZ effect on subdegree scales basically is consistent with the simulation maps produced with σ8 = 0.84. The simulation samples of σ8 = 0.74 show, however, significant deviation from the detected SZ power spectrum. This value can be ruled out with a 99% confidence level if all other cosmological parameters are the same as that given by the three-year WMAP results.