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

We estimate the power spectrum of SZ(Sunyaev-Zel'dovich)-effect-inducedtemperature fluctuations on sub-degree scales by using the cross correlationbetween the three-year WMAP maps and 2MASS galaxy distribution. We produced theSZ effect maps by hydrodynamic simulation samples of the $\Lambda$CDM 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% power ofthe SZ effect temperature fluctuations attributes to top $\sim 1%$ waveletmodes (long tail events). On the other hand, the CMB temperature fluctuationsbasically are Gaussian. Although the mean power of CMB temperature fluctuationson sub-degree scales is much higher than that of SZ effect map, the SZ effecttemperature fluctuations associated with top 2MASS clusters is comparable tothe power of CMB temperature fluctuations on the same scales. Thus, from noisyWMAP maps, one can have a proper estimation of the SZ effect power at thepositions of the top 2MASS clusters. The power spectrum given by these topwavelet modes is useful to constrain the parameter of density fluctuationsamplitude $\sigma_8$. We find that the power spectrum of these top waveletmodes of SZ effect on sub-degree scales basically is consistent with thesimulation maps produced with $\sigma_8=0.84$. The simulation samples of$\sigma_8=0.74$ show, however, significant deviation from detected SZ powerspectrum. It can be ruled out with confidence level 99% if all othercosmological parameters are the same as that given by the three-year WMAPresults.Comment: 26 pages, 10 figures, accepted for publication in Ap