We estimate the power spectrum of SZ ( Sunyaev-Zel ’ dovich ) -effect-induced temperature fluctuations on sub-degree scales by using the cross correlation between the three-year WMAP maps and 2MASS galaxy distribution .
We produced the SZ 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 of the SZ effect temperature fluctuations attributes to top \sim 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 sub-degree scales is much higher than that of 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 to constrain the parameter of density fluctuations amplitude \sigma _ { 8 } .
We find that the power spectrum of these top wavelet modes of SZ effect on sub-degree scales basically is consistent with the simulation maps produced with \sigma _ { 8 } = 0.84 .
The simulation samples of \sigma _ { 8 } = 0.74 show , however , significant deviation from detected SZ power spectrum .
It can be ruled out with confidence level 99 % if all other cosmological parameters are the same as that given by the three-year WMAP results .