Non-Gaussian aspects of thermal and kinetic Sunyaev-Zel’dovich effects

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Abstract
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 pressure trispectrum calculated under the recently popular halo model, we discuss the full covariance of the SZ thermal power spectrum. We use this full covariance matrix to study the 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, also known as the Ostriker-Vishniac effect, is expected to dominate the CMB temperature fluctuations at small angular scales. This effect arises from the baryon modulation of the first order Doppler effect resulting from the relative motion of scatterers. 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. Since the SZ kinetic effect is second order, however, contributions to such a cross-correlation arise to lower order in the form of a three-point correlation function, or a bispectrum in Fourier space. We suggest an additional 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 multifrequency CMB experiments, sensitive to multipoles of a few thousand, will be able to measure the cross-correlation of SZ thermal and SZ kinetic effects through a temperature squared power spectrum.
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