The probability distribution function of the SZ power spectrum: an analytical approach

• Main Authors: Pengjie Zhang, Ravi K. Sheth
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 2008
• Subjects: South Pole; South pole
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.316.8877; http://arxiv.org/pdf/astro-ph/0701879v1.pdf

The Sunyaev Zel’dovich (SZ) signal is highly non-Gaussian, so the SZ power spectrum (along with the mean y parameter) does not provide a complete description of the SZ effect. Therefore, SZ-based constraints on cosmological parameters and on cluster gastrophysics which assume Gaussianity will be biased. We derive an analytic expression for the n-point joint PDF of the SZ power spectrum. Our derivation, which is based on the halo model, has several advantages: it is expressed in an integral form which allows quick computation; it is applicable to any given survey and any given angular scale; it is straightforward to incorporate many of the complexities which arise when modeling the SZ signal. To illustrate, we use our expression to estimate p(Cℓ), the one-point PDF of the SZ power spectrum. For small sky coverage (applicable to BIMA/CBI and the Sunyaev Zel’dovich Array experiments), our analysis shows that p(Cℓ) on the several arc-minute scale is expected to be strongly skewed, peaking at a value well below the mean and with a long tail which extends to tail high Cℓ values. In the limit of large sky coverage (applicable to the South Pole Telescope and Planck), p(Cℓ) approaches a Gaussian form. However, even in this limit, the variance of the power spectrum is very different from the naive Gaussian-based estimate. This is because different ℓ models are strongly correlated, making the cosmic variance of the SZ band-power much larger than the naive estimate. Our analysis should also be useful for modeling the PDF of the power spectrum induced by gravitational lensing at large ℓ. Key words: Cosmology: theory-large scale structure-cosmic microwave backgroundmethods: statistical