The probability distribution function of the SZ power spectrum: an analytical approach
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...
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ftcern:oai:cds.cern.ch:1014361 2023-05-15T18:23:08+02:00 The probability distribution function of the SZ power spectrum: an analytical approach Zhang, P Sheth, R K 2007-01-30 http://cds.cern.ch/record/1014361 eng eng http://cds.cern.ch/record/1014361 astro-ph/0701879 oai:cds.cern.ch:1014361 Astrophysics and Astronomy 2007 ftcern 2018-07-28T08:45:23Z 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 $p(C_\ell)$, 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 $p(C_\ell)$ 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 $C_\ell$ values. In the limit of large sky coverage (applicable to the South Pole Telescope and Planck), $p(C_\ell)$ 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 $\ell$ 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 $\ell$. Other/Unknown Material South pole CERN Document Server (CDS) South Pole |
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Astrophysics and Astronomy Zhang, P Sheth, R K The probability distribution function of the SZ power spectrum: an analytical approach |
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Astrophysics and Astronomy |
description |
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 $p(C_\ell)$, 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 $p(C_\ell)$ 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 $C_\ell$ values. In the limit of large sky coverage (applicable to the South Pole Telescope and Planck), $p(C_\ell)$ 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 $\ell$ 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 $\ell$. |
author |
Zhang, P Sheth, R K |
author_facet |
Zhang, P Sheth, R K |
author_sort |
Zhang, P |
title |
The probability distribution function of the SZ power spectrum: an analytical approach |
title_short |
The probability distribution function of the SZ power spectrum: an analytical approach |
title_full |
The probability distribution function of the SZ power spectrum: an analytical approach |
title_fullStr |
The probability distribution function of the SZ power spectrum: an analytical approach |
title_full_unstemmed |
The probability distribution function of the SZ power spectrum: an analytical approach |
title_sort |
probability distribution function of the sz power spectrum: an analytical approach |
publishDate |
2007 |
url |
http://cds.cern.ch/record/1014361 |
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South Pole |
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South Pole |
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South pole |
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South pole |
op_relation |
http://cds.cern.ch/record/1014361 astro-ph/0701879 oai:cds.cern.ch:1014361 |
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1766202574730428416 |