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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ftdatacite:10.48550/arxiv.astro-ph/0701879 2023-05-15T18:23:03+02:00 The probability distribution function of the SZ power spectrum: an analytical approach Zhang, Pengjie Sheth, Ravi K. 2007 https://dx.doi.org/10.48550/arxiv.astro-ph/0701879 https://arxiv.org/abs/astro-ph/0701879 unknown arXiv https://dx.doi.org/10.1086/522913 Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004 http://arxiv.org/licenses/assumed-1991-2003/ Astrophysics astro-ph FOS Physical sciences article-journal Article ScholarlyArticle Text 2007 ftdatacite https://doi.org/10.48550/arxiv.astro-ph/0701879 https://doi.org/10.1086/522913 2022-04-01T15:53:07Z 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 $\ell$. : v2: added one figure and discussions. Will appear in ApJ December issue. 12 pages, 8 figures Text South pole DataCite Metadata Store (German National Library of Science and Technology) South Pole |
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Astrophysics astro-ph FOS Physical sciences |
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Astrophysics astro-ph FOS Physical sciences Zhang, Pengjie Sheth, Ravi K. The probability distribution function of the SZ power spectrum: an analytical approach |
topic_facet |
Astrophysics astro-ph FOS Physical sciences |
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 $\ell$. : v2: added one figure and discussions. Will appear in ApJ December issue. 12 pages, 8 figures |
format |
Text |
author |
Zhang, Pengjie Sheth, Ravi K. |
author_facet |
Zhang, Pengjie Sheth, Ravi K. |
author_sort |
Zhang, Pengjie |
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 |
publisher |
arXiv |
publishDate |
2007 |
url |
https://dx.doi.org/10.48550/arxiv.astro-ph/0701879 https://arxiv.org/abs/astro-ph/0701879 |
geographic |
South Pole |
geographic_facet |
South Pole |
genre |
South pole |
genre_facet |
South pole |
op_relation |
https://dx.doi.org/10.1086/522913 |
op_rights |
Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004 http://arxiv.org/licenses/assumed-1991-2003/ |
op_doi |
https://doi.org/10.48550/arxiv.astro-ph/0701879 https://doi.org/10.1086/522913 |
_version_ |
1766202481988075520 |