Preprint typeset using L ATEX style emulateapj v. 10/10/03 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 be bia...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.317.7432 2023-05-15T18:23:09+02:00 Preprint typeset using L ATEX style emulateapj v. 10/10/03 THE PROBABILITY DISTRIBUTION FUNCTION OF THE SZ POWER SPECTRUM: AN ANALYTICAL APPROACH Pengjie Zhang Ravi K. Sheth The Pennsylvania State University CiteSeerX Archives 2008 application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.317.7432 http://arxiv.org/pdf/astro-ph/0701879v2.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.317.7432 http://arxiv.org/pdf/astro-ph/0701879v2.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://arxiv.org/pdf/astro-ph/0701879v2.pdf text 2008 ftciteseerx 2016-09-04T00:10:34Z 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. Subject headings: Cosmology: theory-large scale structure-cosmic microwave background-methods: statistical Text South pole Unknown South Pole |
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English |
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(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. Subject headings: Cosmology: theory-large scale structure-cosmic microwave background-methods: statistical |
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The Pennsylvania State University CiteSeerX Archives |
format |
Text |
author |
Pengjie Zhang Ravi K. Sheth |
spellingShingle |
Pengjie Zhang Ravi K. Sheth Preprint typeset using L ATEX style emulateapj v. 10/10/03 THE PROBABILITY DISTRIBUTION FUNCTION OF THE SZ POWER SPECTRUM: AN ANALYTICAL APPROACH |
author_facet |
Pengjie Zhang Ravi K. Sheth |
author_sort |
Pengjie Zhang |
title |
Preprint typeset using L ATEX style emulateapj v. 10/10/03 THE PROBABILITY DISTRIBUTION FUNCTION OF THE SZ POWER SPECTRUM: AN ANALYTICAL APPROACH |
title_short |
Preprint typeset using L ATEX style emulateapj v. 10/10/03 THE PROBABILITY DISTRIBUTION FUNCTION OF THE SZ POWER SPECTRUM: AN ANALYTICAL APPROACH |
title_full |
Preprint typeset using L ATEX style emulateapj v. 10/10/03 THE PROBABILITY DISTRIBUTION FUNCTION OF THE SZ POWER SPECTRUM: AN ANALYTICAL APPROACH |
title_fullStr |
Preprint typeset using L ATEX style emulateapj v. 10/10/03 THE PROBABILITY DISTRIBUTION FUNCTION OF THE SZ POWER SPECTRUM: AN ANALYTICAL APPROACH |
title_full_unstemmed |
Preprint typeset using L ATEX style emulateapj v. 10/10/03 THE PROBABILITY DISTRIBUTION FUNCTION OF THE SZ POWER SPECTRUM: AN ANALYTICAL APPROACH |
title_sort |
preprint typeset using l atex style emulateapj v. 10/10/03 the probability distribution function of the sz power spectrum: an analytical approach |
publishDate |
2008 |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.317.7432 http://arxiv.org/pdf/astro-ph/0701879v2.pdf |
geographic |
South Pole |
geographic_facet |
South Pole |
genre |
South pole |
genre_facet |
South pole |
op_source |
http://arxiv.org/pdf/astro-ph/0701879v2.pdf |
op_relation |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.317.7432 http://arxiv.org/pdf/astro-ph/0701879v2.pdf |
op_rights |
Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
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1766202632402108416 |