The probability distribution function of the SZ power spectrum: an analytical approach
| dc.creator | Zhang, Pengjie | |
| dc.creator | Sheth, Ravi K. | |
| dc.date | 2007-01-30 | |
| dc.date | 2007-09-10 | |
| dc.date.accessioned | 2026-07-07T11:42:44Z | |
| dc.date.available | 2026-07-07T11:42:44Z | |
| dc.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 $\ell$. | |
| dc.description | v2: added one figure and discussions. Will appear in ApJ December issue. 12 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/astro-ph/0701879 | |
| dc.identifier | http://arxiv.org/abs/astro-ph/0701879 | |
| dc.identifier | Astrophys.J.671:14-26,2007 | |
| dc.identifier | doi:10.1086/522913 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/200991 | |
| dc.subject | Astrophysics | |
| dc.title | The probability distribution function of the SZ power spectrum: an analytical approach | |
| dc.type | text |