Wide Angle Redshift Distortions Revisited

Istvan Szapudi

doi:10.1086/423168

paper

Wide Angle Redshift Distortions Revisited

arXiv:astro-ph/0404477 · doi:10.1086/423168

Abstract

We explore linear redshift distortions in wide angle surveys from the point of view of symmetries. We show that the redshift space two-point correlation function can be expanded into tripolar spherical harmonics of zero total angular momentum $S_{l_{1} l_{2} l_{3}} (x^_{1}, x^_{2}, x^)$ . The coefficients of the expansion $B_{l_{1} l_{2} l_{3}}$ are analogous to the $C_{l}$ 's of the angular power spectrum, and express the anisotropy of the redshift space correlation function. Moreover, only a handful of $B_{l_{1} l_{2} l_{3}}$ are non-zero: the resulting formulae reveal a hidden simplicity comparable to distant observer limit. The $B_{l_{1} l_{2} l_{3}}$ depend on spherical Bessel moments of the power spectrum and $f = Ω^{0.6} / b$ . In the plane parallel limit, the results of \cite{Kaiser1987} and \cite{Hamilton1993} are recovered. The general formalism is used to derive useful new expressions. We present a particularly simple trigonometric polynomial expansion, which is arguably the most compact expression of wide angle redshift distortions. These formulae are suitable to inversion due to the orthogonality of the basis functions. An alternative Legendre polynomial expansion was obtained as well. This can be shown to be equivalent to the results of \cite{SzalayEtal1998}. The simplicity of the underlying theory will admit similar calculations for higher order statistics as well.

6 pages, 1 figure, ApJL submitted

Wide Angle Redshift Distortions Revisited

Abstract

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