Wide angle redshift distortions revisited

Apr, 2004
6 pages
Published in:
  • Astrophys.J. 614 (2004) 51-55
e-Print:

Citations per year

2006201120162021202502468101214
Abstract: (arXiv)
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 Sl1l2l3(x^1,x^2,x^)S_{l_1 l_2 l_3}(\hat x_1, \hat x_2, \hat x). The coefficients of the expansion Bl1l2l3B_{l_1 l_2 l_3} are analogous to the ClC_l's of the angular power spectrum, and express the anisotropy of the redshift space correlation function. Moreover, only a handful of Bl1l2l3B_{l_1 l_2 l_3} are non-zero: the resulting formulae reveal a hidden simplicity comparable to distant observer limit. The Bl1l2l3B_{l_1 l_2 l_3} depend on spherical Bessel moments of the power spectrum and f=Ω0.6/bf = \Omega^{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.
  • cosmic microwave background
  • cosmology: theory
  • methods: statistical