Astronomy and Astrophysics – Astrophysics
Scientific paper
1999-08-06
Astronomy and Astrophysics
Astrophysics
45 pages including 9 figures, To Appear in Astrophys. J. 535 (2000)
Scientific paper
10.1086/308827
A general formula for the correlation function in redshift space is derived in linear theory. The formula simultaneously includes wide-angle effects and cosmological distortions. The formula is applicable to any pair with arbitrary angle $\theta$ between lines of sight, and arbitrary redshifts, $z_1$, $z_2$, which are not necessarily small. The effects of the spatial curvature both on geometry and on fluctuation spectrum are properly taken into account, and thus our formula holds in a Friedman-Lema\^{\i}tre universe with arbitrary cosmological parameters $\Omega_0$ and $\lambda_0$. We illustrate the pattern of the resulting correlation function with several models, and also show that validity region of the conventional distant observer approximation is $\theta \le 10^\circ$.
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