The Correlation Function in Redshift Space: General Formula with Wide‐Angle Effects and Cosmological Distortions | Zendy

Takahiko Matsubara | Zendy

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The Correlation Function in Redshift Space: General Formula with Wide‐Angle Effects and Cosmological Distortions

Author(s) -

Takahiko Matsubara

Publication year - 2000

Publication title -

the astrophysical journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.376

H-Index - 489

eISSN - 1538-4357

pISSN - 0004-637X

DOI - 10.1086/308827

Subject(s) - physics , redshift , correlation function (quantum field theory) , redshift space distortions , curvature , observer (physics) , function (biology) , space (punctuation) , universe , correlation , classical mechanics , theoretical physics , statistical physics , astrophysics , quantum mechanics , geometry , redshift survey , mathematics , galaxy , linguistics , philosophy , evolutionary biology , dielectric , biology

A general formula for the correlation function in redshift space is derivedin linear theory. The formula simultaneously includes wide-angle effects andcosmological distortions. The formula is applicable to any pair with arbitraryangle $\theta$ between lines of sight, and arbitrary redshifts, $z_1$, $z_2$,which are not necessarily small. The effects of the spatial curvature both ongeometry and on fluctuation spectrum are properly taken into account, and thusour formula holds in a Friedman-Lema\^{\i}tre universe with arbitrarycosmological parameters $\Omega_0$ and $\lambda_0$. We illustrate the patternof the resulting correlation function with several models, and also show thatvalidity region of the conventional distant observer approximation is $\theta\le 10^\circ$.Comment: 45 pages including 9 figures, To Appear in Astrophys. J. 535 (2000

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