Redshift Space Distortion for Parallel Lines-of-Sight

Albert Stebbins
Fermilab Theoretical Astrophysics Group
26 June 1998

Here is presented some theory of redshift space distortion of some (unspecified scalar) quantity. In particular a description of the distorted 2-point function is given and this description applied to relating the redshift space 2-point statistics to the 1-d statistics along one or more parallel rays. The application in mind being an understanding of the statistics of the Lyman- forest seen in the spectra of nearby QSO's.
Here we only give the results, derviations of these results can be found in an accompanying Mathematica (v3) notebook. Note that the physical theory of the redshift space distortion is not presented here, only a descriptive theory.

Auto-Correlation Function in Redshift Space

Power-Spectrum in Redshift Space

Legendre Polynomial Expansion of Correlation Function and Power Spectrum

Auto- and Cross Correlation and Power Spectra Along One or More Lines-of-Sight

Power Law Power Spectra

Anisotropies up to only

Plots of the ratio of the cross- to auto- power spectra for power law models for up to 2