80 An introduction to the physics of cosmology
Figure 2.13. The redshift–space correlation function for the 2dFGRS,ξ(σ,π), plotted
as a function of transverse (σ) and radial (π) pair separation. The function was
estimated by counting pairs in boxes of side 0. 2 h−^1 Mpc, and then smoothing with
a Gaussian of rms width 0. 5 h−^1 Mpc. This plot clearly displays redshift distortions,
with ‘fingers of God’ elongations at small scales and the coherent Kaiser flattening at
large radii. The overplotted contours show model predictions with flattening parameter
β≡^0.^6 /b= 0 .4 and a pairwise dispersion ofσp= 4 h−^1 Mpc. Contours are plotted at
ξ= 10 , 5 , 2 , 1 , 0. 5 , 0. 2 , 0 .1.
evaluatingξ(σ,π), the optimal radial weight discussed earlier has been applied,
so that the noise at largershould be representative of true cosmic scatter.
The 2dFGRS results for the redshift-space correlation function results are
shown in figure 2.13, and display very clearly the two signatures of redshift-
space distortions discussed earlier. Thefingers of Godfrom small-scale random
velocities are very clear, as indeed has been the case from the first redshift surveys
(e.g. Davis and Peebles 1983). However, this is arguably the first time that the
large-scale flattening from coherent infall has been really obvious in the data.
A good way to quantify the flattening is to analyse the clustering as a function
of angle into Legendre polynomials:
ξ"(r)=2 "+ 1
2
∫ 1
− 1ξ(σ=rsinθ,π=rcosθ)P"(cosθ)dcosθ.