Quantifying large-scale structure 79Figure 2.12.A four-degree thick slice of the southern strip of the 2dF Galaxy Redshift
Survey. This restricted region alone contains 16 419 galaxies.
However, while the survey is in progress, there exist parts of the sky where
the overlapping tiles have not yet been observed, and so the effective sampling
fraction is only50%. These effects can be allowed for in two different ways. In
clustering analyses, we compare the counts of pairs (orn-tuplets) of galaxies in
the data to the corresponding counts involving an unclustered random catalogue.
The effects of variable sampling can therefore be dealt with either by making the
density of random points fluctuate according to the sampling, or by weighting
observed galaxies by the reciprocal of the sampling factor for the zone in which
they lie. The former approach is better from the point of view of shot noise, but
the latter may be safer if there is any suspicion that the sampling fluctuations are
correlated with real structure on the sky. In practice, both strategies give identical
answers for the results below.
At the two-point level, the most direct quantity to compute is theredshift–
space correlation function. This is an anisotropic function of the orientation of a
galaxy pair, owing to peculiar velocities. We therefore evaluateξas a function
of 2D separation in terms of coordinates both parallel and perpendicular to the
line of sight. If the comoving radii of two galaxies arey 1 andy 2 and their total
separation isr, then we define coordinates
π≡|y 1 −y 2 |; σ=√
r^2 −π^2.The correlation function measured in these coordinates is shown in figure 2.13. In