The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe
Abstract
We present a detailed analysis of the twopoint correlation function, ξ(σ, π), from the 2dF Galaxy Redshift Survey (2dFGRS). The large size of the catalogue, which contains ~220000 redshifts, allows us to make highprecision measurements of various properties of the galaxy clustering pattern. The effective redshift at which our estimates are made is z_{s}~ 0.15, and similarly the effective luminosity, L_{s}~ 1.4L*. We estimate the redshiftspace correlation function, ξ(s), from which we measure the redshiftspace clustering length, s_{0}= 6.82 +/ 0.28 h^{1} Mpc. We also estimate the projected correlation function, Ξ(σ), and the realspace correlation function, ξ(r), which can be fit by a power law (r/r_{0})^{γr}, with r_{0}= 5.05 +/ 0.26 h^{1} Mpc, γ_{r}= 1.67 +/ 0.03. For r>~ 20 h^{1} Mpc, ξ drops below a power law as, for instance, is expected in the popular Λ cold dark matter model. The ratio of amplitudes of the real and redshiftspace correlation functions on scales of 830 h^{1} Mpc gives an estimate of the redshiftspace distortion parameter β. The quadrupole moment of ξ(σ, π) on scales 3040 h^{1} Mpc provides another estimate of β. We also estimate the distribution function of pairwise peculiar velocities, f(v), including rigorously the significant effect due to the infall velocities, and we find that the distribution is well fit by an exponential form. The accuracy of our ξ(σ, π) measurement is sufficient to constrain a model, which simultaneously fits the shape and amplitude of ξ(r) and the two redshiftspace distortion effects parametrized by β and velocity dispersion, a. We find β= 0.49 +/ 0.09 and a= 506 +/ 52 km s^{1}, although the bestfitting values are strongly correlated. We measure the variation of the peculiar velocity dispersion with projected separation, a(σ), and find that the shape is consistent with models and simulations. This is the first time that β and f(v) have been estimated from a selfconsistent model of galaxy velocities. Using the constraints on bias from recent estimates, and taking account of redshift evolution, we conclude that β (L=L*, z= 0) = 0.47 +/ 0.08, and that the presentday matter density of the Universe, Ω_{m}~ 0.3, consistent with other 2dFGRS estimates and independent analyses.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 November 2003
 DOI:
 10.1046/j.13652966.2003.07063.x
 arXiv:
 arXiv:astroph/0212375
 Bibcode:
 2003MNRAS.346...78H
 Keywords:

 surveys;
 galaxies: distances and redshifts;
 galaxies: statistics;
 cosmological parameters;
 largescale structure of Universe;
 Astrophysics
 EPrint:
 19 pages, revised following referee's report, and accepted by MNRAS. Higher resolution Figures, an animated version of Figure 12 and a colour version of Figure 22 are available from http://www.nottingham.ac.uk/~ppxeh/