The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe
Abstract
We present a detailed analysis of the two-point correlation function, from the 2dF Galaxy Redshift Survey (2dFGRS). The large size of the catalogue, which contains ~220000 redshifts, allows us to make high precision measurements of various properties of the galaxy clustering pattern. We estimate the redshift-space correlation function, xi(s), from which we measure the redshift-space clustering length, s0 = 6.82 +/- 0.28 Mpc/h. We also estimate the projected correlation function, and the real-space correlation function, xi(r), which can be fit by a power-law, with r0 = 5.05 +/- 0.26 Mpc/h and slope gamma = 1.67 +/- 0.03. For r > 20 Mpc/h, xi drops below a power-law as, for instance, is expected in the popular LCDM model. The ratio of amplitudes of the real and redshift-space correlation functions on scales of 8 - 30 Mpc/h gives an estimate of the redshift-space distortion parameter beta. The quadrupole moment of xi on scales 30 - 40 Mpc/h provides another estimate of beta. We also estimate the distribution function of pairwise peculiar velocities, f(v), taking the effect of the infall velocities into account. The distribution is well fit by an exponential model. The accuracy of our xi measurement is sufficient to constrain a combined model, which simultaneously fits the shape and amplitude of xi(r) and the redshift-space distortion effects parameterized by beta and velocity dispersion, a. We find beta = 0.49 +/- 0.09 and a = 506 +/- 52 km/s. This is the first time that beta and f(v) have been estimated from a self-consistent model of galaxy velocities. Using the constraints on bias from recent estimates, and taking account of redshift evolution, we conclude that the present day matter density of the Universe, Omega_m is approximately 0.3, consistent with other 2dFGRS estimates and independent analyses.Keywords
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