The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe

TL;DR

The study analyzes the 2dF Galaxy Redshift Survey to extract the real-space and redshift-space two-point correlation functions, along with their projections, to quantify clustering, redshift-space distortions, and peculiar velocities. By combining a Kaiser-like model for coherent infall with an exponential distribution for random motions and fitting to a grid of \\xi(\\sigma,\\pi) and its projections, the authors constrain the distortion parameter \\beta and the pairwise velocity dispersion \\!a, yielding \\beta = 0.49 ± 0.09 and \\!a = 506 ± 52 \\hbox{km s^{-1}}. The real-space clustering is characterized by \\xi(r) with \\!r_0 ≈ 5.05 \\hbox{h}^{-1} Mpc and \\gamma_r ≈ 1.67, while the redshift-space length scale is \\!s_0 ≈ 6.82 \\hbox{h}^{-1} Mpc; these results, when evolved to the present day and combined with bias estimates, imply \\Omega_m ≈ 0.3 and are consistent with the concordance \\LambdaCDM cosmology and CMB measurements. The analysis highlights the importance of jointly modeling \\beta and f(v), and demonstrates that robust error estimates require mock catalogs to account for cosmic variance and survey systematics. Overall, the 2dFGRS clustering measurements reinforce a low-density universe with non-linear galaxy bias.

Abstract

We present a detailed analysis of the two-point correlation function, from the 2dF Galaxy Redshift Survey (2dFGRS). We estimate the redshift-space correlation function, xi(s), from which we measure the redshift-space clustering length, s_0=6.82+/-0.28 Mpc/h. We also estimate the projected correlation function, Xi(sigma), and the real-space correlation function, xi(r), which can be fit by a power-law, with r_0=5.05+/-0.26Mpc/h, gamma_r=1.67+/-0.03. For r>20Mpc/h, xi drops below a power-law as is expected in the popular LCDM model. The ratio of amplitudes of the real and redshift-space correlation functions on scales of 8-30Mpc/h gives an estimate of the redshift-space distortion parameter beta. The quadrupole moment of xi on scales 30-40Mpc/h provides another estimate of beta. We also estimate the distribution function of pairwise peculiar velocities, f(v), including rigorously the effect of infall velocities, and find that it is well fit by an exponential. The accuracy of our xi measurement is sufficient to constrain a model, which simultaneously fits the shape and amplitude of xi(r) and the two redshift-space distortion effects parameterized by beta and velocity dispersion, a. We find beta=0.49+/-0.09 and a=506+/-52km/s, though the best fit values are strongly correlated. We measure the variation of the peculiar velocity dispersion with projected separation, a(sigma), and find that the shape is consistent with models and simulations. Using the constraints on bias from recent estimates, and taking account of redshift evolution, we conclude that beta(L=L*,z=0)=0.47+/-0.08, and that the present day matter density of the Universe is 0.3, consistent with other 2dFGRS estimates and independent analyses.

Figures (18)

• Figure 1: The redshift completeness masks for the NGP (top) and SGP (bottom). The greyscale shows the completeness fraction.
• Figure 2: Top panel: $w(\theta)$ for the mean of the NGP and SGP redshift catalogues (solid points), the mean of the masked parent catalogues (solid line), and the full APM result (error bars). Bottom panel: The parent catalogue result divided by the redshift catalogue results (uncorrected - solid points; collision corrected (see Section \ref{['s:weight']}) - open points). The solid line is the curve used to correct the fibre collisions. The top axis converts $\theta$ into a projected separation, $\sigma$, at the effective redshift of the survey, $z_s = 0.15$.
• Figure 3: Redshift distributions, $N(z)$, for the 2dFGRS data (solid lines) and the normalised random catalogues generated using the survey luminosity function (dashed lines) for the (a) SGP and (b) NGP.
• Figure 4: Grey-scale plots of the 2dFGRS $\xi(\sigma, \pi)$ (in $1\;h^{-1}{\rm Mpc}$ bins) for (a) the SGP region, (b) the NGP region and (c) the combined data. Contours are overlaid at $\xi=4.0, 2.0, 1.0, 0.5, 0.2$ and $0.1$.
• Figure 5: The redshift-space correlation function for the NGP (open points) and SGP (solid points) 2dFGRS data with error bars from the rms of mock catalogue results. Inset plotted on a linear scale.