We present a detailed analysis of the two-point correlation function , \xi ( \sigma, \pi ) , from the 2dF Galaxy Redshift Survey ( 2dFGRS ) .
The large size of the catalogue , which contains \sim 220 000 redshifts , allows us to make high precision measurements of various properties of the galaxy clustering pattern .
The effective redshift at which our estimates are made is z _ { s } \approx 0.15 , and similarly the effective luminosity , L _ { s } \approx 1.4 L ^ { \ast } .
We estimate the redshift-space correlation function , \xi ( s ) , from which we measure the redshift-space clustering length , s _ { 0 } = 6.82 \pm 0.28 h ^ { -1 } { Mpc } .
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 ( r / r _ { 0 } ) ^ { - \gamma _ { r } } , with r _ { 0 } = 5.05 \pm 0.26 h ^ { -1 } { Mpc } , \gamma _ { r } = 1.67 \pm 0.03 .
For r \gtrsim 20 h ^ { -1 } { Mpc } , \xi drops below a power-law as , for instance , is expected in the popular \Lambda { CDM } model .
The ratio of amplitudes of the real and redshift-space correlation functions on scales of 8 - 30 h ^ { -1 } { Mpc } gives an estimate of the redshift-space distortion parameter \beta .
The quadrupole moment of \xi ( \sigma, \pi ) on scales 30 - 40 h ^ { -1 } { Mpc } provides another estimate of \beta .
We also estimate the distribution function of pairwise peculiar velocities , f ( v ) , including rigorously the significant effect due to the infall velocities , and find that the distribution is well fit by an exponential form .
The accuracy of our \xi ( \sigma, \pi ) 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 \pm 0.09 and a = 506 \pm 52 { km s ^ { -1 } } , 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 .
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 \beta ( L = L ^ { * } ,z = 0 ) = 0.47 \pm 0.08 , and that the present day matter density of the Universe , \Omega _ { m } \approx 0.3 , consistent with other 2dFGRS estimates and independent analyses .