CLUSTERING IN THE 1.2-JY IRAS GALAXY REDSHIFT SURVEY .2. REDSHIFT DISTORTIONS AND XI(R(P),PI)

We examine the effect of redshift space distortions on the galaxy two- point correlation function xi(r(p), pi) as a function of separations p arallel (r(p)) and perpendicular (pi) to the line of sight. Modelling of xi(r(p), pi) measured from a full-sky redshift survey of IRAS galax ies allows us to characterize the moments of the velocity distribution function of pairs of galaxies. We are guided in our parametrization o f models by results from numerical simulations of cold dark matter (CD M) models. It is essential that the models for xi(r(p), pi) contain th e effects of both the first and second moments of the velocity distrib ution function, as they distort the redshift space correlations in opp osing directions. We develop a method of fitting for the amplitudes of the velocity moments, and show that we can recover the correct values in Monte Carlo realizations of the data drawn from N-body simulations . We find that the relative velocity dispersion of pairs of IRAS galax ies is sigma(r) = 317(-49)+40 km s-1 at r = 1 h-1 Mpc, consistent with previous estimates derived from optically selected galaxy catalogues. Unfortunately, the use of this result to estimate OMEGA via the cosmi c virial theorem is thwarted by large systematic uncertainties, making the application of this theorem to existing redshift surveys of littl e value. We also fit for the mean relative streaming velocity of pairs , upsilon12(r), which describes the growth of fluctuations on both lin ear and non-linear scales. We find that upsilon12(r) = 167(-67)+99 km s-1 at r = 4 h-1 Mpc, so that on average, approximately half the Hubbl e expansion velocity of pairs at this separation is cancelled by infal l. At r = 10 h-1 Mpc, the amplitude of the streaming is lower and upsi lon12(r) = 109(-47)+64 km s-1. Linear perturbation theory then implies that OMEGA0.6/b = 0.45(-0.18)+0.27 on scales approximately 10-15 h-1 Mpc. The amplitude of upsilon12(r) is sensitive to the assumed shape o f sigma(r). Our derived result for beta is intermediate between that f ound on approximately 1 h-1 Mpc scales and that found on 15-40 h-1 Mpc scales, arguing for either a strong dependence of beta on scale, or a n error in the determination of beta on one or more scales.