Clustering in the 1.2-Jy IRAS Galaxy Redshift Survey - II. Redshift distortions and Formula

We examine the effect of redshift space distortions on the galaxy two-point correlation function | (r_ p, ) | as a function of separations parallel (⁠|r_ p|⁠) and perpendicular (π) to the line of sight. Modelling of | (r_ p, ) | measured from a full-sky redshift survey of IRAS galaxies allows us to characterize the moments of the velocity distribution function of pairs of galaxies. We are guided in our parametrization of models by results from numerical simulations of cold dark matter (CDM) models. It is essential that the models for | (r_ p, ) | contain the effects of both the first and second moments of the velocity distribution function, as they distort the redshift space correlations in opposing 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 galaxies is | (r) =317^+40-₄₉ 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 Ω via the cosmic virial theorem is thwarted by large systematic uncertainties, making the application of this theorem to existing redshift surveys of little value. We also fit for the mean relative streaming velocity of pairs, | ₁₂ (r) |⁠, which describes the growth of fluctuations on both linear and non-linear scales. We find that |₁₂ (r) =167^+99-₆₇ km s^-1 at r=4 h^-1| Mpc, so that on average, approximately half the Hubble expansion velocity of pairs at this separation is cancelled by infall. At |r=10 h^-1| Mpc, the amplitude of the streaming is lower and |v₁₂ (r) =109^+64-₄₇ km s^-1|⁠. Linear perturbation theory then implies that |^0. 6/b=0. 45^+0. 27-₀. ₁₈ on scales 10-15 h^-1| Mpc. The amplitude of |v₁₂ (r) | is sensitive to the assumed shape of | (r) |⁠. Our derived result for beta is intermediate between that found on | 1 h^-1| Mpc scales and that found on |15-40 h^-1| Mpc scales, arguing for either a strong dependence of β on scale, or an error in the determination of β on one or more scales.