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

Abstract

We examine the effect of redshift space distortions on the galaxy two-point correlation function $\xi(r_p,\pi)$ as a function of separations parallel ($r_p$) and perpendicular ($\pi$) to the line of sight. We find that the relative velocity dispersion of pairs of IRAS galaxies is $\sigma(r)= 317^{+40}_{-49}$ \kms at $r=1 \mpc$, consistent with previous estimates derived from optically selected galaxy catalogues. Unfortunately, the use of this result to estimate $\Omega$ via the Cosmic Virial Theorem is thwarted by large systematic uncertainties. We also fit for the mean relative streaming velocity of pairs, $v_{12}(r)$, which describes the growth of fluctuations on both linear and nonlinear scales. We find that $v_{12}(r) = 167^{+99}_{-67}$ \kms at $r=4$\mpc, so that on average, approximately half the Hubble expansion velocity of pairs at this separation is canceled by infall. At $r=10$\mpc, the amplitude of the streaming is lower and $v_{12}(r) = 109^{+64}_{-47} \kms$. Linear perturbation theory then implies that $\Omega^{0.6}/b =0.45^{+0.27}_{-0.18}$ on scales $\sim 10-15 \mpc$. The amplitude of $v_{12}(r)$ is sensitive to the assumed shape of $\sigma(r)$; if the latter deviates substantially from a virialized form on small scale, our best fit amplitude of $v_{12}(r)$ can deviate by a factor of two.