Slow relative motion of IRAS galaxies at small separations: implications for galaxy formation models

We report on the measurement of the two-point correlation function and the pairwise peculiar velocity of galaxies in the IRAS PSCz survey. The real space two-point correlation function can be fitted to a power law $\xi® = (r_0/r)^{\gamma}$with$\gamma=1.69$and$r_0=3.70 \mpc$. The pairwise peculiar velocity dispersion ${\sigma }_{12}(r_p)$ is close to $400\text{kms}$ at $r_p=3\text{mpc}$ and decreases to about $150\text{kms}$ at $r_p\approx 0.2\text{mpc}$. These values are significantly lower than those obtained from the Las Campanas Redshift Survey, but agree very well with the results of blue galaxies reported by the SDSS team later on. We have constructed mock samples from N-body simulations with a cluster-weighted bias and from the theoretically constructed GIF catalog. We find that the two-point correlation function of the mock galaxies can be brought into agreemnt with the observed result, but the model does not reduce the velocity dispersions of galaxies to the level measured in the PSCz data. Thus we conclude that the peculiar velocity dispersions of the PSCz galaxies require a biasing model which substantially reduces the peculiar velocity dispersion on small scales relative to their spatial clustering. The results imply that either the cosmogony model needs to be revised or the velocity bias is important for the velocity dispersion of the IRAS galaxies.