The transition to nonlinearity and new constraints on biasing

Abstract

We present two new dynamical tests of the biasing hypothesis. The first is based on the amplitude and the shape of the galaxy-galaxy correlation function, $ξ_g(r)$, where $r$ is the separation of the galaxy pair. The second test uses the mean relative peculiar velocity for galaxy pairs, $\vs(r)$. This quantity is a measure of the rate of growth of clustering and it is related to the two-point correlation function for the matter density fluctuations, $ξ(r)$. Under the assumption that galaxies trace the mass ($ξ_g = ξ$), the expected relative velocity can be calculated directly from the observed galaxy clustering. The above assumption can be tested by confronting the expected $\vs$ with direct measurements from velocity-distance surveys. Both our methods are checked against N-body experiments and then compared with the $ξ_g(r)$ and $\vs$ estimated from the {\sc APM} galaxy survey and the Mark III catalogue, respectively. Our results suggest that cosmological density parameter is low, $Ω_m \approx 0.3$, and that the {\sc APM} galaxies trace the mass at separations $r \ga 5 \Mlu$, where $h$ is the Hubble constant in units of 100 km s$^{-1}$Mpc. The present results agree with earlier studies, based on comparing higher order correlations in the {\sc APM} with weakly non-linear perturbation theory. Both approaches constrain the linear bias factor to be within 20% of unity. If the existence of the feature we identified in the {\sc APM} $ξ_g(r)$ -- the inflection point near $ξ_g = 1$ -- is confirmed by more accurate surveys, we may have discovered gravity's smoking gun: the long awaited ``shoulder'' in $ξ$, generated by gravitational dynamics and predicted by Gott and Rees 25 years ago.