Strong clustering of underdense regions and the environmental dependence of clustering from Gaussian initial conditions

We discuss two slightly counterintuitive findings about the environmental dependence of clustering in the Sloan Digital Sky Survey. First, we find that the relation between clustering strength and density is not monotonic: galaxies in the densest regions are more strongly clustered than are galaxies in regions of moderate overdensity; galaxies in moderate overdensities are more strongly clustered than are those in moderate underdensities; but galaxies in moderate underdensities are less clustered than galaxies in the least dense regions. We argue that this is natural if clustering evolved gravitationally from a Gaussian field, since the highest peaks and lowest troughs in Gaussian fields are similarly clustered. The precise non-monotonic dependence of galaxy clustering on density is very well reproduced in a mock catalogue which is based on a halo model decomposition of galaxy clustering. In the mock catalogue, haloes of different masses are all about 200 times denser than the critical density, and the dependence of small-scale clustering on environment is entirely a consequence of the fact that the halo mass function in dense regions is top-heavy - another natural prediction of clustering from Gaussian initial conditions. Secondly, the distribution of galaxy counts in our sample is rather well described by a Poisson cluster model. We show that, despite their Poisson nature, correlations with environment are expected in such models. More remarkably, the expected trends are very like those in standard models of halo bias, despite the fact that correlations with environment in these models arise purely from the fact that dense regions are dense because they happen to host more massive haloes. This is in contrast to the usual analysis which assumes that it is the large-scale environment which determines the halo mass function.