The definition of environment and its relation to the quenching of galaxies at z=1-2 in a hierarchical Universe

A well calibrated method to describe the environment of galaxies at all redshifts is essential for the study of structure formation. Such a calibration should include well understood correlations with halo mass, and the possibility to identify galaxies which dominate their potential well (centrals), and their satellites. Focusing on z = 1 and 2 we propose a method of environmental calibration which can be applied to the next generation of low to medium resolution spectroscopic surveys. Using an up-to-date semi-analytic model of galaxy formation, we measure the local density of galaxies in fixed apertures on different scales. There is a clear correlation of density with halo mass for satellite galaxies, while a significant population of low mass centrals is found at high densities in the neighbourhood of massive haloes. In this case the density simply traces the mass of the most massive halo within the aperture. To identify central and satellite galaxies, we apply an observationally motivated stellar mass rank method which is both highly pure and complete, especially in the more massive haloes where such a division is most meaningful. Finally we examine a test case for the recovery of environmental trends: the passive fraction of galaxies and its dependence on stellar and halo mass for centrals and satellites. With careful calibration, observationally defined quantities do a good job of recovering known trends in the model. This result stands even with reduced redshift accuracy, provided the sample is deep enough to preserve a wide dynamic range of density.