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.
