Measures of Galaxy Environment - I. What is "Environment"?
  The influence of a galaxy's environment on its evolution has been studied and
compared extensively in the literature, although differing techniques are often
used to define environment. Most methods fall into two broad groups: those that
use nearest neighbours to probe the underlying density field and those that use
fixed apertures. The differences between the two inhibit a clean comparison
between analyses and leave open the possibility that, even with the same data,
different properties are actually being measured. In this work we apply twenty
published environment definitions to a common mock galaxy catalogue constrained
to look like the local Universe. We find that nearest neighbour-based measures
best probe the internal densities of high-mass haloes, while at low masses the
inter-halo separation dominates and acts to smooth out local density
variations. The resulting correlation also shows that nearest neighbour galaxy
environment is largely independent of dark matter halo mass. Conversely,
aperture-based methods that probe super-halo scales accurately identify
high-density regions corresponding to high mass haloes. Both methods show how
galaxies in dense environments tend to be redder, with the exception of the
largest apertures, but these are the strongest at recovering the background
dark matter environment. We also warn against using photometric redshifts to
define environment in all but the densest regions. When considering environment
there are two regimes: the 'local environment' internal to a halo best measured
with nearest neighbour and 'large-scale environment' external to a halo best
measured with apertures. This leads to the conclusion that there is no
universal environment measure and the most suitable method depends on the scale
being probed.
