A hierarchical clustering method for quantifying satellite abundance
  We present a new method for quantifying the abundance of satellites around
field galaxies and in groups. The method is designed to work with samples, such
as local photometric redshift catalogues, that do not have full spectroscopic
coverage, but for which some redshift or distance information is available. It
consists of identifying the galaxies most likely to be centrals, and using the
clustering signal around them as a template to iteratively decompose the full
population into satellite and central populations. In that sense it is similar
to performing crowded-field photometry, after having first used isolated stars
to determine the point spread function of the image. The method does not
identify individual satellites or centrals conclusively, but assigns a
probability to each galaxy of being one or the other. Averaged over a large
sample, it provides a statistical estimate of satellite abundance, even in
crowded fields with large redshift uncertainties. We test the method using data
from the COSMOS field, which includes a large set of local objects with
accurate photometric redshifts. We measure satellite abundance as a function of
central stellar or halo mass, as well as the satellite luminosity function, and
find results consistent with previous studies, but extending over a broader
range of central masses. We also consider a number of possible systematic
uncertainties in the method, and show that they are generally smaller than our
random errors. Having presented the method in this paper, we will use it to
study the properties of the satellite populations in a forthcoming one.
