Asymmetric galaxy correlation functions
  We study the two-point cross-correlation function between two populations of
galaxies: for instance a bright population and a faint population. We show that
this cross-correlation is asymmetric under the exchange of the line-of-sight
coordinate of the galaxies, i.e. that the correlation is different if the
bright galaxy is in front of, or behind, the faint galaxy. We give an
intuitive, quasi-Newtonian derivation of all the effects that contribute to
such an asymmetry in large-scale structure: gravitational redshift, Doppler
shift, lensing, light-cone, evolution and Alcock-Paczynski effects -
interestingly, the gravitational redshift term is exactly canceled by some of
the others, assuming geodesic motion. Most of these effects are captured by
previous calculations of general relativistic corrections to the observed
galaxy density fluctuation; the asymmetry arises from terms that are suppressed
by the ratio H/k - H is the Hubble constant and k is the wavenumber - which are
more readily observable than the terms suppressed by (H/k)^2. Some of the
contributions to the asymmetry, however, arise from terms that are generally
considered 'Newtonian' - the lensing and evolution - and thus represent a
contaminant in the search for general relativistic corrections. We propose
methods to disentangle these different contributions. A simple method reduces
the contamination to a level of < 10% for redshifts z<1. We also clarify the
relation to recent work on measuring gravitational redshifts by stacking
clusters.
