Galaxy pairs in the Sloan Digital Sky Survey - XI. A new method for
  measuring the influence of the closest companion out to wide separations
  We describe a statistical approach for measuring the influence that a
galaxy's closest companion has on the galaxy's properties out to arbitrarily
wide separations. We begin by identifying the closest companion for every
galaxy in a large spectroscopic sample of Sloan Digital Sky Survey galaxies. We
then characterize the local environment of each galaxy by using the number of
galaxies within 2 Mpc and by determining the isolation of the galaxy pair from
other neighbouring galaxies. We introduce a sophisticated algorithm for
creating a statistical control sample for each galaxy, matching on stellar
mass, redshift, local density and isolation. Unlike traditional studies of
close galaxy pairs, this approach is effective in a wide range of environments,
regardless of how far away the closest companion is (although a very distant
closest companion is unlikely to have a measurable influence on the galaxy in
question). We apply this methodology to measurements of galaxy asymmetry, and
find that the presence of nearby companions drives a clear enhancement in
galaxy asymmetries. The asymmetry excess peaks at the smallest projected
separations (< 10 kpc), where the mean asymmetry is enhanced by a factor of 2.0
$\pm$ 0.2. Enhancements in mean asymmetry decline as pair separation increases,
but remain statistically significant (1-2$\sigma$) out to projected separations
of at least 50 kpc.
