New techniques for relating dynamically close galaxy pairs to merger and accretion rates: Application to the Second Southern Sky Redshift Survey

The galaxy merger and accretion rates, and their evolution with time, provi de important tests for models of galaxy formation and evolution. Close pair s of galaxies are the best available means of measuring redshift evolution in these quantities. In this study, we introduce two new pair statistics, w hich relate close Fairs to the merger and accretion rates. We demonstrate t he importance of correcting these (and other) pair statistics for selection effects related to sample depth and completeness. In particular, we highli ght the severe bias that can result from the use of a flux-limited survey. The first statistic, N-c, gives the number of companions per galaxy within a specified range in absolute magnitude. N-c is directly related to the gal axy merger rate. The second statistic, L-c, gives the total luminosity in c ompanions, per galaxy. This quantity can be used to investigate the mass ac cretion rate. Both N-c and L-c are related to the galaxy correlation functi on xi and luminosity function phi(M) in a straightforward manner. Both stat istics have been designed with selection effects in mind. We outline techni ques that account for various selection effects and demonstrate the success of this approach using Monte Carlo simulations. If one assumes that cluste ring is independent of luminosity (which is appropriate for reasonable rang es in luminosity), then these statistics may be applied to flux-limited sur veys. These techniques are applied to a sample of 5426 galaxies in the Seco nd Southern Sky Redshift Survey (SSRS2). This is the first large, well-defi ned low-z survey to be used for pair statistics. Using close (5 h(-1) kpc l ess than or equal to r(p) less than or equal to 20 h(-1) kpc) dynamical (De lta nu less than or equal to 500 km s(-1)) pairs, we find N-c(-21 less than or equal to M-B less than or equal to -18) = 0.0226 +/- 0.0052 and L-c(-21 less than or equal to M-B less than or equal to -18) = 0.0216 +/- 0.0055 x 10(10) h(2) L-circle dot at z = 0.015. These are the first secure estimate s of low-redshift pair statistics, and they will provide local benchmarks f or ongoing and future pair studies. If N-c remains fixed with redshift, sim ple assumptions imply that similar to 6.6% of present day galaxies with -21 less than or equal to M-B less than or equal to -18 have undergone mergers since z = 1. When applied to redshift surveys of more distant galaxies, th ese techniques will yield the first robust estimates of evolution in the ga laxy merger and accretion rates.