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, provide important tests for models of galaxy formation and evolution. Close pairs of galaxies are the best available means of measuring redshift evolution in these quantities. In this study, we introduce two new pair statistics, which relate close Fairs to the merger and accretion rates. We demonstrate the importance of correcting these (and other) pair statistics for selection effects related to sample depth and completeness. In particular, we highlight 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 galaxy merger rate. The second statistic, L-c, gives the total luminosity in companions, per galaxy. This quantity can be used to investigate the mass accretion rate. Both N-c and L-c are related to the galaxy correlation function xi and luminosity function phi(M) in a straightforward manner. Both statistics have been designed with selection effects in mind. We outline techniques that account for various selection effects and demonstrate the success of this approach using Monte Carlo simulations. If one assumes that clustering is independent of luminosity (which is appropriate for reasonable ranges in luminosity), then these statistics may be applied to flux-limited surveys. These techniques are applied to a sample of 5426 galaxies in the Second Southern Sky Redshift Survey (SSRS2). This is the first large, well-defined low-z survey to be used for pair statistics. Using close (5 h(-1) kpc less than or equal to r(p) less than or equal to 20 h(-1) kpc) dynamical (Delta 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 estimates of low-redshift pair statistics, and they will provide local benchmarks for ongoing and future pair studies. If N-c remains fixed with redshift, simple 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, these techniques will yield the first robust estimates of evolution in the galaxy merger and accretion rates.