New Techniques for Relating Dynamically Close Galaxy Pairs to Merger and Accretion Rates : Application to the SSRS2 Redshift Survey

We introduce two new pair statistics, which relate close galaxy pairs 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, denoted 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, called 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 and luminosity function in a straightforward manner. We outline techniques which 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 SSRS2 redshift survey. Using close dynamical pairs, we find N_c(-21<M_B<-18) = 0.0226+/-0.0052 and L_c(-21<M_B<-18) = 0.0216+/-0.0055 10^{10} h^2 L_sun at z=0.015. These are the first secure estimates of low-z close pair statistics. If N_c remains fixed with redshift, simple assumptions imply that ~ 6.6% of present day galaxies with -21<M_B<-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. [Abridged]