A calibration of the relation between the abundance of close galaxy pairs and the rate of galaxy mergers

Estimates of galaxy merger rates based on counts of close pairs typically assume that most of the observed systems will merge within a few hundred Myr (for projected pair separations <25 kpc/h). Here we investigate these assumptions using virtual galaxy catalogues derived from the Millennium Simulation, a very large N-body simulation of structure formation in the concordance LCDM cosmology. These catalogues have been shown to be at least roughly consistent with a wide range of properties of the observed galaxy population at both low and high redshift. Here we show that they also predict close pair abundances at low redshift which agree with those observed. They thus embed a realistic and realistically evolving galaxy population within the standard structure formation paradigm, and so are well-suited to calibrate the relation between close galaxy pairs and mergers. We show that observational methods, when applied to our mock galaxy surveys, do indeed identify pairs which are physically close and due to merge. The sample-averaged merging time depends only weakly on the stellar mass and redshift of the pair. At z<2 this time-scale is T ~ T0 r25 M*^-0.3, where r25 is the maximum projected separation of the pair sample in units of 25 kpc/h, M* is the typical stellar mass of the pairs in units of 3x10^10 Msol/h, and the coefficient T0 is 1.1 Gyr for samples selected to have line-of-sight velocity difference smaller than 300 km/s and 1.6 Gyr for samples where this velocity difference is effectively unconstrained. These timescales increase slightly with redshift and are longer than assumed in most observational studies, implying that merger rates have typically been overestimated.