A SCALING RELATION BETWEEN MERGER RATE OF GALAXIES AND THEIR CLOSE PAIR COUNT

We study how to measure the galaxy merger rate from the observed close pair count. Using a high-resolution N-body/SPH cosmological simulation, we find an accurate scaling relation between galaxy pair counts and merger rates down to a stellar mass ratio of about 1:30. The relation explicitly accounts for the dependence on redshift (or time), on pair separation, and on mass of the two galaxies in a pair. With this relation, one can easily obtain the mean merger timescale for a close pair of galaxies. The use of virial masses, instead of the stellar mass, is motivated by the fact that the dynamical friction timescale is mainly determined by the dark matter surrounding central and satellite galaxies. This fact can also minimize the error induced by uncertainties in modeling star formation in the simulation. Since the virial mass can be determined from the well-established relation between the virial masses and the stellar masses in observations, our scaling relation can easily be applied to observations to obtain the merger rate and merger timescale. For major merger pairs (1:1-1:4) of galaxies above a steller mass of 4 x 10(10) h(-1) M-circle dot at z = 0.1, it takes about 0.31 Gyr to merge for pairs within a projected distance of 20 h(-1) kpc with a stellar mass ratio of 1:1, while the time goes up to 1.6 Gyr for mergers with stellar mass ratio of 1:4. Our results indicate that a single timescale usually used in the literature is not accurate to describe mergers with a stellar mass ratio spanning even a narrow range from 1:1 to 1:4.