  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
stellar masses, is motivated by the fact that the dynamical friction time scale
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 read
from the well-established relation between the virial masses and the stellar
masses in observation, our scaling relation can be easily applied to
observations to obtain the merger rate and merger time scale. For major merger
pairs (1:1-1:4) of galaxies above a stellar mass of 4*10^10 M_sun/h at z=0.1,
it takes about 0.31 Gyr to merge for pairs within a projected distance of 20
kpc/h with stellar mass ratio of 1:1, while the time taken 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 literature is not accurate to describe mergers with
the stellar mass ratio spanning even a narrow range from 1:1 to 1:4.
