  We compare three analytical prescriptions for merger times available from the
literature to simulations of isolated mergers. We probe three different
redshifts, and several halo concentrations, mass ratios, orbital circularities
and orbital energies of the satellite. We find that prescriptions available in
the literature significantly under-predict long timescales for mergers at high
redshift. We argue that these results have not been highlighted previously
either because the evolution of halo concentration of satellite galaxies has
been neglected (in previous isolated merger simulations), or because long
merger times and mergers with high initial orbital circularities are
under-represented (for prescriptions based on cosmological simulations).
Motivated by the evolution of halo concentration at fixed mass, an explicit
dependence on redshift added as t_merger,modified(z) = (1+z)^0.44 t_merger to
the prescription based on isolated mergers gives a significant improvement in
the predicted merger times up to ~20 t_dyn in the redshift range 0<z<2. When
this modified prescription is used to compute galaxy stellar mass functions, we
find that it leads up to a 25 per cent increase in the number of low mass
galaxies surviving at z=0, and a 10 per cent increase for more massive
galaxies. This worsen the known over-prediction in the number of low mass
galaxies by hierarchical models of galaxy formation.
