An improved prescription for merger time-scales from controlled simulations

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 underpredict long time-scales 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 tmergermod(z) = (1 + z)0.44 tmerger to the prescription based on isolated mergers gives a significant improvement in the predicted merger times up to ˜20 tdyn 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 worsens the known overprediction in the number of low-mass galaxies by hierarchical models of galaxy formation.