A Fitting Formula for the Merger Timescale of Galaxies in Hierarchical Clustering

We study galaxy mergers using a high-resolution cosmological hydro/N-body simulation with star formation and compare the measured merger timescales with theoretical predictions based on the Chandrasekhar formula. In contrast to Navarro et al., our numerical results indicate that the commonly used equation for the merger timescale given by Lacey and Cole systematically underestimates the merger timescales for minor mergers and overestimates those for major mergers. This behavior is partly explained by the poor performance of their expression for the Coulomb logarithm, ln (mpri/msat) . The two alternative forms ln (1 + mpri/msat) and ½ln[1 + (mpri/msat)2] for the Coulomb logarithm can account for the mass dependence of merger timescale successfully, but both of them underestimate the merger timescale by a factor 2. Since ln (1 + mpri/msat) represents the mass dependence slightly better, we adopt this expression for the Coulomb logarithm. Furthermore, we find that the dependence of the merger timescale on the circularity parameter ϵ is much weaker than the widely adopted power law ϵ0.78, whereas 0.94ϵ0.60 + 0.60 provides a good match to the data. Based on these findings, we present an accurate and convenient fitting formula for the merger timescale of galaxies in cold dark matter models.