Y Extracting Galaxy Merger Time-Scales Ii: A New Fitting Formula

Predicting the merger time-scale (tau(merge)) of merging dark matter haloes, based on their orbital parameters and the structural properties of their hosts, is a fundamental problem in gravitational dynamics that has important consequences for our understanding of cosmological structure formation and galaxy formation. Previous models predicting tau(merge) have shown varying degrees of success when compared to the results of cosmological N-body simulations. We build on this previous work and propose a new model for tau(merge) that draws on insights derived from these simulations. We find that published predictions can provide reasonable estimates for tau(merge) based on orbital properties at infall, but tend to underpredict tau(merge) inside the host virial radius (R-200) because tidal stripping is neglected, and overpredict it outside R-200 because the host mass is underestimated. Furthermore, we find that models that account for orbital angular momentum via the circular radius R-circ underpredict (overpredict) tau(merge) for bound (unbound) systems. By fitting for the dependence of tau(merge) on various orbital and host halo properties, we derive an improved model for tau(merge) that can be applied to a merging halo at any point in its orbit. Finally, we discuss briefly the implications of our new model for tau(merge) for semi-analytical galaxy formation modelling.y