Extracting Galaxy Merger Timescales II: A new fitting formula

Predicting the merger timescale (\(\tau_{\rm merge}\)) of merging dark matter halos, 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 \(\tau_{\rm merge}\) 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 \(\tau_{\rm merge}\) that draws on insights derived from these simulations. We find that published predictions can provide reasonable estimates for \(\tau_{\rm merge}\) based on orbital properties at infall, but tend to underpredict \(\tau_{\rm merge}\) 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 \(R_{\rm circ}\) underpredict (overpredict) \(\tau_{\rm merge}\) for bound (unbound) systems. By fitting for the dependence of \(\tau_{\rm merge}\) on various orbital and host halo properties,we derive an improved model for \(\tau_{\rm merge}\) 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 \(\tau_{\rm merge}\) for semi-analytical galaxy formation modelling.