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.