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.
