Extracting Galaxy Merger Timescales II: A new fitting formula

Abstract

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

12 pages, 11 figures, accepted for publication in MNRAS