More accurate analytical trajectory model for major cluster mergers

Develop a more accurate analytical approximation formula for the trajectories of major galaxy-cluster mergers, within two-body point-mass models that include modified Chandrasekhar dynamical friction, that remains valid over longer time scales.

Background

The paper models merger trajectories using a two-body point-mass framework augmented with a modified Chandrasekhar dynamical friction term, calibrated against simulations from the Galaxy Cluster Merger Catalog. This approximation achieves positional accuracy of roughly 0.1–0.3 Mpc for up to ~3 Gyr across several mass ratios and impact parameters, but exhibits larger discrepancies in specific major-merger configurations.

Because the current analytical approach shows degraded fidelity for some near-equal-mass, finite-impact-parameter cases and over longer time scales, the authors explicitly identify the need for improved analytical trajectory formulas that can better reproduce numerical simulation results in major cluster mergers over extended durations.