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Abstract

Theoretical models are vital for exploring the galaxy merger process, which plays a crucial role in the evolution of galaxies. Recent advances in modelling have placed tight constraints on the build-up of stellar material in galaxies across cosmic time. Despite these successes, extracting the merger rates from observable data remains a challenge. Differences in modelling techniques, combined with limited observational data, drive conflicting conclusions on the merging time-scales of close pairs. We employ an empirical model for galaxy formation that links galaxy properties to the growth of simulated dark matter haloes, along with mock light-cone galaxy catalogues, to probe the dependences of pair merging probabilities and merging time-scales. In this work, we demonstrate that the pair merging probabilities are best described by a logistic function and that mean merging time-scales can be well approximated by a linear relation in the projected separation and line of sight velocity difference in observed pairs. Together, our fitting formulas can accurately predict merger rates from galaxy pairs to at least z ∼ 4 under a wide variety of pair selection criteria. Additionally, we show that some commonly used pair selection criteria may not represent a suitable sample of galaxies to reproduce underlying merger rates. Finally, we conclude from our analysis that observation time-scales are primarily driven by dynamics and are not strongly impacted by the star formation properties of the component galaxies.