Close pairs as proxies for galaxy cluster mergers

Galaxy cluster merger statistics are an important component in understanding the formation of large-scale structure. Cluster mergers are also potential sources of systematic error in the mass calibration of upcoming cluster surveys. Unfortunately, it is difficult to study merger properties and evolution directly because the identification of cluster mergers in observations is problematic. We use large N- body simulations to study the statistical properties of massive halo mergers, specifically investigating the utility of close halo pairs as proxies for mergers. We examine the relationship between pairs and mergers for a wide range of merger timescales, halo masses, and redshifts (0 < z << 1). We also quantify the utility of pairs in measuring merger bias. While pairs at very small separations will reliably merge, these constitute a small fraction of the total merger population. Thus, pairs do not provide a reliable direct proxy to the total merger population. We do find an intriguing universality in the relation between close pairs and mergers, which in principle could allow for an estimate of the statistical merger rate from the pair fraction within a scaled separation, but including the effects of redshift space distortions strongly degrades this relation. We find similar behavior for galaxy- mass halos, making our results applicable to field galaxy mergers at high redshift. We investigate how the halo merger rate can be statistically described by the halo mass function via the merger kernel (coagulation), finding an interesting environmental dependence of merging: halos within the mass resolution of our simulations merge less efficiently in overdense environments. Specifically, halo pairs with separations less than a few h(-1) Mpc are more likely to merge in underdense environments; at larger separations, pairs are more likely to merge in overdense environments.