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We present a novel method to constrain the past collisional evolution ofobserved globular cluster (GC) systems, in particular their mass functions. Weapply our method to a pair of galaxies hypothesized to have recently undergonean episode of violent relaxation due to a strong galaxy-galaxy interaction,namely NGC 1052-DF2 and NGC 1052-DF4. We begin by exploring the observationalevidence for a collisional origin for these two recently discoveredultra-diffuse galaxies observed in the NGC 1052 group, posited in theliterature to be dark matter (DM)-free. We compute the timescales for infall tothe central nucleus due to dynamical friction (DF) for the GCs in thesegalaxies, using the shortest of these times to constrain how long ago agalaxy-galaxy interaction could have occurred. We go on to quantify the initialGC numbers and densities needed for significant collisional evolution to occurwithin the allotted times, and show that, if the hypothesis of a previousgalaxy-galaxy interaction is correct, a paucity of low-mass GCs should berevealed by deeper observational surveys. If any are found, they should be morespatially extended than the currently observed GC population. Finally, we applyour method to these galaxies, in order to illustrate its efficacy inconstraining their dynamical evolution. Our results motivate more completeobservations of the GC luminosity functions in these galaxies, in addition tofuture studies aimed at combining the method presented here with a suite ofnumerical simulations in order to further constrain the origins of the curiousGC populations in these (and other) galaxies.

A new method to constrain the origins of dark matter-free galaxies and their unusual globular clusters