Abstract

We present a novel method to constrain the past collisional evolution of observed globular cluster (GC) systems, in particular their mass functions. We apply our method to a pair of galaxies hypothesized to have recently undergone an episode of violent relaxation due to a strong galaxy-galaxy interaction, namely, NGC 1052-DF2 and NGC 1052-DF4. We begin by exploring the observational evidence for a collisional origin for these two recently discovered ultradiffuse galaxies observed in the NGC 1052 group, posited in the literature to be dark matter free. We compute the timescales for infall to the central nucleus due to dynamical friction for the GCs in these galaxies, using the shortest of these times to constrain how long ago a galaxy-galaxy interaction could have occurred. We go on to quantify the initial GC numbers and densities needed for significant collisional evolution to occur within the allotted times and show that, if the hypothesis of a previous galaxy-galaxy interaction is correct, a paucity of low-mass GCs should be revealed by deeper observational surveys. If any are found, they should be more spatially extended than the currently observed GC population. Finally, we apply our method to these galaxies, in order to illustrate its efficacy in constraining their dynamical evolution. Our results motivate more complete observations of the GC luminosity functions in these galaxies, in addition to future studies aimed at combining the method presented here with a suite of numerical simulations in order to further constrain the origins of the curious GC populations in these (and other) galaxies.