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The ultra-diffuse galaxy NGC 1052-DF2 has an overabundance of luminousglobular clusters (GCs), and its kinematics is consistent with the presence oflittle to no dark matter. As the velocity dispersion among the GCs iscomparable to the expected internal dispersions of the individual GCs, thegalaxy might be highly conducive to GC-GC merging. If true, this could explainthe puzzling luminosity function of its GCs. Here, we examine this possibilityby re-simulating three of our earlier simulations of the GC system (DuttaChowdhury et al. 2019), where the GCs were modeled as single particles, withlive GCs. Somewhat surprisingly, we infer a low merger rate of $\sim 0.03\ \rmGyr^{-1}$. The main reason is that the GCs are too dense for tidal shockcapture, caused by impulsive encounters among them, to operate efficiently (weinfer a tidal capture rate of only $\sim 0.002\ \rm Gyr^{-1}$). Therefore,whatever mergers occur are driven by other mechanisms, which we find to becaptures induced by dynamical friction and compressive tides from other GCs.The low merger rate inferred here makes it unlikely that the unusually largeluminosities of the GCs can be explained as a result of past GC-GC mergers. Oursimulations also indicate that, if NGC 1052-DF2 is indeed largely devoid ofdark matter, its tidal field is too weak to induce any significant mass lossfrom the GCs. Therefore, in such a scenario, we predict that it is improbablefor the GCs to reveal tidal features, something that can be tested with futuredeep observations.

On the Evolution of the Globular Cluster System in NGC 1052-DF2: Dynamical Friction, Globular-Globular Interactions and Galactic Tides