On the Evolution of the Globular Cluster System in NGC 1052-DF2:
  Dynamical Friction, Globular-Globular Interactions and Galactic Tides
  The ultra-diffuse galaxy NGC 1052-DF2 has an overabundance of luminous
globular clusters (GCs), and its kinematics is consistent with the presence of
little to no dark matter. As the velocity dispersion among the GCs is
comparable to the expected internal dispersions of the individual GCs, the
galaxy might be highly conducive to GC-GC merging. If true, this could explain
the puzzling luminosity function of its GCs. Here, we examine this possibility
by re-simulating three of our earlier simulations of the GC system (Dutta
Chowdhury et al. 2019), where the GCs were modeled as single particles, with
live GCs. Somewhat surprisingly, we infer a low merger rate of $\sim 0.03\ \rm
Gyr^{-1}$. The main reason is that the GCs are too dense for tidal shock
capture, caused by impulsive encounters among them, to operate efficiently (we
infer 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 be
captures induced by dynamical friction and compressive tides from other GCs.
The low merger rate inferred here makes it unlikely that the unusually large
luminosities of the GCs can be explained as a result of past GC-GC mergers. Our
simulations also indicate that, if NGC 1052-DF2 is indeed largely devoid of
dark matter, its tidal field is too weak to induce any significant mass loss
from the GCs. Therefore, in such a scenario, we predict that it is improbable
for the GCs to reveal tidal features, something that can be tested with future
deep observations.
