On the Orbital Decay of Globular Clusters in NGC 1052-DF2: Testing a Baryon-only Mass Model

The dark matter content of the ultra-diffuse galaxy NGC 1052-DF2, as inferred from globular cluster (GC) and stellar kinematics, carries a considerable amount of uncertainty, with current constraints also allowing for the complete absence of dark matter. We test the viability of such a scenario by examining whether in a baryon-only mass model the observed GC population experiences rapid orbital decay due to dynamical friction. Using a suite of 50 multi-GC N-body simulations that match observational constraints on both the stellar component of NGC 1052-DF2 and its GC population but differ in the initial line-of-sight positions and the tangential velocities of the GCs, we show that there is a substantial amount of realization-to-realization variance in the evolution of the GCs. Nevertheless, over similar to 10 Gyr, some of the GCs experience significant orbital evolution. Others evolve less. A combination of reduced dynamical friction in the galaxy core and GC-GC scattering keeps the GCs afloat, preventing them from sinking all the way to the galaxy center. While the current phase-space coordinates of the GCs are not unlikely for a baryon-only mass model, the GC system does evolve over time. Therefore, if NGC 1052-DF2 has no dark matter, some of its GCs must have formed farther out, and the GC system must have been somewhat more extended in the past. The presence of a low-mass cuspy halo, while allowed by the kinematics, seems improbable, as significantly shorter inspiral timescales in the central region would quickly lead to the formation of a nuclear star cluster.