Orbital decay of Globular Clusters in the galaxy with little dark matter: more mass needed

Recently, van Dokkum et. al. have presented an important discovery of an ultra diffuse galaxy, NGC1052-DF2, with a dark matter content significantly less than predicted from its stellar massalone. The analysis relies on measured radial velocities of 10 " Globular Clusters" (GCs), of estimated individual masses of a few $ \times 10^6 M_\odot$. This is about $1\%$ the inferred mass of NGC1052-DF2 of $2\times 10^8 M_\odot$ within a half-light radius, $R_e=2.2 \mathrm{kpc} $. The large relative mass and the old age of these objects imply that they might be susceptible to orbital decayby dynamical friction. Analytic estimates and N-body simulationsof an isolated systemmatching the inferred mass profile of NGC1052-DF2 , show that orbits of the most massive GCs should already have decayed on a time scale of a few Gyrs. This implies that either the mass of the GCs are overestimated or that the mass of NGC1052-DF2 is underestimated by an order of magnitude or so.