Orbital decay of Globular Clusters in the galaxy with little dark matter

Recently, cite{vanDokkum2018} have presented an important discovery of an ultra diffuse galaxy, NGC1052-DF2, with a dark matter content significantly less than predicted from its stellar mass alone. 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 $1%$ of the inferred mass of NGC1052-DF2 of $2times 10^8 M_odot$ within a half-light radius, $R_mathrm{e}=2.2, mathrm{kpc}$. The large relative mass and the old age of these objects imply that they might be susceptible to orbital decay by dynamical friction. Using analytic estimates and N-body simulations of an isolated system matching the inferred mass profile of NGC1052-DF2, we show that orbits of the most massive GCs should already have decayed on a time scale of a few Gyrs. These findings should help in constraining mass profile and formation scenarios of NGC1052-DF2.