Dark matter and no dark matter: On the halo mass of NGC 1052

The NGC 1052 group, and in particular the discovery of two ultra diffuse galaxies with very low internal velocity dispersions, has been the subject of much attention recently. Here we present radial velocities for a sample of 77 globular clusters associated with NGC 1052 obtained on the Keck telescope. Their mean velocity and velocity dispersion are consistent with that of the host galaxy. Using a simple tracer mass estimator, we infer the enclosed dynamical mass and dark matter fraction of NGC 1052. Extrapolating our measurements with an NFW mass profile we infer a total halo mass of 6.2 ($\pm$0.2) $\times$ 10$^{12}$ M$_{\odot}$. This mass is fully consistent with that expected from the stellar mass--halo mass relation, suggesting that NGC 1052 has a normal dark matter halo mass (i.e. it is not deficient in dark matter in contrast to two ultra diffuse galaxies in the group). We present a phase space diagram showing the galaxies that lie within the projected virial radius (390 kpc) of NGC 1052. Finally, we briefly discuss the two dark matter deficient galaxies (NGC 1052--DF and DF4) and consider whether MOND can account for their low observed internal velocity dispersions.