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 a Navarro-Frenk-White (NFW) mass profile we infer a total halo mass of 6.2(+/- 0.2) x 10(12) M-circle dot. 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-DF2 and NGC 1052-DF4) and consider whether modified Newtonian dynamics (MOND) can account for their low observed internal velocity dispersions.