MOND and the dynamics of NGC 1052-DF2

The dwarf galaxy NGC 1052-DF2 has recently been identified as potentially lacking dark matter. If correct, this could be a challenge for modified Newtonian dynamics (MOND), which predicts that low surface brightness galaxies should evince large mass discrepancies. However, the correct prediction of MOND depends on both the internal field of the dwarf and the external field caused by its proximity to the giant elliptical NGC 1052. Taking both into consideration, we find σ _MOND=13.4^{+4.8}_{-3.7} km s^{-1} - where the quoted error only reflects the uncertainty on the stellar mass-to-light ratio - if the dwarf is at the projected distance from its host and the MOND interpolating function is the so-called `simple' one. More generally, we find that acceptable values of σ_MOND range from 8.9 to 19 km s^{-1} depending on the interpolating function, stellar mass-to-light ratio, and three-dimensional distance to the host. We also discuss a few caveats on both the observational and theoretical side. On the theory side, the internal virialization time in this dwarf may be longer than the time-scale of variation of the external field. On the observational side, the paucity of data and their large uncertainties call for further analysis of the velocity dispersion of NGC 1052-DF2, to check whether it poses a challenge to MOND or is a success thereof.