MOND and the dynamics of NGC1052-DF2

Abstract: The dwarf galaxy NGC1052-DF2 has recently been identified as potentially lacking dark matter. If correct, this could be a challenge for 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 NGC1052. Taking both into consideration under plausible assumptions, we find $\sigma_{\rm MOND} = 13.4^{+4.8}_{-3.7}\;\mathrm{km}\,\mathrm{s}^{-1}$. This is only marginally higher than the claimed 90\% upper limit on the velocity dispersion ($\sigma < 10.5\;\mathrm{km}\,\mathrm{s}^{-1}$), and compares well with the observed root mean square velocity dispersion ($\sigma = 14.3\;\mathrm{km}\,\mathrm{s}^{-1}$). 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 that 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 NGC1052-DF2, to check whether it poses a challenge to MOND or is a success thereof.