A new formulation of the external field effect in MOND and numerical simulations of ultra-diffuse dwarf galaxies – application to NGC 1052-DF2 and NGC 1052-DF4

Abstract

The ultra-diffuse dwarf galaxy NGC 1052-DF2 (DF2) has ten (eleven) measured\nglobular clusters (GCs) with a line-of-sight velocity dispersion of\n$\\sigma=7.8^{+5.2}_{-2.2}\\,$km/s ($\\sigma=10.6^{+3.9}_{-2.3}\\,$km/s). Our\nconventional statistical analysis of the original ten GCs gives\n$\\sigma=8.0^{+4.3}_{-3.0}\\,$km/s. The overall distribution of velocities agrees\nwell with a Gaussian of this width. Due to the non-linear Poisson equation in\nMOND, a dwarf galaxy has weaker self-gravity when in close proximity to a\nmassive host. This external field effect is investigated using a new analytic\nformulation and fully self-consistent live $N$-body models in MOND. Our\nformulation agrees well with that of Famaey and McGaugh (2012). These new\nsimulations confirm our analytic results and suggest that DF2 may be in a\ndeep-freeze state unique to MOND. The correctly calculated MOND velocity\ndispersion agrees with our inferred dispersion and that of van Dokkum et al.\n(2018b) if DF2 is within 150 kpc of NGC 1052 and both are 20 Mpc away. The GCs\nof DF2 are however significantly brighter and larger than normal GCs, a problem\nwhich disappears if DF2 is significantly closer to us. A distance of 10-13 Mpc\nmakes DF2 a normal dwarf galaxy even more consistent with MOND and the 13 Mpc\ndistance reported by Trujillo et. al. (2019). We discuss the similar dwarf DF4,\nfinding good agreement with MOND. We also discuss possible massive galaxies\nnear DF2 and DF4 along with their distances and peculiar velocities, noting\nthat NGC 1052 may lie at a distance near 10 Mpc.\n