MOND Prediction for the Velocity Dispersion of the `Feeble Giant' Crater II

Crater II is an unusual object among the dwarf satellite galaxies of the Local Group in that it has a very large size for its small luminosity. This provides a strong test of MOND, as Crater II should be in the deep MOND regime ($g_{in} \approx 34\;\mathrm{km}^2\,\mathrm{s}^{-2}\,\mathrm{kpc}^{-1} \ll a_0 = 3700\;\mathrm{km}^2\,\mathrm{s}^{-2}\,\mathrm{kpc}^{-1}$). Despite its great distance ($\approx 120$ kpc) from the Milky Way, the external field of the host ($g_{ex} \approx 282\; \mathrm{km}^2\,\mathrm{s}^{-2}\,\mathrm{kpc}^{-1}$) comfortably exceeds the internal field. Consequently, Crater II should be subject to the external field effect, a feature unique to MOND. This leads to the prediction of a very low velocity dispersion: $\sigma_{efe} = 2.1^{+0.9}_{-0.6}\;\mathrm{km}\,\mathrm{s}^{-1}$.