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{k}\mathrm{m}$^2,$\mathrm{s}$^{-2},$\mathrm{k}\mathrm{p}\mathrm{c}$^{-1} \ll a_0 = 3700;$\mathrm{k}\mathrm{m}$^2,$\mathrm{s}$^{-2},$\mathrm{k}\mathrm{p}\mathrm{c}$^{-1}$). Despite its great distance ($\approx 120$ kpc) from the Milky Way, the external field of the host ($g_{ex}\approx 282{\mathrm{k}\mathrm{m}}^2{\mathrm{s}}^{-2}{\mathrm{k}\mathrm{p}\mathrm{c}}^{-1}$) 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{k}\mathrm{m}$,$\mathrm{s}$^{-1}$.