  We derive the distribution of the phantom dark matter in the eight classical
dwarf galaxies surrounding the Milky Way, under the assumption that modified
Newtonian dynamics (MOND) is the correct theory of gravity. According to their
observed shape, we model the dwarfs as axisymmetric systems, rather than
spherical systems, as usually assumed. In addition, as required by the
assumption of the MOND framework, we realistically include the external
gravitational field of the Milky Way and of the large-scale structure beyond
the Local Group. For the dwarfs where the external field dominates over the
internal gravitational field, the phantom dark matter has, from the star
distribution, an offset of ~0.1-0.2 kpc, depending on the mass-to-light ratio
adopted. This offset is a substantial fraction of the dwarf half-mass radius.
For Sculptor and Fornax, where the internal and external gravitational fields
are comparable, the phantom dark matter distribution appears disturbed with
spikes at the locations where the two fields cancel each other; these features
have little connection with the distribution of the stars within the dwarfs.
Finally, we find that the external field due to the large-scale structure
beyond the Local Group has a very minor effect. The features of the phantom
dark matter we find represent a genuine prediction of MOND, and could thus
falsify this theory of gravity in the version we adopt here if they are not
observationally confirmed.
