  Dwarf galaxies populating the Galactic halo are assumed to host the largest
fractions of dark matter, as calculated from their velocity dispersions. Their
major axes are preferentially aligned with the Vast Polar Structure (VPOS) that
is perpendicular to the Galactic disk, and we find their velocity gradients
aligned as well. It suggests that tidal forces exerted by the Milky Way are
distorting dwarf galaxies.
  Here we demonstrate on the basis of the impulse approximation that the
Galactic gravitational acceleration induces the dwarf line-of-sight velocity
dispersion, which is also evidenced by strong dependences between both
quantities. Since this result is valid for any dwarf mass value, it implies
that dark matter estimate in Milky Way dwarfs cannot be deduced from the
product of their radius to the square of their line-of-sight velocity
dispersion. This questions the high dark-matter fractions reported for these
evanescent systems, and the universally adopted total-to-stellar mass
relationship in the dwarf regime. It suggests that many dwarfs are at their
first passage and are dissolving into the Galactic halo. It opens a promising
way to estimate the Milky Way total mass profile at large distances.
