  The Local Group is a unique environment in which to study the astrophysics of
galaxy formation. The proximity of the Milky Way and M31 enhances the frequency
of interactions of the low-mass halo population with more massive dark matter
haloes, which increases their concentrations and strips them of gas and other
material. Some low-mass haloes pass through the haloes of the Milky Way or M31
and are either ejected into the field or exchanged between the two primary
hosts. We use high resolution gas-dynamical simulations to describe a new class
of field haloes that passed through the haloes of both the Milky Way and M31 at
early times and are almost twice as concentrated as field haloes that do not
interact with the primary pair. These 'Hermeian' haloes are distributed
anisotropically at larger distances from the Local Group barycentre than the
primary haloes and appear to cluster along the line connecting the Milky Way
and M31. Hermeian haloes facilitate the exchange of dark matter, gas, and stars
between the Milky Way and M31 and can enhance the star formation rate of the
gas in the primary haloes during their interactions with them. We also show
that some Hermeian haloes can host galaxies that, because they are embedded in
haloes that are more concentrated than regular field haloes, are promising
targets for indirect dark matter searches beyond the Milky Way virial radius
and can produce signals that are competitive with those of some dwarf galaxies.
Hermeian galaxies in the Local Group should be detectable by forthcoming
wide-field imaging surveys.
