  Galaxy hierarchical formation theories, numerical simulations, the discovery
of the Sagittarius Dwarf Elliptical Galaxy (SagDEG) in 1994 and more recent
investigations suggest that the dark halo of the Milky Way can have a rich
phenomenology containing non thermalized substructures. In the present
preliminary study, we investigate the case of the SagDEG (the best known
satellite galaxy in the Milky Way crossing the solar neighbourhood) analyzing
the consequences of its dark matter stream contribution to the galactic halo on
the basis of the DAMA/NaI annual modulation data. The present analysis is
restricted to some WIMP candidates and to some of the astrophysical, nuclear
and particle Physics scenarios. Other candidates such as e.g. the light bosonic
ones, we discussed elsewhere, and other non thermalized substructures are not
yet addressed here.

Astrophysics