The recently discovered Virgo stellar over-density, which expands over ~1000deg^2 perpendicularly to the Galactic disk plane (7< Z <15 kpc, R~7 kpc), is the largest clump of tidal debris ever detected in the outer halo and is likely related with the accretion of a nearby dwarf galaxy by the Milky Way. We carry out N-body simulations of the Sagittarius stream to show that this giant stellar over-density is a confirmation of theoretical model predictions for the leading tail of the Sagittarius stream to cross the Milky Way plane in the Solar neighborhood. Radial velocity measurements are needed to confirm this association and to further constrain the shape of the Milky Way dark matter halo through a new generation of theoretical models. If the identification of Virgo over-density and the Sagittarius leading arm is correct, we predict highly negative radial velocities for the stars of Virgo over-density. The detection of this new portion of the Sagittarius tidal stream would represent an excellent target for the on-going and future kinematic surveys and for dark matter direct detection experiments in the proximity of the Sun.
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