The recently discovered Virgo stellar over-density , which expands over \sim 1000deg ^ { 2 } perpendicularly to the Galactic disk plane ( 7 < Z < 15 kpc , R \sim 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 .