plane with a typical density of less than 3 stars per $0.5 \times 0.5 \rm (km~s^{-1})^2$. Such a flat distribution is fully consistent with the broad velocity dispersion of Galactic field stars. On the other hand, the velocity distribution of the young stars shows an impressive overdensity with a peak at with a maximum of more than 150 stars per $0.5 \times 0.5 \rm (km~s^{-1})^2$. This over-density is a strong signature for an autonomous coherent group consisting essentially of stars younger than about 40 Myr (Fig. \[HRDnew\_fig3.pdf\]).

In Fig. \[V\_par\_sen\_young\] we define this group by manually cutting the stars falling into the peak mentioned above. Indeed they are populating the bins at a level of more than 30 N$_{Stars}$. This cut is indicated by contour lines and the selected sample contains 1844 objects. We call this sample the Crux Moving Group (CMG) henceforth.

In the following discussion we use barycentric Galactic Cartesian coordinates $X, Y, Z$ instead of the equatorial coordinates as before. The axes $X, Y, Z$ are directed to the Galactic center, the direction of Galactic rotation and to the Galactic north pole, respectively. The corresponding velocity coordinates are $U, V, W$. When we compare both samples, we 