Orbital param. of the MW thick-disk giant stars

The vertical and perpendicular angular momentum components, LZ and LP, of the MAPs in narrow bins have significant variations across the [{alpha}/M]-[M/H] plane. LZ and LP systematically change with [M/H] and [{alpha}/M] and can be alternatively quantified by the chemical gradients: d[M/H]/dLZ=1.2x10^-3^dex/kpc/km.s, d[M/H]/dLP=-5.0x10^-3^dec.kpc^-1^.km^-1^.s, and d[{alpha}/M]/dLZ=-3.0x10^-4^dex.kpc^-1^.km^-1^.s, d[{alpha}/M]/dLP=1.2x10^-3^dec.kpc^-1^.km^-1^.s.

These correlations can also be explained as the chemical dependence of the spatial distribution shape of the MAPs. We also exhibit the corresponding age dependence of the angular momentum components. Under the assumption that the guiding radius (Rg) is proportional to LZ, this provides direct observational evidence of the inside-out structure formation scenario of the thick disk, with dRg/dAge=-1.9kpc/Gyr.