We present a semi-empirical , largely model-independent approach for estimating Galactic birth radii , r _ { birth } , for Milky Way disk stars .
The technique relies on the justifiable assumption that a negative radial metallicity gradient in the interstellar medium ( ISM ) existed for most of the disk lifetime .
Stars are projected back to their birth positions according to the observationally derived age and [ Fe/H ] with no kinematical information required .
Applying our approach to the AMBRE : HARPS and HARPS-GTO local samples , we show that we can constrain the ISM metallicity evolution with Galactic radius and cosmic time , [ Fe / H ] _ { ISM } ( r,t ) , by requiring a physically meaningful r _ { birth } distribution .
We find that the data are consistent with an ISM radial metallicity gradient that flattens with time from \sim - 0.15 dex/kpc at the beginning of disk formation , to its measured present day value ( -0.07 dex/kpc ) .
We present several chemo-kinematical relations in terms of mono- r _ { birth } populations .
One remarkable result is that the kinematically hottest stars would have been born locally or in the outer disk , consistent with thick disk formation from the nested flares of mono-age populations and predictions from cosmological simulations .
This phenomenon can be also seen in the observed age-velocity dispersion relation , in that its upper boundary is dominated by stars born at larger radii .
We also find that the flatness of the local age-metallicity relation ( AMR ) is the result of the superposition of the AMRs of mono- r _ { birth } populations , each with a well-defined negative slope .
The solar birth radius is estimated to be 7.3 \pm 0.6 kpc , for a current Galactocentric radius of 8 kpc .