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We present a semi-empirical, largely model-independent approach forestimating Galactic birth radii, r_birth, for Milky Way disk stars. Thetechnique relies on the justifiable assumption that a negative radialmetallicity gradient in the interstellar medium (ISM) existed for most of thedisk lifetime. Stars are projected back to their birth positions according tothe observationally derived age and [Fe/H] with no kinematical informationrequired. Applying our approach to the AMBRE:HARPS and HARPS-GTO local samples,we show that we can constrain the ISM metallicity evolution with Galacticradius and cosmic time, [Fe/H]_ISM(r, t), by requiring a physically meaningfulr_birth distribution. We find that the data are consistent with an ISM radialmetallicity gradient that flattens with time from ~-0.15 dex/kpc at thebeginning of disk formation, to its measured present-day value (-0.07 dex/kpc).We present several chemo-kinematical relations in terms of mono-r_birthpopulations. One remarkable result is that the kinematically hottest starswould have been born locally or in the outer disk, consistent with thick diskformation from the nested flares of mono-age populations and predictions fromcosmological simulations. This phenomenon can be also seen in the observedage-velocity dispersion relation, in that its upper boundary is dominated bystars born at larger radii. We also find that the flatness of the localage-metallicity relation (AMR) is the result of the superposition of the AMRsof mono-r_birth populations, each with a well-defined negative slope. The solarbirth radius is estimated to be 7.3+-0.6 kpc, for a current Galactocentricradius of 8 kpc.

Estimating stellar birth radii and the time evolution of the Milky Way's ISM metallicity gradient