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

We present a semi-empirical, largelymodel-independent approach for estimatingGalactic birth radii, rbirth, for Milky Way disc stars. The technique relies on the justifiable assumption that a negative radial metallicity gradient in the interstellar medium (ISM) existed for most of the disc 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 rbirth distribution. We find that the data are consistent with an ISM radial metallicity gradient that flattens with time from ~- 0.15 dex kpc-1 at the beginning of disc formation, to its measured present-day value (-0.07 dex kpc-1). We present several chemokinematical relations in terms of mono-rbirth populations. One remarkable result is that the kinematically hottest stars would have been born locally or in the outer disc, consistent with thick disc 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-rbirth populations, each with a well-defined negative slope. The solar birth radius is estimated to be 7.3 ± 0.6 kpc, for a current Galactocentric radius of 8 kpc.