Estimating stellar birth radii and the time evolution of the Milky Way's
  ISM metallicity gradient
  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 ~-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+-0.6 kpc, for a current Galactocentric
radius of 8 kpc.
