The individual abundance distributions of disc stars across birth radii in GALAH

Individual abundances in the Milky Way disc record stellar birth properties [e.g. age, birth radius (R-birth)], and capture the diversity of the star-forming environments over time. Assuming an analytical relationship between ([Fe/H], [alpha/Fe]), and R-birth, we examine the distributions of individual abundances [X/Fe] of elements C, O, Mg, Si, Ca (alpha), Al (odd-z), Mn (iron-peak), Y, and Ba (neutron-capture) for stars in the Milky Way. We want to understand how these elements might differentiate environments across the disc. We assign tracks of R-birth in the [alpha/Fe] versus [Fe/H] plane as informed by expectations from simulations for similar to 59 000 GALAH stars in the solar neighborhood (R similar to 7-9 kpc) which also have inferred ages. Our formalism for R-birth shows that older stars (similar to 10 Gyrs) have an R-birth distribution with smaller mean values (i.e. $\bar{R}_{\mbox{birth}} \sim 5\pm 0.8$ kpc) compared to younger stars (similar to 6 Gyrs; $\bar{R}_{\mbox{birth}} \sim 10\pm 1.5$ kpc), for a given [Fe/H], consistent with inside-out growth. The alpha-, odd-z, and iron-peak element abundances decrease as a function of R-birth, whereas the neutron-capture abundances increase. The R-birth-[Fe/H] gradient we measure is steeper compared to the present-day gradient (-0.066 dex kpc(-1) versus -0.058 dex kpc(-1)), which we also find true for R-birth-[X/Fe] gradients. These results (i) showcase the feasibility of relating the birth radius of stars to their element abundances, (ii) demonstrate that the Milky Way abundance gradients across R-birth have evolved to be shallower over time, and (iii) offer an observational comparison to element abundance distributions in hydrodynamical simulations.