Orbital migration and heating history of the Galactic disc: a transition between the bimodal discs
Stellar orbits in the Galactic disc evolve from their birth to the current shape through both radial migration and dynamical heating. The history of their secular evolution is imprinted in the current kinematics and age-metallicity distribution. We construct a chrono-chemo-dynamical model of the disc, incorporating inside-out growth, metallicity evolution, radial migration, and heating to fit the observed age-metallicity-kinematics distribution of LAMOST subgiant stars in both the low and high-$\alpha$ disc. By modelling all distribution parameters with spline fitting, we present the first non-parametric stellar migration and heating history of the Galaxy. We determine the heating-to-migration ratio, the ratio of the root-mean-square changes in radial/vertical and azimuthal actions, to be $\approx0.075$ for radial to azimuthal actions and $\approx0.015$ for vertical to azimuthal actions, implying a highly anisotropic diffusion in the action space. Furthermore, we identify a transition in radial migration efficiency coinciding with the transition moment of the bimodal disc, for which the radial migration was more efficient for the high-$\alpha$ disc than for the low-$\alpha$ disc. This transition may be attributed to two correlated scenarios: 1) a bar formation epoch accompanied by violent outward migration, and 2) a drop in the gas mass fraction in the disc when the low-$\alpha$ disc began to form. These findings offer further constraints on the formation mechanisms of bimodal discs, favouring the downsizing scenario. We also briefly discuss the connection between our results and recent high-redshift observations. In addition to the secular evolution history, our model maps the Milky Way ISM metallicity gradient at different lookback times, which we find has only varied a little (in the range of $-0.07~\rm to~-0.10~dex/kpc$) since disc formation.