The Shape of the Vertical Action Distribution Locates the Scatterers that Heat the Galactic Disc

Abstract

The Milky Way's stellar disc is thicker than the cold gas layer from which its stars form. What scatters stars onto orbits with greater vertical motion remains unresolved. Scatterers could fill the disc volume, as bending waves or dark substructure would, or could be confined to the midplane, as giant molecular clouds are. Scattering from a midplane layer occurs only during the fast plane-crossing phase and becomes less effective as that speed increases, whereas a volume-filling perturbation remains effective near the slow turning points. We derive the distribution of vertical action this leaves behind, for any height distribution of scatterers. The geometry turns out to enter only through the logarithmic slope of the diffusivity in action, $D\propto J_z^{b}$, and solving the Fokker-Planck equation gives $p(J_z)\propto\exp[-(J_z/J_0)^{2-b}]$. Scatterers that fill the volume give $b=1$ and an exponential, a thin layer at the midplane gives $b=1/2$ and a sharper cutoff: the shape of $p(J_z)$ records where the scatterers sit, the growth of its scale how strongly they scatter. We fit this model to 7589 low-$α$ red clump stars of Ting & Rix (2019) between 5 and 10 kpc and 2 and 8 Gyr old, leaving the heating history free. This yields $b=0.51^{+0.06}_{-0.07}$, consistent with the thin-layer prediction but not the volume-filling one. Comparing the 2-4 Gyr heating amplitude with the present molecular surface density gives an effective scatterer mass of $2.7\times10^{6}\,M_\odot$. Older stars have experienced more of the Galaxy's gas-richer past; correcting for that history brings all four age bins to $(1.9-2.8)\times10^{6}\,M_\odot$, inside the range cloud catalogues and mass functions give. The Milky Way's disc is heated near the plane, by an evolving population of objects of giant-molecular-cloud mass.