Diffusion of radial action in a galactic disc

Context. Stellar migration of the galactic disc stars has been invoked to explain the dispersion of stellar metallicity observed in the solar neighborhood. Aims. We seek to identify the dynamical mechanisms underlying stellar migration in an isolated galaxy disc under the influence of a bar. Our approach is to analyze the diffusion of dynamical quantities. Methods. We extend our previous work by exploring Chirikov's diffusion rate (and derived timescale) of the radial action $J_\mathrm{R}$ in an idealised N$-$body simulation of an isolated disc galaxy. We limit our study to the evolution of the disc region well after the formation of the bar, in a regime of adiabatic evolution. Results. The $J_\mathrm{R}$ diffusion timescales $T_\mathrm{D}(J_\mathrm{R})$ is less than 3 Gyr for roughly half the galaxy mass. It is always much shorter than the angular momentum diffusion timescale $T_\mathrm{D}(L_\mathrm{z})$ outside the stellar bar. In the disc, $\langle T_\mathrm{D}(J_\mathrm{R}) \rangle \sim 1$ Gyr. All non-axisymmetric morphological structures characteristic of resonances and waves in the disc are associated to particles with $T_\mathrm{D}(J_\mathrm{R}) 10$ Gyr. Short $T_\mathrm{D}(J_\mathrm{R})$ can be explained by the gradual decircularisation of initially circular orbits ($J_\mathrm{R}=0$) under the effect of intermittent ILR scattering by wave trains propagating in the disc, well beyond the bar OLR. This leads to a moderate secular heating of the disc beyond the bar OLR for 7 Gyr, comparable to solar neighbourhood observations. The complex multi-wave structure, mixing permanent and intermittent modes, allows for multiple resonance overlaps.