The influence of interior structure and thermal state on impact melt generation upon large impacts onto terrestrial planets

We investigate the melt production of planetary impacts as a function of planet size ($R/R_\mathrm{Earth}$=0.1-1.5), impactor size ($L$=1-1000 km), and core size ratio ($R_\mathrm{core}/R$=0.2-0.8) using a combination of parameterized convection models and fully dynamical 2D impact simulations. To this end, we introduce a new method to determine impact-induced melt volumes which we normalize by the impactor volume for better comparability. We find that this normalized melt production, or melting efficiency, is enhanced for large planets when struck by smaller impactors, while for small planets, melting efficiency is elevated when impacted by larger impactors. This diverging behavior can be explained by the thickness of the planets' thermal boundary layer and the shapes of their thermal and lithostatic pressure profiles. We also find that melting efficiency maxima are usually highest on Earth-size planets. We show that the melting efficiency is only affected by core size ratio for large cores and older planets, where melt production is decreased significantly compared to smaller core size ratios. Projecting the lunar impactor flux on the generic planets, we find that Moon-sized planets produce the most melt throughout their evolution, relative to planet volume. Contrary to previous scaling laws, our method accounts for melt production by decompression or plastic work in addition to shock melting. We find that traditional scaling laws underestimate melt production on length scales where variations in the target planets' lithology, temperature, and lithostatic pressure become significant. We propose empirical formulas to predict melt generation as a function of radial structure and thermal age.