Asteroidal core growth by crustal sinking ($b^3-b_0^3\sim 3R^2{J}_s(t-t_0)$)

At zero liquid superheat, dense solid released by viscous overturn of a dense crust can sink and remain solid. For a thin crust on an asteroid of fixed radius $R$, efficient deposition and the equal-density volume approximation give $b^3-b_0^3=3R^2{J}_s(t-t_0)$. If surface gravity scales as $R$, the crustal flux scales as $R^{1/3}$ and the core radius as $R^{7/9}{t}^{1/3}$. The approximation ends when remaining liquid is exhausted or the renewed crust is no longer thin.