Feeding zone of a planetary embryo

The region of a disk from which a planetary embryo can efficiently accrete solids. Its width depends on gravitational encounters and the surrounding orbital population. Approximating that width by a multiple of the Hill radius gives a useful local isolation mass.

The mass reached after consuming an idealized local annulus of solids. With full annular width $\Delta a=Ba[M_{\mathrm{iso}}/(3M_{\star }){]}^{1/3}$ and solid surface density ${\Sigma }_s$, the balance $M_{\mathrm{iso}}=2\pi a\Delta a{\Sigma }_s$ gives the displayed value. Radial replenishment, migration and embryo mergers can overcome local isolation; defining the width with a mutual rather than single-body Hill radius changes the numerical coefficient.