Feeding on Pebble Rain: Accretion Rates and Core Growth Times for Embryos at 5 and 10 AU

Once a planetesimal is large enough, it grows not by colliding with its peers but by sweeping up the pebbles that drift past it — pebble accretion, the fastest growth mode known in discs. This paper computes the rates in the two-dimensional Hill regime for pebbles of Stokes number 0.1 in a reference disc. An Earth-mass embryo at 5 AU accretes 4 Earth masses per million years, a mass-doubling time of 0.25 Myr; a hundredth of an Earth mass accretes 0.2 Earth masses per Myr with a doubling time of 0.05 Myr. Integrating the mass-dependent rate, an embryo grows from 0.1 to 10 Earth masses in about 2.3 Myr at 5 AU and 3.3 Myr at 10 AU — inside the characteristic disc lifetime at 5 AU, and comparable to that lifetime at 10 AU. The integrated demand on the pebble supply is a few hundred Earth masses over the growth, comparable to the total solid inventory the disc can deliver, so pebble accretion is fast enough to build giant-planet cores and hungry enough to explain why not every disc does. Computed from stated assumptions, not measured; the disc densities involved sit at 1.7e-66 of the gravitational frame's ceiling.