A balanced budget view on forming giant planets by pebble accretion

Abstract

Pebble accretion refers to the assembly of rocky planet cores from particles whose velocity dispersions are damped by drag from circumstellar disc gas. Accretion cross-sections can approach maximal Hill-sphere scales for particles whose Stokes numbers approach unity. While fast, pebble accretion is also lossy. Gas drag brings pebbles to protocores but also sweeps them past; those particles with the largest accretion cross-sections also have the fastest radial drift speeds and are the most easily drained out of discs. We present a global model of planet formation by pebble accretion that keeps track of the disc's mass budget. Cores, each initialized with a lunar mass, grow from discs whose finite stores of mm-cm sized pebbles drift inward across all radii in viscously accreting gas. For every 1 $M_\oplus$ netted by a core, at least 10 $M_\oplus$ and possibly much more are lost to radial drift. Core growth rates are typically exponentially sensitive to particle Stokes number, turbulent Mach number, and solid surface density. This exponential sensitivity, when combined with disc migration, tends to generate binary outcomes from 0.1-30 AU: either sub-Earth cores remain sub-Earth, or explode into Jupiters, with the latter migrating inward to varying degrees. When Jupiter-breeding cores assemble from mm-cm sized pebbles, they do so in discs where such particles drain out in $\sim$10$^5$ yr or less; such fast-draining discs do not fit mm-wave observations.