The end of runaway: How gap opening limits the final masses of gas giants

Gas giants are thought to form by runaway accretion: An instability driven by the self-gravity of growing atmospheres that causes accretion rates to rise superlinearly with planet mass. Why runaway should stop at a Jupiter or any other mass is unknown.We consider the proposal that final masses are controlled by circumstellar disc gaps (cavities) opened by planetary gravitational torques.We develop a fully time-dependent theory of gap formation and couple it self-consistently to planetary growth rates.When gaps first open, planetary torques overwhelm viscous torques, and gas depletes as if it were inviscid. In low-viscosity discs, of the kind motivated by recent observations and theory, gaps stay predominantly in this inviscid phase and planet masses finalize at Mfinal/M⊙ ∼ (Ωtdisc)0.07(H/a)2.73(Gρ0/Ω2)1/3, with M∗ the host stellar mass, Ω the planet's orbital angular velocity, tdisc the gas disc's lifetime, H/a its aspect ratio, and ρ0 its unperturbed density. This final mass is independent of the dimensionless viscosity α and applies to large orbital distances, typically beyond ∼10 au, where disc scale heights exceed planet radii. It evaluates to a few Jupiter masses at 10-100 au, increasing gradually with distance as gaps become harder to open.