Boundary Layer Circumplanetary Accretion: How Fast Could an Unmagnetized Planet Spin Up through Its Disk?

Abstract

Abstract Gas giant planets are expected to accrete most of their mass via a circumplanetary disk. If the planet is unmagnetized and initially slowly rotating, it will accrete gas via a radially narrow boundary layer and rapidly spin up. Radial broadening of the boundary layer as the planet spins up reduces the specific angular momentum of accreted gas, allowing the planet to find a terminal rotation rate short of the breakup rate. Here, we use axisymmetric viscous hydrodynamic simulations to quantify the terminal rotation rate of planets accreting from their circumplanetary disks. For an isothermal planet-disk system with a disk scale height h/r = 0.1 near the planetary surface, spin-up switches to spin-down at between 70% and 80% of the planet’s breakup rate. In a qualitative difference from vertically averaged models—where spin-down can coexist with mass accretion—we observe decretion accompanying solutions where angular momentum is being lost. The critical spin rate depends upon the disk thickness near the planet. For a disk scale height of h/r = 0.15, the critical spin rate drops to between 60% and 70% of the planet’s breakup rate. In the disk outside the boundary layer, we identify meridional circulation flows, which are unsteady and instantaneously asymmetric across the midplane. The simulated flows are strong enough to vertically redistribute solid material in early stage satellite formation. We discuss how exoplanetary rotation measurements, when combined with spectroscopic and variability studies of protoplanets with circumplanetary disks, could determine the role of magnetic and nonmagnetic processes in setting planet spins.