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

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 angular velocity. In a qualitative difference from vertically-averaged models -- where spin down can co-exist with mass accretion -- we observe \emph{decretion} accompanying solutions where angular momentum is being lost. The critical spin rate depends upon the disk thickness near the planet. For an isothermal system with a disk scale height of $h/r = 0.15$ near the planet, the critical spin rate drops to between 60\% and 70\% of the planet's breakup angular velocity. In the disk outside the boundary layer, we identify meridional circulation flows, which are unsteady and instantaneously asymmetric across the mid-plane. The simulated flows are strong enough to vertically redistribute solid material in early-stage satellite formation. We discuss how extrasolar planetary rotation measurements, when combined with spectroscopic and variability studies of protoplanets with circumplanetary disks, could determine the role of magnetic and non-magnetic processes in setting giant planet spins.