Primordial planet spin driven by boundary layer effects in a decretion disc

Abstract

Accretion of material from a protoplanetary disc on to a forming giant planet can spin the planet up to close to its breakup rate, $\Omega_{\rm b}=(G M_{\rm p}/R_{\rm p}^3)$, where $M_{\rm p}$ is the mass and $R_{\rm p}$ is the radius of the planet. After the protoplanetary disc dissipates, the rapidly rotating planet may eject a decretion (outflowing) disc in a similar way to a Be star. Boundary layer effects in a hydrodynamic disc allow for decretion disc formation at spin rates below the breakup spin rate of the planet. The decretion disc exerts a torque on the planet that slows its spin to an equilibrium value that is sensitive to the planet temperature. By considering steady state circumplanetary decretion disc solutions, we show that the equilibrium spin rate for planets is around $0.4\,\Omega_{\rm b}$ for $H/R=0.2$ and around $0.2\,\Omega_{\rm b}$ for $H/R=0.3$, where $H$ is the disc scale height at radius $R$. These values are in line with the spins of the giant planets in the solar system and observed exoplanet spins.