Breaking the centrifugal barrier to giant planet contraction by magnetic disc braking

During the runaway phase of their formation, gas giants fill their gravitational spheres of influence out to Bondi or Hill radii. When runaway ends, planets shrink several orders of magnitude in radius until they are comparable in size to present-day Jupiter; in 1D models, the contraction occurs on the Kelvin-Helmholtz time-scale t_KH, which is initially a few thousand years. However, if angular momentum is conserved, contraction cannot complete, as planets are inevitably spun up to their breakup periods P_break. We consider how a circumplanetary disc (CPD) can de-spin a primordially magnetized gas giant and remove the centrifugal barrier, provided the disc is hot enough to couple to the magnetic field, a condition that is easier to satisfy at later times. By inferring the planet's magnetic field from its convective cooling luminosity, we show that magnetic spin-down times are shorter than contraction times throughout post-runaway contraction: t_mag/t_KH ∼(P_break/t_KH)^1/21 ≲ 1. Planets can spin-down until they corotate with the CPD's magnetospheric truncation radius, at a period P_max/P_break ∼(t_KH/P_break)^1/7. By the time the disc disperses, P_max/P_break ∼20-30; further contraction at fixed angular momentum can spin planets back up to ∼10P_break, potentially explaining observed rotation periods of giant planets and brown dwarfs.