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 can not 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 } \sim ( P _ { break } / t _ { KH } ) ^ { 1 / 21 } \lesssim 1 .
Planets can spin down until they corotate with the CPD ’ s magnetospheric truncation radius , at a period P _ { max } / P _ { break } \sim ( t _ { KH } / P _ { break } ) ^ { 1 / 7 } .
By the time the disc disperses , P _ { max } / P _ { break } \sim 20–30 ; further contraction at fixed angular momentum can spin planets back up to \sim 10 P _ { break } , potentially explaining observed rotation periods of giant planets and brown dwarfs .