While brown dwarfs show similarities with stars in their early life, their spin evolution is much more akin to that of planets. We have used lightcurves from the K2 mission to measure new rotation periods for 18 young brown dwarfs in the Taurus star-forming region. Our sample spans masses from 0.02 to 0.08 Msol and has been characterised extensively in the past. To search for periods, we utilize three different methods (autocorrelation, periodogram, Gaussian Processes). The median period for brown dwarfs with disks is twice as long as for those without (3.1 vs. 1.6 d), a signature of rotational braking by the disk, albeit with small numbers. With an overall median period of 1.9 d, brown dwarfs in Taurus rotate slower than their counterparts in somewhat older (3-10 Myr) star-forming regions, consistent with spin-up of the latter due to contraction and angular momentum conservation, a clear sign that disk braking overall is inefficient and/or temporary in this mass domain. We confirm the presence of a linear increase of the typical rotation period as a function of mass in the sub-stellar regime. The rotational velocities, when calculated forward to the age of the solar system assuming angular momentum conservation, fit the known spin-mass relation for solar system planets and extra-solar planetary-mass objects. This spin-mass trend holds over six orders of magnitude in mass, including objects from several different formation paths. Our result implies that brown dwarfs by and large retain their primordial angular momentum through the first few Myr of their evolution.
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