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The X-ray afterglow plateau emission observed in many Gamma-ray Bursts (GRBs)has been interpreted as either being fueled by fallback onto a newly formedblack hole, or by the spin-down luminosity of an ultra-magnetized millisecondneutron star. If the latter model is assumed, GRB X-ray afterglow light curvescan be analytically reproduced. We fit a sample of GRB X-ray plateaus,interestingly yielding a distribution in the magnetic field versus spin period(B-P) diagram consistent with $B\propto P^{7/6}$. This is expected from thewell-established physics of the spin-up line minimum period for Galacticmillisecond pulsars. The normalisation of the relation we obtain perfectlymatches spin-up line predictions for the expected masses ($\sim 1 M_{\odot}$)and radii ($\sim 10 {\rm ~km}$) of newly born magnetars, and mass accretionrates consistent with GRB expectations of $10^{-4} M_{\odot}/{\rm s} <\dot{M}<10^{-1} M_{\odot}/{\rm s}$. Short GRBs with extended emission (SEE) appeartowards the high period end of the distribution, while the long GRBs (LGRBs)towards the short period end. This result is consistent with spin-up limitexpectations where the total accreted mass determines the position of theneutron star in the B-P diagram. The P-B distribution for LGRBs and SEE arestatistically different, further supporting the idea that the fundamental planerelation \citep{dainotti16c,Dainotti2017} is a powerful discriminant amongthose populations. Our conclusions are robust against suppositions regardingthe GRB collimation angle and magnetar breaking index, which shifts theresulting magnetar properties parallel to the spin-up line, and stronglysupport a magnetar origin for GRBs presenting X-ray plateaus.

On the magnetar origin of the GRBs presenting X-ray afterglow plateaus