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

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 formed black hole, or by the spin-down luminosity of an ultra-magnetized millisecond neutron star. If the latter model is assumed, GRB X-ray afterglow light curves can 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 the well-established physics of the spin-up line minimum period for Galactic millisecond pulsars. The normalisation of the relation we obtain perfectly matches spin-up line predictions for the expected masses ($\sim 1 M_{\odot}$) and radii ($\sim 10 {\rm ~km}$) of newly born magnetars, and mass accretion rates 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) appear towards the high period end of the distribution, while the long GRBs (LGRBs) towards the short period end. This result is consistent with spin-up limit expectations where the total accreted mass determines the position of the neutron star in the B-P diagram. The P-B distribution for LGRBs and SEE are statistically different, further supporting the idea that the fundamental plane relation \citep{dainotti16c,Dainotti2017} is a powerful discriminant among those populations. Our conclusions are robust against suppositions regarding the GRB collimation angle and magnetar breaking index, which shifts the resulting magnetar properties parallel to the spin-up line, and strongly support a magnetar origin for GRBs presenting X-ray plateaus.