2018ApJ...869..155S

The X-ray afterglow plateau emission observed in many gamma-ray bursts (GRBs) has been interpreted as being fueled either 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 reproduced analytically. We fit a sample of GRB X-ray plateaus, interestingly yielding a distribution in the diagram of magnetic field versus spin period (B-P) consistent with B ∝ P^7/6, which is consistent with GRB expectations of the well-established physics of the spin-up line for accreting Galactic X-ray pulsars. The normalization of the relation that we obtain perfectly matches spin-up line predictions for typical neutron star masses (∼1 M_☉) and radii (∼10 km), and for mass accretion rates typically expected in GRBs, 10^–4M_☉s^–1< {dot}M< 10^–1M_☉s^–1. Short GRBs with extended emission (SEEs) appear toward the long-period end of the distribution, and long GRBs (LGRBs) toward the short-period end. This result is consistent with expectations from the spin-up limit, where the total accreted mass determines the position of the neutron star in the B-P diagram. The B-P distributions for LGRBs and SEEs are statistically different, further supporting the idea that the fundamental plane relation-a tri-dimensional correlation between the X-ray luminosity at the end of the plateau, the end time of the plateau, and the 1 s peak luminosity in the prompt emission-is a powerful discriminant among those populations. Our conclusions are robust against suppositions regarding the collimation angle of the GRB and the magnetar braking index, which shift the resulting properties of the magnetar parallel to the spin-up line, and strongly support a magnetar origin for GRBs presenting X-ray plateaus.