The Period Clustering of Magnetars and X-ray Dim Isolated Neutron Stars

The spin periods of magnetars and X-ray dim isolated neutron stars (XDINS) cluster within a remarkably narrow range. Using the current sample of 30 magnetars with measured periods (ranging from 0.33 to 11.78 s) and 8 XDINS (ranging from 3.45 to 12.76 s), we utilize the point-likelihood technique to constrain the birth and final periods of these sources, assuming a steady-state population. Employing a general braking law characterized by a constant braking index 𝑛, we find that for 𝑛 > 2 the final (cut-off) period of magnetars is constrained to 𝑃f ≃ 11.8 − 12.0 s and XDINS to 𝑃f ≃ 12.8 − 14.9 s, at the 95 per cent confidence level, while the birth periods remain largely unconstrained for dipole spin-down (𝑛 = 3) as in earlier work. The slight increase in the upper cutoff from ∼12to∼15sovertwodecadesofdiscoveries of new sources yielding a threefold increase in the known magnetar population and the extension of the minimum period to ∼ 0.33 s strongly support a physical origin for this clustering. We discuss this result in the context of magnetic-field-decay models and fallback-disc torque-equilibrium scenarios. The combined magnetar and XDINS sample (38 sources) yields the tightest constraints on 𝑃f ≃ 12.8 − 12.9 s, for 𝑛 = 3, suggesting possible evolutionary connections between these populations and pointing toward a common physical mechanism that terminates the observable phase of these neutron stars at periods near 15 s.