The period clustering of magnetars and X-ray dim isolated neutron stars

Abstract

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 $P_f \simeq 11.8 - 12.0$ s and XDINS to $P_f \simeq 12.8 - 14.9$ s, at the 95 per cent confidence level, while the birth periods remains largely unconstrained for dipole spin-down ($n=3$) as in earlier work. The slight increase in the upper cutoff from $\sim$12 to $\sim$15 s over two decades of discoveries of new sources, yielding a threefold increase in the known magnetar population, and the extension of the minimum period to $\sim 0.33$ 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 $P_f\simeq 12.8-12.9$ 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 14 s.