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.

Figures (7)

• Figure 1: Spin-period distribution of the current magnetar and X-ray dim isolated neutron stars (XDINS; "Magnificent Seven") samples on a logarithmic axis. The blue and orange coloured histograms represent the magnetar and XDINS populations, respectively. The bin edges are obtained by Sturges' rule. Smooth kernel density estimates (KDEs) are overlaid for each population and for the total sample (38 sources; solid black curve). Short colored tick marks ("rugs") indicate individual period measurements, with colors matching their respective populations. The current magnetar sample extends to shorter periods ($P \simeq 0.33$ s) than that of PM02 while the maximum period remains at $\sim 12$ s as they have found.
• Figure 2: Posterior probability distributions for the initial period $P_{\rm i}$ (dashed line) and final period $P_{\rm f}$ (solid line) for magnetars, assuming dipole spin-down ($n = 3$). The shaded region indicates the observed period range. (Left panel) The original 10-magnetar sample to reproduce the analysis of PM02. (Right panel) for the current sample of 30 magnetars. The broader period range ($0.33-11.78$ s) provides somewhat tighter constraints on both $P_{\rm i}$ and $P_{\rm f}$.
• Figure 3: Posterior probability distributions for the initial period $P_{\rm i}$ (dashed line) and final period $P_{\rm f}$ (solid line) for the XDINS sample (8 sources) and the combined magnetar and XDINS sample (38 sources).
• Figure 4: Confidence levels (68, 90, and 95 per cent) for the initial period $P_{\rm i}$ (lower region) and final period $P_{\rm f}$ (upper region) as functions of the braking index $n$. The horizontal grey band indicates the observed period range. The vertical dashed line marks the dipole value $n = 3$. (Left panel) is for the original 10-magnetar sample of PM02 to reproduce their Figure 2. (Right panel) is for the current sample of 30 magnetars. The extended period range to shorter values provides tighter constraints on $P_{\rm i}$ for $n > 2$.
• Figure 5: Same as \ref{['fig:confidence_magnetar']}, but for the XDINS sample (left panel) and the combined magnetar and XDINS sample (right panel).