Implications of the Narrow Period Distribution of Anomalous X‐Ray Pulsars and Soft Gamma‐Ray Repeaters

The spin periods of the ten observed Anomalous X-ray Pulsars and SoftGamma-ray Repeaters lie in the very narrow range 6-12 s. We use a pointlikelihood technique to assess the constraints this clustering imposes on thebirth period and on the final period of such systems. We consider a general lawfor their spin evolution described by a constant braking index. We find that,for positive values of the braking index, the observed clustering requires anupper cut-off period that is very close to the maximum observed period of about12 s. We also show that the constraint on the birth period depends verystrongly on the assumed value of the braking index n, ranging from a fewmilliseconds for n>2 to a few seconds for n<2. We discuss the possible ways oftightening these constraints based on similarities with the population of radiopulsars and with future observations of such sources with current X-rayobservatories.Comment: Submitted to ApJ Letter