Period clustering of the Anomalous X-ray Pulsars and magnetic field decay in magnetars

We confront theoretical models for the rotational, magnetic, and thermal evolution of an ultra-magnetized neutron star, or magnetar, with available data on the Anomalous X-ray Pulsars (AXPs). We argue that, if the AXPs are interpreted as magnetars, their clustering of spin periods between 6 and 12 seconds, observed at present in this class of objects, their period derivatives, their thermal X-ray luminosities, and the association of two of them with young supernova remnants, can only be understood globally if the magnetic field in magnetars decays significantly on a time scale of the order of 10^4 years.