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 ultramagnetized 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 s (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 timescale of the order of 104 yr.