On the Evolution of Anomalous X-ray Pulsars and Soft Gamma-ray Repeaters with Fall Back Disks

We show that the period clustering of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs), their X-ray luminosities, ages, and statistics can be explained with fall back disks with large initial specific angular momentum. The disk evolution models are developed by comparison to self-similar analytical models. The initial disk mass and angular momentum set the viscous timescale. An efficient torque, with (1 - Delta *w2 *) dependence on the fastness parameter Delta *w*, leads to period clustering in the observed AXP-SGR period range under a wide range of initial conditions. The timescale t 0 for the early evolution of the fall back disk, and the final stages of fall back disk evolution, when the disk becomes passive, are the crucial determinants of the evolution. The disk becomes passive at temperatures around 100 K, which provides a natural cutoff for the X-ray luminosity and defines the end of evolution in the observable AXP and SGR phase. This low value for the minimum temperature for active disk turbulence indicates that the fall back disks are active up to a large radius, 1012 cm. We find that transient AXPs and SGRs are likely to be older than their persistent cousins. A fall back disk with mass transfer rates corresponding to the low quiescent X-ray luminosities of the transient sources in early evolutionary phases would have a relatively lower initial mass, such that the mass-flow rate in the disk is not sufficient for the inner disk to penetrate into the light cylinder of the young neutron star, making mass accretion onto the neutron star impossible. The transient AXP phase therefore must start later. The model results imply that the transient AXP/SGRs, although older, are likely to be similar in number to persistent sources. This is because the X-ray luminosities of AXPs and SGRs are found to decrease faster at the end of their evolution, and the X-ray luminosities of transient AXP and SGRs in quiescence lie in the luminosity range of X-ray cutoff phase. Taking the range of quiescent X-ray luminosities of transient AXPs and SGRs ~1033-1034 erg s-1, our simulations imply that the duration of the cutoff phase is comparable to the lifetime in the persistent phase for a large range of initial conditions.