Fallback Disks, Magnetars and Other Neutron Stars
  The presence of matter with angular momentum, in the form of a fallback disk around a young isolated neutron star will determine its evolution. This leads to an understanding of many properties of different classes of young neutron stars, in particular a natural explanation for the period clustering of AXPs, SGRs and XDINs. The spindown or spinup properties of a neutron star are determined by the dipole component of the magnetic field. The natural possibility that magnetars and other neutron stars may have different strengths of the dipole and higher multipole components of the magnetic field is now actually required by observations on the spindown rates of some magnetars. This talk gives a broad overview and some applications of the fallback disk model to particular neutron stars. Salient points are: (i) A fallback disk has already been observed around the AXP 4U 0142+61 some years ago. (ii) The low observed spindown rate of the SGR 0418+5729 provides direct evidence that the dipole component of the field is in the $10^{12} G$ range. All properties of the SGR 0418+5729 at its present age can be explained by spindown under torques from a fallback disk. (iii) The anomalous braking index of PSR J1734-3333 can also be explained by the fallback disk model which gives the luminosity, period, period derivative and the period second derivative at the present age. (iv) These and all applications to a variety of other sources employ the same disk physics and evolution, differing only in the initial conditions of the disk. 
M. Ali Alpar, S. Caliskan and U. Ertan
astro-ph.HE