We propose that the quiescent emission of AXPs/SGRs is powered by accretion from a fallback disk , requiring magnetic dipole fields in the range 10 ^ { 12 } -10 ^ { 13 } G , and that the luminous hard tails of their X-ray spectra are produced by bulk-motion Comptonization in the radiative shock near the bottom of the accretion column .
This radiation escapes as a fan beam , which is partly absorbed by the polar cap photosphere , heating it up to relatively high temperatures .
The scattered component and the thermal emission from the polar cap form a polar beam .
We test our model on the well-studied AXP 4U 0142+61 , whose energy-dependent pulse profiles show double peaks , which we ascribe to the fan and polar beams .
The temperature of the photosphere ( kT \sim 0.4 keV ) is explained by the heating effect .
The scattered part forms a hard component in the polar beam .
We suggest that the observed high temperatures of the polar caps of AXPs/SGRs , compared with other young neutron stars , are due to the heating by the fan beam .
Using beaming functions for the fan beam and the polar beam and taking gravitational bending into account , we fit the energy-dependent pulse profiles and obtain the inclination angle and the angle between the spin axis and the magnetic dipole axis , as well as the height of the radiative shock above the stellar surface .
We do not explain the high luminosity bursts , which may be produced by the classical magnetar mechanism operating in super-strong multipole fields .