Study of observed spin evolution of long-period X-ray pulsars challenges quasi-spherical and Keplerian disk accretion scenarios. It suggests that the magnetospheric radius of the neutron stars is substantially smaller than Alfvén radius and the spin-down torque applied to the star from accreting material significantly exceeds the value predicted by the theory. We show that these problems can be avoided if the fossil magnetic field of the accretion flow itself is incorporated into the accretion model. The initially spherical flow in this case decelerates by its own magnetic field and converts into a non-Keplerian disk (magnetic slab) in which the material is confined by its intrinsic magnetic field ("levitates") and slowly moves towards the star on a diffusion timescale. Parameters of pulsars expected within this magneto-levitation accretion scenario are evaluated.
Fallback Accretion Model for the Years-to-decades X-Ray Counterpart to GW170817