The accretion rate and minimum spin period of accreting pulsars

We consider combined rotational, magnetic, and thermal evolution of the neutron star during the accretion phase in a binary system. A rapid accretion-driven decay of the magnetic field decreases substantially the efficiency of angular momentum transfer. As a result, the neutron star cannot spin up to periods shorter than some limiting value even if accretion is very long and accretion rate is high. The proposed mechanism can explain a discrepancy between the shortest detected period and minimal possible spin period of neutron stars.