Evolution of magnetic field and spin period in accreting neutron stars

Based on the accretion-induced magnetic field decay model, in which a frozen field and an incompressible fluid are assumed, we obtain the following results: (1) an analytic relation between the magnetic field and spin period, if the fastness parameter of the accretion disk is neglected (The evolutionary tracks of accreting neutron stars in the P-B diagram in our model are different from the equilibrium period lines when the influence of the fastness parameter is taken into account.); (2) the theoretical minimum spin period of an accreting neutron star is max(1.1ms (DeltaM/M(circle dot))(-1)R(6)(-5/14) I(45)(M/M(circle dot))(-1/2),1.1ms (M/M(circle dot))(-1/2) R(6)(17/14)), independent of the accretion rate (X-ray luminosity) but dependent on the total accretion mass, DeltaM; however, the minimum magnetic field depends on the accretion rate; (3) the magnetic field strength decreases faster with time than does the period.