Evolution of magnetic field and spin period in accreting neutron stars

Based on the accretion-induced magnetic field decay model, in which a froze n field and an incompressible fluid are assumed, we obtain the following re sults: (1) an analytic relation between the magnetic field and spin period, if the fastness parameter of the accretion disk is neglected (The evolutio nary 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 fastn ess parameter is taken into account.); (2) the theoretical minimum spin per iod of an accreting neutron star is max(1.1ms (DeltaM/M-circle dot)R--1(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; howe ver, the minimum magnetic field depends on the accretion rate; (3) the magn etic field strength decreases faster with time than does the period.