The Evolution of Magnetic Field and Spin Period of Accreting Neutron Stars

Based on the accretion induced magnetic a 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 $\max (1.1{\rm ms}(\frac{\Delta M}{M_{\odot}})^{-1} R^{-5/14}6 I{45}(\frac{M}{M_{\odot}})^{-1/2}, 1.1{\rm ms} (\frac{M}{M_{\odot}})^{-1/2} R^{17/14}_6)$, independent of the accretion rate (X-ray luminosity) but dependent on the total accretion mass $\mathrm{\Delta }M$. However, the minimum magnetic field depends on the accretion rate. (3) The magnetic field strength decreases faster with time than the period.