Evolution of magnetic field and spin period in accreting neutron stars

Abstract

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 accret-ing neutron star is max(1.1ms (ΔM/M ⊙) -1R 6 -5/14 I 45(M/M ⊙) -1/2, 1.1ms (M/M ⊙) -1/2 R 6 17/14) independent of the accretion rate (X-ray luminosity) but dependent on the total accretion mass, ΔM; however, the minimum magnetic field depends on the accretion rate; (3) the magnetic field strength decreases faster with time than does the period.