The Relation between the Magnetic Field and Spin Period of a Millisecond Pulsar

Based on the function of the accretion induced magnetic decay, the analytical relationship between the magnetic field B and spin period P of a millisecond pulsar (MSP) is investigated, from which the minimum spin period of about one millisecond can be obtained. With this minimum spin period, the range of the neutron star (NS) radius is constrained in comparison with the measured spin period of MSP. Furthermore, we also study the relation between the spin period and the accretion mass ΔM of the NS, and find that the minimum spin period is achieved with the accretion mass of about ～0.2M_?, while the bottom magnetic field of about 10⁸ G is obtained.