The minimum magnetic field of millisecond pulsars calculated according to accretion: application to the X-ray neutron star SAX J1808.4-3658 in a low-mass X-ray binary

Based on the model of the accretion-induced magnetic field decay of a neutron star (NS), millisecond pulsars (MSPs) will obtain their minimum magnetic field when the NS magnetosphere radius shrinks to the stellar surface during the binary accretion phase. We find that this minimummagnetic field is related to the accretion rate Mdot as Bmin ~2.0*10^7 G( Mdot/Mdot_min)^1/2, where Mdot_min = 4.6*10^15 g/s is the average minimum accretion rate required for MSP formation and is constrained by the long-term accretion time, which corresponds to the companion lifetime, being less than the Hubble time. The value of Bmin is consistent with that of observed radio MSPs and accreting MSPs in low-mass X-ray binaries, which can be found the illustrated case of the minimum and present field strength of SAX J1808.4-3658. The prediction of the minimum magnetic field of MSPs would be the lowest field strength of NSs in the Universe, which could constrain the evolution mechanism of the magnetic field of accreting NSs.