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Based on the model of the accretion-induced magnetic field decay of a neutronstar (NS), millisecond pulsars (MSPs) will obtain their minimum magnetic fieldwhen the NS magnetosphere radius shrinks to the stellar surface during thebinary accretion phase. We find that this minimummagnetic field is related tothe 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 MSPformation and is constrained by the long-term accretion time, which correspondsto the companion lifetime, being less than the Hubble time. The value of Bminis consistent with that of observed radio MSPs and accreting MSPs in low-massX-ray binaries, which can be found the illustrated case of the minimum andpresent field strength of SAX J1808.4-3658. The prediction of the minimummagnetic field of MSPs would be the lowest field strength of NSs in theUniverse, which could constrain the evolution mechanism of the magnetic fieldof accreting NSs.

monthly notices of the royal astronomical society

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