2023MNRAS.526.5021W

Millisecond pulsars (MSPs) are believed to be old neutron stars that have undergone spin-up by the accreting material from the donor. However, the discovery of eccentric MSPs (eMSPs) in the Galactic field challenges such a scenario of producing MSP-white dwarf systems only in a circular orbit. As the orbital periods and companion masses of these eMSPs are located in a narrow range, it is reasonable to postulate that they have the same origin. Although many models have been proposed to interpret the origin of eMSPs, the origin of the narrow range of the orbital period is still an open question. The accretion-induced collapse (AIC) of the oxygen-neon white dwarf is considered to be an important pathway to form MSPs, as it is expected to result in the formation of MSPs in a circular orbit due to tidal circularization. Here we revisited this scenario using binary population synthesis including the specific circularization calculation. Our results indicate that binaries with insufficient circularization in this scenario can evolve into eMSPs. The narrow initial binary parameters required by insufficient circularization can naturally account for the narrow range of the orbital period. Although the evolution of the white dwarf AIC process is not yet well understood, the characteristic of a narrow range in the orbital period of eMSPs can still set constraints on the physics of their evolution.