Exploring the accretion-induced evolution of the spin period and magnetic field strength of Be/X-ray Pulsars

Based on the detected spin periods ($P$) and inferred magnetic field strengths ($B$) by the cyclotron resonance scattering features, we analyze the $B-P$ properties of Be/X-ray Pulsars (BeXPs). We find that the $P$ distribution of BeXPs exhibits a bimodal feature separated at $P\sim 40$ s, where the average spin period of the BeXPs with $P>40$ s ($⟨P⟩\sim 267$ s) is larger than that of the sources with $P<40$ s ($⟨P⟩\sim 10$ s) by about one magnitude of order. Meanwhile, the average magnetic field strength of the long period BeXPs ($⟨B⟩\sim 4.9\times {10}^{12}$ G) is higher than that of the short period sources ($⟨B⟩\sim 2.7\times {10}^{12}$ G) by a factor of $\sim 2$. We try to explain these phenomena by the accretion-induced evolution process, and find that for the neutron star (NS) with the initial magnetic field strength of $B_0\sim {10}^{12.2}-{10}^{13}$ G, when it accretes about $\Delta M\sim {10}^{-6.5}{M}_{\odot }$ companion matter, its spin period can shorten from $P_0\sim 1000$ s to $P\sim 260$ s, while its magnetic field strength decays little. Furthermore, when the NS accretes about $\Delta M\sim {10}^{-5.5}{M}_{\odot }$ matter, its spin period can shorten to $P\sim 10$ s, while its magnetic field strength decays by half. Finally, we also notice that as the continuing of the accretion process in Be/X-ray binary, when its NS accretes about $\sim {10}^{-3}{M}_{\odot }$ mater, it has the possibility to evolve to the double neutron star.