An application of the Ghosh & Lamb model to the accretion powered X-ray pulsar X Persei

The accretion-induced pulse-period changes of the Be/X-ray binary pulsar X Persei were investigated over a period of 1996 January to 2017 September. This study utilized the monitoring data acquired with the RXTE/ASM in 1.5$-$12 keV and MAXI/GSC in 2$-$20 keV. The source intensity changed by a factor of 5$-$6 over this period. The pulsar was spinning down for 1996$-$2003, and has been spinning up since 2003, as already reported. The spin up/down rate and the 3$-$12 keV flux, determined every 250 d, showed a clear negative correlation, which can be successfully explained by the accretion torque model proposed by Ghosh & Lamb (1979). When the mass, radius and distance of the neutron star are allowed to vary over a range of 1.0$-$2.4 solar masses, 9.5$-$15 km, and 0.77$-$0.85 kpc, respectively, the magnetic field strength of $B=(4-25) \times10^{13}\ \rm G$ gave the best fits to the observation. In contrast, the observed results cannot be explained by the values of $B\sim {10}^{12}\mathrm{G}$ previously suggested for X Persei, as long as the mass, radius, and distance are required to take reasonable values. Assuming a distance of $0.81\pm 0.04$ kpc as indicated by optical astrometry, the mass of the neutron star is estimated as $M=2.03\pm 0.17$ solar masses.