Application of the Ghosh & Lamb Relation to the Spin-Up/Down Behavior in the X-Ray Binary Pulsar 4u 1626-67

We analyzed continuous MAXI/GSC data of the X-ray binary pulsar 4U 1626-67 from 2009 October to 2013 September, and determined the pulse period and the pulse-period derivative for every 60-d interval by the epoch folding method. The obtained periods are consistent with those provided by the Fermi/GBM pulsar project. In all the 60-d intervals, the pulsar was observed to spin up, with the spin-up rate positively correlated with the 2-20 keV flux. We applied the accretion torque model proposed by Ghosh Lamb (1979, ApJ, 234, 296) to the MAXI/GSC data, as well as the past data including both spin-up and spin-down phases. The Ghosh Lamb relation was confirmed to successfully explain the observed relation between the spin-up/down rate and the flux. By comparing the model-predicted luminosity with the observed flux, the source distance was constrained as 5-13 kpc, which is consistent with that by Chakrabarty (1998, ApJ, 492, 342). Conversely, if the source distance is assumed, the data can constrain the mass and radius of the neutron star, because the Ghosh Lamb model depends on these parameters. We attempted this idea, and found that an assumed distance of, e.g., 10 kpc gives a mass in the range of 1.81-1.90 solar mass, and a radius of 11.4-11.5 km, although these results are still subject to considerable systematic uncertainties other than that in the distance.