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

Application of the Ghosh & Lamb Relation to the Spin-up/down Behavior in the X-ray Binary Pulsar 4U 1626-67