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

Using the relation proposed by Ghosh & Lamb (1979) between the pulse-period derivative and the X-ray luminosity in binary X-ray pulsars, we tried to constrain the mass and radius of a neutron star. To apply the relation to the binary X-ray pulsar 4U 1626-67, we compiled previous measurements of its period, period derivative, and flux, and added measurements with the MAXI/GSC onboard the International Space Station. The measured period derivative was tightly correlated with the flux, and the relation is successfully explained by the Ghosh & Lamb relation. We found that an assumed distance of, e.g., 8 kpc, gives a mass of 1.39-1.46 solar mass, and a radius as 11.9-12.0 km. This method thus provides a valuable tool to constrain these parameters, even though we need to precisely know the distance [2].