Observational tests of accretion-driven spin-up/down process in X-ray binary pulsars with 7-year MAXI and Fermi/GBM data

The relation between the luminosity and the spin-period change in X-ray binary pulsars reflects the manner of mass accretion onto the magnetized neutron stars, and thus provides us information on the neutron-star physical parameters related to the mass M, radius R, and the surface magnetic field B. To observationally study the relation, we analyzed X-ray light curves obtained by the MAXI all-sky survey and pulse-period data taken by the Fermi Gamma-ray Burst Monitor pulsar project, both continuously cover 7 years since 2009 August.In 4U 1626-67, a low-mass X-ray binary pulsar which repeated transitions between spin-up and spin-down phases every few ten years, the observed relation between the X-ray intensity and the pulse-period change has been successfully explained by the disk-magnetosphere interaction model proposed by Ghosh & Lamb (1979), including both the spin-up to the spin-down phases over the past 6 years. Assuming a distance of 10 kpc and using the surface magnetic field B measured with the cyclotron resonance, the model indicates the mass M=1.8-1.9M_⊙ and the radius R=11.4-11.5 km (Takagi et al. 2016). Thus, the method provides a new way of constraining the mass-radius relations.For a more systematic study, we selected 12 Be binary pulsars which showed, in these 7 years, large outbursts with the peak luminosity exceeding 10^{37} erg s^{-1}. In all the 12 objects, the luminosities and the spin-frequency derivatives, observed during the outbursts, were found to follow positive correlations that are close to the proportionality, as expected by most of the theoretical models. The coefficient of the proportionality agrees, within a factor of 3, with the prediction by the Ghosh & Lamb (1979) when assuming a typical mass and radius, and employing the surface magnetic field measured with the cyclotron resonance. The scatter of the observed coefficients around the model predictions is reasonably explained by uncertainties in the pulsed-emission anisotropy and the distance estimate (Sugizaki et al. 2017).After calibrating the theoretical model, we also analyzed the data of X Persei, the Be binary pulsar with a low luminosity (≲ 2× 10^{35} erg s^{-1}), which once showed a transition from the spin-down to spin-up in 2002 (Lutovinov et al. 2012). Although the Ghosh & Lamb (1979) model again successfully explained the observed relation between the luminosity and the spin-period change covering both the spin-up and spin-down phases, the data require a strong magnetic field B ≳ 10^{13} G as well as a relatively high mass M≃ 1.7 M_⊙. These results point to an intriguing possibility that X Persei is a magnetar-equivalent object in a binary, and such strong-field neutron stars possibly have somewhat higher mass than the ordinary ones with B∼ 10^{12} G.