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Study of luminosity and spin-up relation in X-ray binary pulsars with long-term monitoring by MAXI/GSC and Fermi/GBM

We study the relation between luminosity and spin-period change in X-ray binary pulsars using long-term light curve obtained by the MAXI/GSC all-sky survey and pulse period data from the Fermi/GBM pulsar project. X-ray binaries, consisting of a highly magnetized neutron star and a stellar companion, originate X-ray emission according to the energy of the accretion matter onto the neutron star. The accretion matter also transfers the angular momentum at the Alfven radius, and then spin up the neutron star. Therefore, the X-ray luminosity and the spin-up rate are supposed to be well correlated. We analyzed the luminosity and period-change relation using the data taken by continuous monitoring of MAXI/GSC and Fermi/GBM for Be/X-ray binaries, GX 304$-$1, A 0535$+$26, GRO J1008$-$57, KS 1947$+$300, and 2S 1417$-$624, which occurred large outbursts in the last four years. We discuss the results comparing the obtained observed relation with that of the theoretical model by Ghosh \& Lamb (1979).