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The outer gap model is used here to explain the spectrum and the energydependent light curves of the X-ray and soft gamma-ray radiations of thespin-down powered pulsar PSR B1509-58.In the outer gap model, most pairs insidethe gap are created around the null charge surface and the gap's electric fieldseparates the two charges to move in opposite directions. Consequently, theregion from the null charge surface to the light cylinder is dominated by theoutflow of particles and that from the null charge surface to the star isdominated by the inflow of particles. The inflow and outflow of particles movealong the magnetic field lines and emit curvature photons, and the incomingcurvature photons are converted to pairs by the strong magnetic field of thestar. These pairs emit synchrotron photons. We suggest that the X-rays and softgamma-rays of PSR B1509-58 result from the synchrotron radiation of thesepairs, and the viewing angle of PSR B1509-58 only receives the inflowradiation. The magnetic pair creation requires a large pitch angle, which makesthe pulse profile of the synchrotron radiation distinct from that of thecurvature radiation. We carefully trace the pulse profiles of the synchrotronradiation with different pitch angles. We find that the differences between thelight curves of different energy bands are due to the different pitch angles ofthe secondary pairs, and the second peak appearing at E>10MeV comes from theregion near the star, where the stronger magnetic field allows the paircreation to happen with a smaller pitch angle.

Radiation Mechanism of the Soft Gamma-ray Pulsar PSR B1509-58