The outer gap model is used here to explain the spectrum and the energy dependent light curves of the X-ray and soft gamma-ray radiations of the spin-down powered pulsar PSR B1509-58.In the outer gap model, most pairs inside the gap are created around the null charge surface and the gap's electric field separates the two charges to move in opposite directions. Consequently, the region from the null charge surface to the light cylinder is dominated by the outflow of particles and that from the null charge surface to the star is dominated by the inflow of particles. The inflow and outflow of particles move along the magnetic field lines and emit curvature photons, and the incoming curvature photons are converted to pairs by the strong magnetic field of the star. These pairs emit synchrotron photons.

We suggest that the X-rays and soft gamma-rays of PSR B1509-58 result from the synchrotron radiation of these pairs, and the viewing angle of PSR B1509-58 only receives the inflow radiation. The magnetic pair creation requires a large pitch angle, which makes the pulse profile of the synchrotron radiation distinct from that of the curvature radiation. We carefully trace the pulse profiles of the synchrotron radiation with different pitch angles. We find that the differences between the light curves of different energy bands are due to the different pitch angles of the secondary pairs, and the second peak appearing at E>10MeV comes from the region near the star, where the stronger magnetic field allows the pair creation to happen with a smaller pitch angle.