Abstract
We use the outer gap model 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 opposite charges to move in opposite directions. Consequently, the region from the null charge surface to the light cylinder is dominated by the outflow current and that from the null charge surface to the star is dominated by the inflow current. We suggest that the viewing angle of PSR B1509-58 only receives the inflow radiation. The incoming curvature photons are converted to pairs by the strong magnetic field of the star. The X-rays and soft ${\gamma}$-rays of PSR B1509-58 result from the synchrotron radiation of these pairs. 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 > 10 MeV comes from the region near the star, where the stronger magnetic field allows the pair creation to happen with a smaller pitch angle.