  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.
