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. In the outer gap, on the two sides of the null charge surface, the particles with different signs move in opposite directions. The particles moving outwards from null charge surface to the light cylinder are accelerated by the strong electric field, and convert the potential drop of the gap to the GeV curvature photons.
On the other hand, the incoming particles can gain energy near the null charge surface, after that, their energy losses caused by the curvature radiation cannot be compensated by the weak electric field. The curvature photons emitted by these incoming particles go pass by the stellar surface and become pairs via the magnetic pair creation. The soft gamma-ray radiation of PSR B1509 is explained as the synchrotron radiation of these pairs, and the outgoing GeV photons, which are observed in other spin-down powered pulsars, are missed by the small viewing angle. The magnetic pair creation requires a large pitch angle, which makes the pulse profile of the synchrotron radiation distinct with that of the curvature radiation.
We use a new method to simulate the pulse profile of the synchrotron radiation with a large pitch angle, and 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 that appears when $E>10$MeV originates from the curvature photons emitted closer to the stellar surface, where the stronger magnetic field allows the pair creation to happen under a smaller pitch angle of the photon.