Abstract
The overall spectrum of PSR B1509-58 is unusually soft compared to spectra of other gamma-ray pulsars. It also possesses the highest inferred magnetic field (1.6 10 13 G at the surface) among high-energy pulsars. In this paper, we explore the possibility that the unusually soft spectrum is a manifestation of this high magnetic field. The high magnetic field, particularly near the surface, provides two mechanisms for annihilation of high-energy photons: photon-magnetic field pair production and single photon splitting in high magnetic fields. We conclude that the above two mechanisms can only produce a spectral turnover at ≳ 100 MeV with a conventionally estimated polar cap. With observations constraining the spectral break to be lower than 50 MeV, an enlargement of the emission polar cap by at least twice in radius of that implied by the open field lines is required if those emissions originate from a polar cap region.