Photon Splitting Cascades in Gamma-Ray Pulsars and the Spectrum of   PSR1509-58
  Magnetic photon splitting, a QED process that becomes important only in magnetic fields approaching the quantum critical value, B_cr = 4.41 X 10^13 Gauss, is investigated as a mechanism for attenuation of gamma-rays emitted near the surface of strongly-magnetized pulsars. We model photon splitting attenuation and subsequent splitting cascades in gamma-ray pulsars, including the dipole field and curved spacetime geometry of the neutron star magnetosphere. We focus specifically on PSR1509-58, which has the highest surface magnetic field of all the gamma-ray pulsars (B_0 = 3 X 10^13 Gauss). We find that splitting will not be important for most gamma-ray pulsars, i.e. those with B_0 <~ 0.2 B_cr, but will be important for gamma-ray pulsars having B_0 >~ 0.3 B_cr, where the splitting attenuation lengths and escape energies become comparable to or less than those for pair production. We compute Monte Carlo spectral models for PSR1509-58. We find that photon splitting, or combined splitting and pair production, can explain the unusually low cutoff energy (between 2 and 30 MeV) of PSR1509-58, and that the model cascade spectra, which display strong polarization, are consistent with the observed spectral points and upper limits for polar cap emission at a range of magnetic colatitudes up to ~ 25 degrees. 
Alice K. Harding, Matthew G. Baring and Peter L. Gonthier