The optical, X-ray and gamma-ray light curves and spectra of crab-like pulsars: PSR B0540-69 and PSR B1509-58

Based on the three dimensional outer magnetosphere model of pulsars proposed by Cheng, Ruderman and Zhang, we calculate the light curves and spectra of the Crab-like pulsars: PSR B0540-69 and PSR B1509-58. In this model, thermal photon emission from the entire stellar surface is due to the bombardment of the backflow charged particles from the outer gap and cyclotron resonance scattering (Cheng & Zhang 1999). Non-thermal photons are emitted by e± pairs produced by backflow charged particles from the outer gap through a synchrotron radiation mechanism near the stellar surface and in a finite region just above the outer gap through a synchrotron self-Compton mechanism. For PSR B1509-58, when the magnetic inclination and viewing angle are 60° and 75° respectively, the photon emission region has a mean thickness of ∼ 0.11RL, where RL is the radius of the light cylinder. The expected broad single pulse in optical, X-ray and γ-ray energy bands are comparable with the observed light curves with a correct phase off-set with respect to the radio pulse, and the model spectrum is consistent with the observed spectrum. For PSR B0540-69, the calculated mean thickness of the photon emission region is ∼ 0.21RL and the model light curve and spectrum are similar to the observed data if the magnetic inclination and viewing angle are 50° and 76° respectively.