1999MNRAS.303..477R

For a subclass of polar-cap models based on electromagnetic cascades induced by curvature radiation (CR) we calculate broad-band high-energy spectra of pulsed emission expected for classical and millisecond pulsars. The spectra are a combination of curvature and synchrotron components. The spectrum of the curvature component breaks at 150 MeV, and neither its slope nor the level below this energy is compatible with phase-averaged spectra of pulsed X-ray emission inferred from observations. Spectral properties in the combined energy range of ROSAT and ASCA (0.1–10 keV) depend upon the location of the cyclotron turnover energy ε_ct = [h- (e B)/(m_ec) ]/sin ψ in the synchrotron component. Unlike in outer-gap models, the available range of pitch angles ψ is rather narrow and confined to low values. For classical pulsars, a gradual turnover begins at ∼ 1 MeV, and the level of the synchrotron spectrum decreases. At ∼ 10 keV the curvature component eventually takes over, but with photon index α = 2/3, which disagrees with observations. For millisecond pulsars, the X-ray spectra are dominated by the synchrotron component with α ≃ 1.5, and a sharp turnover into α ≃ -1 at ε_ct ∼ 100 eV. Relationships of pulsed luminosity L_X to spin-down luminosity L_sd are presented for classical and millisecond pulsars. We conclude that spectral properties and fluxes of pulsed non-thermal X-ray emission of some objects, like the Crab or the millisecond pulsar B1821-24, pose a challenge to the subclass of polar-cap models based on curvature and synchrotron radiation alone.