The spectra of hard radiation from radio pulsars

The kinetic equation for the distribution function of relativistic electrons is solved taking into account quasi-linear interactions with waves and radiative processes. Mean values of the pitch angles ψ are calculated. If the particles of the primary beam with Lorentz factors γ_b～10⁶ are resonant, then the condition γ_bψ_b?1 is satisfied, the particle distribution is described by the function f _‖(γ) ∝ γ^?4, and the synchrotron radiation spectrum is characterized by the spectral index α=3/2. On the other hand, if a cyclotron resonance is associated with particles of the high-energy tail of the secondary plasma (γ_t～10⁵), then γ_tψ_t?1, and the distribution function has two parts—f _‖(γ) ∝ γ and f _‖(γ) ∝ γ^?2—which correspond to the spectral indices α₁=+1 and α₂=?0.5. This behavior is similar to that observed for the pulsar B0656+14. The predicted frequency of the maximum ν_m=7.5×10¹⁶ Hz coincides with the peak frequency for this pulsar. The model estimate for the total synchrotron luminosity of a typical radio pulsar with hard radiation L _s =3×10³³ erg/s is in agreement with observed values.