The spectra of hard radiation from radio pulsars

Abstract

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 γb∼106 are resonant, then the condition γbψb≲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 (γt∼105), then γtψt≫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 νm=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.