2001ApJ...554..587M

It is well known that the distribution function of relativistic particles is one-dimensional at the pulsar surface. Any transverse momentum will be lost via synchrotron emission during a very short time (≤10^–20 s). However, the cyclotron instability causes an appearance of transverse momenta of relativistic particles in the outer parts of pulsar magnetospheres. We formulate the equation controlling such processes, and obtain the solution of this equation. It gives the distribution of pitch angles ψ for particles emitting the synchrotron radiation. We show that this radiation is generated near the light cylinder. The mean value of the pitch angle corresponds to optical frequencies in this region. For example, ψ{d1}∼10^–6 for the radio pulsar PSR B0656+14 (in the observer's frame), and the frequency of the spectral peak is equal to 3x10¹⁴ Hz. The flux observed in the optical range requires for this pulsar a density of radiating electrons ∼10⁹ cm^–3. Some other models of synchrotron emission are discussed. We show that optical emission will be observed in pulsars with small angles β between the rotation and magnetic axes. Pulsars with shorter periods must have harder spectra.