On optical synchrotron emission of radio pulsars

It is well known that the distribution function of relativistic particles i s one-dimensional at the pulsar surface. Any transverse momentum will be lo st via synchrotron emission during a very short time (less than or equal to 10(-20) s). However, the cyclotron instability causes an appearance of tra nsverse momenta of relativistic particles in the outer parts of pulsar magn etospheres. We formulate the equation controlling such processes, and obtai n the solution of this equation. It gives the distribution of pitch angles psi for particles emitting the synchrotron radiation. We show that this rad iation is generated near the light cylinder. The mean value of the pitch an gle corresponds to optical frequencies in this region. For example, <(<psi> )over bar> similar to 10(-6) for the radio pulsar PSR B0656+14 (in the obse rver's frame), and the frequency of the spectral peak is equal to 3 x 10(14 ) Hz. The flux observed in the optical range requires for this pulsar a den sity of radiating electrons similar to 10(9) cm(-3). Some other models of s ynchrotron emission are discussed. We show that optical emission will be ob served in pulsars with small angles beta between the rotation and magnetic axes. Pulsars with shorter periods must have harder spectra.