Pulsar hulling is a phenomenon of sudden cessation of pulse emission for a number of periods. The nulling fraction was often used to characterize the phenomenon. We propose a new method to analyse pulsar hulling phenomenon, by involving two key parameters, the nulling degree, X, which is defined as the angle in a rectangular coordinates for the numbers of nulling periods and bursting periods, and the nulling scale, N, which is defined as the effective length of the consecutive nulling periods and bursting periods. The nulling degree X can be calculated by tanX = Nnulling/Nbursting and the mean is related to the nulling fraction, while the nulling scale, N, is also a newly defined fundamental parameter which indicates how often the nulling occurs. We determined the distributions ofx and N for 10 pulsars by using the data in literature. We found that the nulling degree X indicates the relative length of nulling to that of bursting, and the nulling scale N is found to be related to the derivative of rotation frequency and hence the loss rate of rotational energy of pulsars. Their deviations reflect the randomness of the nulling process.
Repeated scatterings of unpolarized photons by non-relativistic electrons in a static and uniform magnetic field are investigated by using the Boltzmann equation with quantum mechanical correction factors for the stimulated scattering effects.The resulting Kompaneets equation depends explicitly on the electron cyclotron frequency and the incidence angle of the incoming photons relative to the direction of the magnetic field.The evolutionary behavior of the photon spectrum and energy density is highly anisotropic with respect to the static external magnetic field.Possible applications of our results to the X-ray emission from compact and massive stellar objects are discussed in detail and those to the interaction of the microwave background radiation with the hot electrons in galactic clusters are discussed briefly.
