In the present paper an alternative theoretical interpretation to the generally assumed thermal emission models of the observed X-ray spectrum of isolated pulsar RX J0420.0-5022 is presented. It is well known that the distribution function of relativistic particles is one-dimensional at the pulsar surface. However, cyclotron instability causes an appearance of transverse momenta of relativistic electrons, which as a result, start to radiate in the synchrotron regime. On the basis of the Vlasovs kinetic equation we study the process of the quasi-linear diffusion (QLD) developed by means of the cyclotron instability. This mechanism provides generation of optical and X-ray emission on the light cylinder lengthscales. The analysis of the three archival XMM-Newton observations of RX J0420.0-5022 is performed. Considering a different approach of the synchrotron emission theory, the spectral energy distribution is obtained that is in a good agreement with the observational data. A fit to the X-ray spectrum is performed using both the present synchrotron emission model spectrum absorbed by cold interstellar matter and generally assumed absorbed black-body model.
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