Abstract
Abstract We show that the radiation transfer equation for the photon splitting eascade has a one-parameter set of self-similar solutions and show that they are very useful for the proper treatment of a general solution. The main advantage is that any initial spectrum converges quickly to the self-similar spectrum provided most of the initial energy is injected at the hard spectral edge. When turning to the astrophysical consequences of photon splitting we focus mainly on its general qualitative features and spectral imprints which are not sensitive to the specific emission mechanism and details of magnetosphere structure. The analysis includes possible polarization and effective softening of the post-cascade spectrum as well as remarkable formation of a spectral break and condensation of all hard-energy radiation in the vicinity of that break.
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