2005ApJ...624..213B

Radio waves propagating from distant pulsars in the interstellar medium (ISM) are refracted by electron density inhomogeneities, so the intensity of observed pulses fluctuates with time. The observed pulse shapes are used to diagnose electron density distribution in the ISM. The theory relating the observed pulse time shapes to the electron density correlation function has developed for 30 years; however, two puzzles have remained. First, observational scaling of pulse broadening with the pulsar distance is anomalously strong; it is consistent with the standard model only when nonuniform statistics of electron fluctuations along the line of sight are assumed. Second, the observed pulse shapes are consistent with the standard model only when the scattering material is concentrated in a narrow slab between the pulsar and the Earth. We propose that both paradoxes are resolved at once if one assumes stationary and uniform but non-Gaussian statistics of the electron density distribution in the ISM. Such statistics must be of Lévy type, and the propagating ray should exhibit a Lévy flight rather than the Gaussian random walk implied by the standard model. We propose that a natural realization of such statistics may be provided by the ISM with random electron density discontinuities. A Lévy distribution has a divergent second moment; therefore, the standard approach based on the electron density correlation function does not apply. We develop a theory of wave propagation in such a non-Gaussian random medium and demonstrate its good agreement with observations. The qualitative introduction of the approach and the resolution of the anomalous-scaling paradox was presented earlier.