Radio‐Wave Propagation in the Non‐Gaussian Interstellar Medium

Radio waves propagating from distant pulsars in the interstellar medium(ISM), are refracted by electron density inhomogeneities, so that the intensityof observed pulses fluctuates with time. The theory relating the observed pulsetime-shapes to the electron-density correlation function has developed for 30years, however, two puzzles have remained. First, observational scaling ofpulse broadening with the pulsar distance is anomalously strong; it isconsistent with the standard model only when non-uniform statistics of electronfluctuations along the line of sight are assumed. Second, the observed pulseshapes are consistent with the standard model only when the scattering materialis concentrated in a narrow slab between the pulsar and the Earth. We propose that both paradoxes are resolved at once if one assumes stationaryand uniform, but non-Gaussian statistics of the electron-density distribution.Such statistics must be of Levy type, and the propagating ray should exhibit aLevy flight. We propose that a natural realization of such statistics may beprovided by the interstellar medium with random electron-densitydiscontinuities. We develop a theory of wave propagation in such a non-Gaussianrandom medium, and demonstrate its good agreement with observations. Thequalitative introduction of the approach and the resolution of theanomalous-scaling paradox was presented earlier in [PRL 91, 131101 (2003); ApJ584, 791 (2003)].Comment: 27 pages, changes to match published versio