Observations and Levy statistics in interstellar scattering

Abstract

Levy flights are similar to random walks, but are dominated by rare, large events rather than the accumulation of many steps. Levy flights are not subject to the Central Limit Theorem because the distribution of steps has no second moment; they converge to Levy-stable distributions, which have power-law tails and are stable in form under convolution with themselves. A variety of physical models can produce Levy flights. For such models, the distribution of differences in refractive index has no convergent moments, so that propagation of waves through such a medium is difficult to treat with traditional theoretical methods. Calculations show that Levy flights may help to understand some surprising aspects of radio-wave scattering in the interstellar plasma, including the scaling of broadening time τ with dispersion measure DM, the shape of scatter-broadened images, and the impulse-response function for temporal broadening of narrow pulses.