Radio Scintillation due to Discontinuities in the Interstellar Plasma Density

We develop the theory of interstellar scintillation as caused by an irregular plasma having a power-law spatial density spectrum with a spectral exponent of 4 corresponding to a medium with abrupt changes in its density. An ``outer scale'' is included in the model representing the typical scale over which the density of the medium remains uniform. Such a spectrum could be used to model plasma shock fronts in supernova remnants or other plasma discontinuities. We investigate and develop equations for the decorrelation bandwidth of diffractive scintillations and the refractive scintillation index and compare our results with pulsar measurements. We consider both a medium concentrated in a thin layer and an extended irregular medium. We conclude that the discontinuity model gives satisfactory agreement for many diffractive measurements, in particular the VLBI meaurements of the structure function exponent between 5/3 and 2. However, it gives less satisfactory agreement for the refractive scintillation index than does the Kolmogorov turbulence spectrum. The comparison suggests that the medium consists of a pervasive background distribution of turbulence embedded with randomly placed discrete plasma structures such as shocks or HII regions. This can be modeled by a composite spectrum following the Kolmogorov form at high wavenumbers and steepening at lower wavenumbers corresponding to the typical (inverse) size of the discrete structures. Such a model can also explain the extreme scattering events. However, lines of sight through the enhanced scattering prevalent at low galactic latitudes are accurately described by the Kolmogorov spectrum in an extended medium and do not appear to have a similar low-wavenumber steepening.