On the Theory of Pulse Propagation and Two‐Frequency Field Statistics in Irregular Interstellar Plasmas

Abstract

We have computed two-frequency second moments and pulse profiles for plane and spherical waves both propagating in an extended plasma and incident on a thin plasma phase screen located between the source and the observer. The various models we consider for the power spectrum of the interstellar electron density fluctuations versus wavenumber are the simple power-law model, the power-law model with an inner scale, the model, and the square-law structure function model. The power-law model with spectral exponent β=11/3 corresponds to the Kolmogorov turbulence spectrum. The β=4 model describes the random distribution in location and orientation of discrete objects with relatively sharp boundaries, such as shocks, across the line of sight. An outer scale is included in the β=4 model to account for the average size of such objects. The results for the various spectral models generally lie between the extremes represented by the simple Kolmogorov and square-law structure function models. In the strong scattering limit, the diffractive decorrelation bandwidth is related to the scattering broadening time via a Fourier uncertainty relation. We have computed numerical values for the uncertainty constant for the various geometries and spectral models and find values ranging over a factor of 2. For the Kolmogorov spectrum, the value is less than that in the widely-used Taylor, Manchester, & Lyne (1993) catalog by factors of 1.98 and 2.34 for a point source in an extended medium and in screen geometries, respectively. Thus observers must use the appropriate constant when comparing observations with a specific spectral and geometrical model. We also note that high signal-to-noise ratio observations of the scattering tails of pulsar pulses may be used to constrain the various spectral models of the Galactic electron density fluctuations, independent of the distribution of the scattering material along the line of sight.