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The Voyager 1/2 plasma wave instruments have observed low-frequency (1.5-4kHz) radio waves apparently generated near the heliopause. The waves are found in two distinct bands.
Detailed first estimates are presented of angular broadening in the outer heliosphere due to scattering of radio waves by density irregularities. The application is to the 2-3 kHz radiation observed by Voyager. Two plausible turbulence models, which account very well for scattering within 1 AU, are extrapolated beyond 10 AU. Both models predict significant angular broadening in the outer heliosphere, accounting semi- quantitatively alone for the source sizes inferred from roll modulation data. Predictions are presented for radial variations in the apparent source size if scattering is important. Comparisons with available data argue that scattering is important (and indeed is the dominant contributor to the apparent source size) and that the radiation source is located in the outer heliosphere. Other evidence that scattering is important, such as the fluctuations in apparent source direction and intensity, are also identified. The effects of scattering should be included in future analyses of the 2-3 kHz emissions.
Current models for the 2-3 kHz emissions observed by the Voyager spacecraft in the outer heliosphere involve 2f(p) radiation generated near the termination shock or the heliopause. Radio wave scattering by solar wind density irregularities strongly affects observed sources of f(p) and 2f(p) emission in the inner heliosphere and the characteristics of astrophysical sources. In particular, the angular size, brightness temperature, and time variability of the source are strongly affected by scattering, thereby having major implications for the inferred size, energy budget, time variability, location, and nature of the source if scattering is ignored. This paper addresses whether scattering is important for interpreting the Voyager 2-3 kHz emissions. Quantitative calculations (with and without diffraction) are performed for the angular broadening of an outer heliospheric source as a function of path length, radiation frequency relative to f(p) and the spectrum of density irregularities. The effects of scattering in both the solar wind and the heliosheath are considered. Predictions for radial gradients in the source's apparent angular size and in the source's modulation index are presented. The calculations are compared with observations and the results discussed. First estimates suggest that scattering plausibly dominates the observed source size. The observed trend in modulation index with heliocentric distance is consistent with scattering being important and the source being in the outer heliosphere. Additional arguments for scattering being important are summarized.
Angular broadening of radiation due to scattering by density irregularities is usually described using geometric optics (GO) or the parabolic wave equation (PWE) with the assumptions that the radiation frequency f greatly exceeds the local plasma frequency f(sub p0) or that f(sub p0)/f is constant along the path. These assumptions are inappropriate for many solar system radio phenomena. Here the PWE and GO formalisms are extended to treat angular broadening in plasmas with nonzero, spatially varying ratios, f(sub p0)(z)/f < 1. The new PWE results show that the correlation function, scattered angular spectrum, and other quantities are modified by inclusion of a denominator factor [1 - f(sup 2, sub p0)(z prime)/f prime] inside the path integral over z prime, while the mean-square scattering angle depends on both f(sub p0)(z)/f at the observer and the foregoing factor inside the path integral. The PWE and GO predictions for are identical and involve equivalent assumptions. Previous GO and PWE results are recovered in the limits that f(sub p0)(z prime)/f is constant or zero. The new PWE and GO results will permit more accurate calculation of angular broadening for solar system and astrophysical sources. Moreover and importantly, due to the PWE and GO results for being identical, previous GO analyses of in solar system contexts are essentially correct, except for the neglect of or minor deficiencies in the treatment of nonzero, spatially varying f(sub p0)/f effects. The identical GO and PWE results for and the form of the PWE equation for the correlation function raise questions as to whether diffraction is unimportant for angular broadening (under the usual PWE conditions). Future direct comparisons of the PWE predictions with angular spectra calculated using existing GO ray-tracing codes should answer these questions. Diffraction effects are probably important when the medium and turbulence are not sufficiently homogeneous transverse to the central ray path. The implications are also discussed for studies of the 2-3.5 kHz radiation observed in the outer heliosphere.