Coronal turbulence and the angular broadening of radio sources - the role of the structure function

TL;DR

This paper introduces a general structure function for analyzing radio source broadening caused by solar corona turbulence, improving accuracy over previous asymptotic methods, especially near the inner scale of turbulence.

Contribution

It develops and advocates for the use of a general structure function that accurately models turbulence effects across all regimes, including anisotropic scattering, replacing approximate asymptotic formulas.

Findings

GSF provides more accurate predictions than asymptotic formulas in relevant regimes.

Inner scale effects significantly influence scatter broadening estimates.

Anisotropic scattering effects are incorporated into the model.

Abstract

The amplitude of density turbulence in the extended solar corona, especially near the dissipation scale, impinges on several problems of current interest. Radio sources observed through the turbulent solar wind are broadened due to refraction by and scattering off density inhomogeneities, and observations of scatter broadening are often employed to constrain the turbulence amplitude. The extent of such scatter broadening is usually computed using the structure function, which gives a measure of the spatial correlation measured by an interferometer. Most such treatments have employed analytical approximations to the structure function that are valid in the asymptotic limits $s \gg l_{i}$ or $s \ll l_{i}$, where $s$ is the interferometer spacing and $l_{i}$ is the inner scale of the density turbulence spectrum. We instead use a general structure function (GSF) that straddles these regimes, and quantify the errors introduced by the use of these approximations. We have included the effects of anisotropic scattering for distant cosmic sources viewed through the solar wind at small elongations. We show that the regimes where the GSF predictions are more accurate than those of the asymptotic expressions are not only of practical relevance, but are where inner scale effects influence estimates of scatter broadening. Taken together, we argue that the GSF should henceforth be used for scatter broadening calculations and estimates of turbulence amplitudes in the solar corona and solar wind.