Radio interferometer observations of solar wind turbulence from the orbit of Helios to the solar corona

We report observations of Very Long Baseline Interferometer (VLBI) phase scintillations due to turbulence in the solar wind. The observations were made at 5.00 and 8.42 GHz with the Very Long Baseline Array (VLBA) on three dates in 1991 July and August. We observed the sources 0851 + 202 and 0735 + 178 at solar elongations ranging from 2.66 deg to 13.29 deg; the closest approach of the line of sight to the Sun ranged from 10 to 49.8 solar radii. We have also included previously unpublished 5 GHz VLBI phase scintillation measurements from 1989. These measurements probe solar wind density fluctuations on spatial scales from about 200 km to 2000 km. Our measurements are in quite good agreement with the Coles & Harmon model for the radio phase structure function, which was largely determined from observations on both shorter and larger spatial scales. Departures from the Coles & Harmon functions are attributable to day-to-day variations in the solar wind conditions. Phase scintillations at the greatest solar elongations are in very good agreement with extrapolated estimates from direct measurements made with the Helios spacecraft at slightly larger heliocentric distances. Thus there is a consistency between the in-situ spacecraft and radio sensing measurements of density turbulence. All of the VLBI data are consistent with a Kolmogorov spectrum for the density fluctuations, although at the closest elongations there may be excess power at small spatial scales. An advantage of interferometric techniques over other radio propagation measurements is that they provide a measure of the anisotropy of the irregularities. Our observations at closest approach (10 solar radii) show weak evidence for anisotropic, field-aligned density irregularities with an axial ratio of order 2. This degree of anisotropy would appear to be less than that measured at similar solar elongations but on smaller spatial scales by Armstrong and colleagues. Finally, a combination of the radio propagation data and in situ Helios measurements is used to determine the heliocentric distance dependence of the normalization coefficient of the density power spectrum, C(sup 2)(sub N). Modeling C(sup2)(sub N) varies as (R/solar radii)(sup -Kappa), we find Kappa = 3.72 +/- 0.30. Subject to a number of assumptions, this result is consistent with the conclusion of D. A. Roberts that turbulence within 0.28 astronomical units adheres to a WKB formula for turbulence amplitude as a function of heliocentric distance.