The Transport of Density Fluctuations Throughout the Heliosphere

The solar wind is recognized as a turbulent magnetofluid, for which the properties of the turbulent velocity and magnetic field fluctuations are often described by the equations of incompressible magnetohydrodynamics (MHD). However, low-frequency density turbulence is also ubiquitous. On the basis of a nearly incompressible formulation of MHD in the expanding inhomogeneous solar wind, we derive the transport equation for the variance of the density fluctuations (Rho(exp 2)). The transport equation shows that density fluctuations behave as a passive scalar in the supersonic solar wind. In the absence of sources of density turbulence, such as within 1AU, the variance (Rho(exp 2)) approximates r(exp -4). In the outer heliosphere beyond 1 AU, the shear between fast and slow streams, the propagation of shocks, and the creation of interstellar pickup ions all act as sources of density turbulence. The model density fluctuation variance evolves with heliocentric distance within approximately 300 AU as (Rho(exp 2)) approximates r(exp -3.3) after which it flattens and then slowly increases. This is precisely the radial profile for the density fluctuation variance observed by Voyager 2. Using a different analysis technique, we confirm the radial profile for Rho(exp 2) of Bellamy, Cairns, & Smith using Voyager 2 data. We conclude that a passive scalar description for density fluctuations in the supersonic solar wind can explain the density fluctuation variance observed in both the inner and the outer heliosphere.