What causes the flux excess in the heliospheric magnetic field?

Abstract

Ulysses results indicate that the total magnetic flux inside the heliosphere, Φ, can be obtained from the radial field component measured at a single spacecraft multiplied by the square of the radial distance and averaged over a solar rotation, < r²B_R >. However, that result is contrary to a large increase in Φ with distance, called the flux excess, that has been reported by Owens et al. (2008a) and attributed to variations in solar wind speed by Lockwood et al. (2009a, 2009b). Ulysses data and a mathematical simulation are used to show that the cause of the flux excess is the replacement of B_R by the modulus, |B_R|. The modulus rectifies some of the large amplitude magnetic field variations normally present in measurements of B_R and increases the mean, < r² |B_R| > relative to < r²B_R >. The variance of the magnetic fluctuations, σ, decreases less rapidly with distance than B_R and that produces a progressively larger error in < r² |B_R| > resulting in the flux excess. The advisability of defining Φ in terms of |B_R|, of using < r² |B_R| > beyond 1 AU and the applicability of the Lockwood et al. (2009b) correction to < r² |B_R| > are questioned.