Solar wind proton velocity distributions: Comparison of the bi-Maxwellian based 16-moment expansion with observations

Abstract

Satellite measurements indicate that velocity distributions for solar wind protons can take on a great variety of shapes. The distributions can be isotropic, can have isotropic cores and anisotropic tails, can be elongated in the magnetic field direction ( B), can have cores elongated perpendicular to B and high-velocity tails parallel to B, and can have two peaks. Past attempts to empirically fit distribution functions for solar wind protons using theoretical distribution functions have met with some success. The theoretical distribution functions considered were based on either a zeroth-order isotropic Maxwellian or a zeroth-order bi-Maxwellian, with heat flow correction terms. The purpose of this paper is to study the possible types of velocity distributions that can be obtained from the bi-Maxwellian based 16-moment expansion of the distribution function, assuming macroscopic parameter values characteristic of the range of solar wind conditions. The 16-moment distribution accounts not only for heat flow effects but for the effects of viscous stress as well. While previous studies also took heat flow into account, the theoretical expansions for ƒ and the definitions of the physical moments adopted in these studies were different from those used in this paper. Our choice of the 16-moment expansion and corresponding moment definitions was motivated by the fact that this is the correct generalization of the widely-used Maxwellian-based 13-moment expansion to the case where the zeroth-order distribution is a bi-Maxwellian. We found that most of the features characteristic of solar wind proton distributions can be reproduced with the 16-moment distribution, including the appearance of secondary peaks. We were also able to show how each of the physically significant velocity moments affects the shape of the distribution function. We conclude that the 16-moment distribution function can be a useful tool in interpreting measured distribution functions.