Electron Heat Flux in the Solar Wind: Generalized Approaches to Fluid Transport with a Variety of Skewed Velocity Distributions

In the solar corona and solar wind, electron heat conduction is an important process that transports energy over large distances and helps determine the spatial variation of temperature. High-density regions undergoing rapid particle-particle collisions exhibit a heat flux described well by classical Spitzer-Harm theory. However, much of the heliosphere is closer to a more collisionless state, and there is no standard description of heat conduction for fluid-based (e.g., magnetohydrodynamic) models that applies generally. Some proposed models rely on electron velocity distributions that exhibit negative values of the phase-space density. In this paper, we explore how positive-definite velocity distributions can be used in fluid-based conservation equations for the electron heat flux along magnetic-field lines in the corona and solar wind. We study both analytic forms of skewed distributions (e.g., skew-normal distributions, two-sided bi-Maxwellians, and constant-collision-time electrostatic solutions) and empirical fits to measurements of core, halo, and strahl electrons in interplanetary space. We also present example solutions to a generalized conservation equation for the heat flux in the solar wind, with some limiting cases found to resemble known free-streaming approximations. The resulting values of the electron heat flux vary as a function of radial distance and Knudsen number in ways that resemble observed data. We note that this model does not include the effects of kinetic instabilities (which may impose saturation limits when active), so for now its regime of applicability is limited to collisionless heat-flux evolution away from the known instability boundaries in parameter space.