The nature of the solar wind electron temperature and electron heat flux

Abstract

Aims. We analyze the properties of a phenomenological model of the solar wind electron energy equation in a spherical expansion, with a radial power law for the electron heat flux, a radial interplanetary magnetic field (IMF), and a constant or smooth increase of the solar wind speed. Methods. We define a critical electron heat flux that is a fraction of the electron thermal energy convected at the solar wind speed, and which plays a crucial role in the electron energy equation solution. When the electron heat flux is equal to the critical heat flux, the electron temperature is driven solely by the dissipation of the heat flux and the electron temperature is a simple radial power law. This defines an heat dissipation dominated (HDD) expansion of the electrons. When the electron heat flux is not equal to the critical electron heat flux, both adiabatic cooling and dissipation of the heat flux drive the electron temperature evolution. These two processes are quantitatively evaluated all along the expansion, in a composite expression of the electron temperature. Results. We establish generic radial electron temperature laws for different values of the electron heat flux index α. We discuss the derivation of the electron temperature as ∝r−2/7 in the solar wind. We show that a model of the electron energy equation where the Spitzer and Härm (SH) heat conduction law is a closure, with a constant or smooth increase of the solar wind speed and a radial IMF, is an HDD expansion. We also show that the electron temperature follows a radial power law as ∝r−0.4. We obtain constraints on the nature of the electron temperature and the electron heat flux power law index for the SH law to be verified in a large range of radial distance from the Sun. An application of the generic temperature law to kinetic numerical simulations of the solar wind accurately predicts the electron temperature characteristics and evolution.