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

II. Case of a spiral interplanetary magnetic field

¹ Department of Chemistry, University of British Columbia, Vancouver V6T 1Z1, Canada
e-mail: damahubert@gmail.com
² Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA
e-mail: salem@ssl.berkeley.edu

Received: 27 May 2022
Accepted: 22 February 2023

Abstract

Aims. We aim to analyze the solutions of the solar wind electron energy equation in a spherical expansion with a spiral interplanetary magnetic field (IMF), a radial power law of the electron heat flux with a constant index α, and a constant or a smooth increase of the solar wind speed.

Methods. Generic analytical electron temperature profiles for constant co-latitude of the radial vector r and different power law indices of the electron heat flux are established. We concentrate on the solution of the energy equation for an expansion in the heliospheric equatorial plane. We define a critical electron heat flux that is a fraction of the electron thermal energy convected at the solar wind speed and plays a crucial role in the electron energy equation solution.

Results. When the electron heat flux density is equal to the critical heat flux, the electron temperature is driven by the dissipation of the electron heat flux and the effect of the IMF. This corresponds to a heat dissipation dominated (HDD) expansion of the electrons. When the electron heat flux is not equal to the critical electron heat flux, three effects drive the electron temperature evolution: an adiabatic cooling, the dissipation of the electron heat flux and the spiral IMF effect. These contributions are quantitatively evaluated along the radial expansion. For a same electron heat flux and solar wind velocity, we show an important effect, that the solar wind electron temperature with a spiral IMF is higher than with a radial IMF up to some large radial distances, and that this difference increases with an increasing power law index α up to −2. Based on the phenomenological energy equation, we show that the Spitzer and Härm law is approximately verified in a spiral IMF for moderate radial distances from the Sun lower than 2 AU, with an electron heat flux power law index a little lower than −2.40 and an electron temperature with a power law a little higher than −0.40. A complete study requires the solution of the electron fluid equation for different solar wind speed profiles. The study of data collected on the Ulysses mission, along a portion of a southward high-latitude orbit, needs a specific analysis because a large variation of the co-latitude is observed along that orbit leg. From this study, we conclude that the dissipation of the electron heat flux between 1.52 and 2.3 AU cannot sustain the measured total electron temperature in this distance range; we show that the core-strahl electron population has a temperature driven by the heat flux dissipation between 1.52 and 2.3 AU, and that this core-strahl temperature profile has the property of an HDD expansion.

Conclusions. The results, in Parts 1 and 2, suggest we should study the energetics of the solar wind core-strahl electron population as a whole and revisit the Spitzer and Härm law corresponding to this population while taking into account the spiral IMF.