Revisiting Ulysses electron data with a triple fit of velocity distributions

¹ Institut für Theoretische Physik, Lehrstuhl IV: Plasma-Astroteilchenphysik, Ruhr-Universität Bochum, 44780 Bochum, Germany
e-mail: kls@tp4.rub.de
² Research Department, Plasmas with Complex Interactions, Ruhr-Universität Bochum, 44780 Bochum, Germany
³ Centre for mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
⁴ Department of Physics and Astronomy, University of Turku, 20014 Turku, Finland

Received: 4 March 2022
Accepted: 6 May 2022

Abstract

Context. Given their uniqueness, the Ulysses data can still provide us with valuable new clues about the properties of plasma populations in the solar wind, and especially about their variations with heliographic coordinates. In the context of kinetic waves and instabilities in the solar wind plasma, the electron temperature anisotropy plays a crucial role. To date, two electron populations (the core and the halo) have been surveyed using anisotropic fitting models, limited in general to the ecliptic observations.

Aims. We revisit the electron data reported by the SWOOPS instrument on board the Ulysses spacecraft between 1990 and early 2008. These observations reveal velocity distributions out of thermal equilibrium, with anisotropies (e.g., parallel drifts and/or different temperatures, parallel and perpendicular to the background magnetic field), and quasi-thermal and suprathermal populations with different properties.

Methods. We apply a 2D non-linear least squares fitting procedure, using the Levenberg–Marquardt algorithm, to simultaneously fit the velocity electron data (up to a few keV) with a triple model combining three distinct populations: the more central quasi-thermal core, the suprathermal halo, and a second suprathermal population consisting mainly of the electron strahl (or beaming population with a major field-aligned drift). The recently introduced κ-cookbook is used to describe each component with the following anisotropic distribution functions (recipes): Maxwellian distribution, regularized κ-distribution, and generalized κ-distribution. Most relevant are triple combinations selected as best fits (BFs) with minimum relative errors and standard deviations.

Results. The number of BFs obtained for each fitting combination is 80.6% of the total number of events (70.7% in the absence of coronal mass ejections). Showing the distribution of the BFs for the entire data set, during the whole interval of time, enables us to identify the most representative fitting combinations associated with either fast or slow winds, and different phases of solar activity. The temperature anisotropy quantified by the best fits is considered a case study of the main parameters characterizing electron populations. By comparison to the core, both suprathermal populations exhibit higher temperature anisotropies, which slightly increase with the energy of electrons. Moreover, these anisotropies manifest different dependences on the solar wind speed and heliographic coordinates, and are highly conditioned by the fitting model.

Conclusions. These results demonstrate that the characterization of plasma particles is highly dependent on the fitting models and their combinations, and this method must be considered with caution. However, the multi-distribution function fitting of velocity distributions has a significant potential to advance our understanding of solar wind kinetics and deserves further quantitative analyses.