Generalized anisotropic $\kappa$-cookbook: 2D fitting of Ulysses electron data

TL;DR

This paper extends the isotropic ${ ext{kappa}}$-cookbook to anisotropic and multi-component particle velocity distributions in space plasmas, providing analytical tools and a 2D fitting method for Ulysses electron data.

Contribution

It introduces a generalized anisotropic ${ ext{kappa}}$-cookbook with analytical expressions and a 2D fitting procedure, improving analysis of space plasma particle distributions.

Findings

Confirmed three distinct electron populations in Ulysses data.

Best fits involve a Maxwellian core and two generalized ${ ext{kappa}}$-distributions.

Enhanced confidence in distribution characterization over 1D methods.

Abstract

Observations in space plasmas reveal particle velocity distributions out of thermal equilibrium, with anisotropies (e.g., parallel drifts or/and different temperatures, $T_\parallel$ - parallel and $T_\perp$ - perpendicular, with respect to the background magnetic field), and multiple quasithermal and suprathermal populations with different properties. The recently introduced (isotropic) $\kappa$-cookbook is generalized in the present paper to cover all these cases of anisotropic and multi-component distributions reported by the observations. We derive general analytical expressions for the velocity moments and show that the common (bi-)Maxwellian and (bi-)$\kappa-$distributions are obtained as limiting cases of the generalized anisotropic $\kappa$-cookbook (or recipes). Based on this generalization, a new 2D fitting procedure is introduced, with an improved level of confidence compared to the 1D fitting methods widely used to quantify the main properties of the observed distributions. The nonlinear least-squares fit is \led{applied to electron data sets} measured by the Ulysses spacecraft confirming the existence of three different populations, a quasithermal core and two suprathermal (halo and strahl) components. In general, the best overall fit is given by the sum of a Maxwellian and two generalized $\kappa$-distributions.