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

Observations in space plasmas reveal particle velocity distributions out of thermal equilibrium, with anisotropies (e.g. parallel drifts and/or different temperatures, T-H - parallel and T-perpendicular to - perpendicular, with respect to the background magnetic field), and multiple quasi-thermal and suprathermal populations with different properties. The recently introduced (isotropic) kappa-cookbook is generalized in this paper to cover all these cases of anisotropic and multicomponent 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 two-dimensional 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 non-linear least-squares fit is applied to electron data sets measured by the Ulysses spacecraft confirming the existence of three different populations, a quasi-thermal core and two suprathermal (halo and strahl) components. In general, the best overall fit is given by the sum of a Maxwellian distribution and two generalized kappa-distributions.