Kinetic-based macro-modeling of the solar wind at large heliocentric distances: Kappa electrons at the exobase

Abstract

Recent evidence from Parker Solar Probe on the suprathermal electrons with Kappa-type velocity distributions in the outer corona has revived interest in the kinetic-based macro-modelling of the solar (SW), aiming to explain its properties. Invoked in kinetic modelling of nonequilibrium plasmas, standard Kappa distributions (SKDs) have been adjusted to the regularized Kappa distributions (RKDs) to fix the inconsistencies of SKD and develop consistent fluid modelling of space plasmas. We propose a new analysis of these properties at large heliocentric distances based on the existence of RKD electrons at the exobase. This new semi-analytic formalism is inspired by the methodology proposed initially by Meyer-Vernet and Issautier (1998), https://doi.org/10.1029/98ja02853. Compared to SKDs, the results for RKDs have extended applicability, since all moments can be defined and calculated consistently for all values of the $κ$ parameter, even lower than the critical ones (e.g., $κ_c=3/2$ imposed to the second-order moment) of SKDs. However, the excess energy of the more energetic suprathermal electrons associated with low values of $κ\lesssim 3/2$, is regulated by the RKD-specific cutoff parameter $α< 1$. The estimates for, e.g., the temperature and bulk velocity of the SW, remain at realistic values even for small $3/2 < κ\lesssim 2$, which would otherwise exceed specific observations. One can thus model a higher abundance of suprathermal electrons at the exobase (e.g., $κ\leqslant 3/2$), which is plausible for the sources of energetic events (flares and coronal mass ejections), and also in the astrospheres of stars with coronas hotter than the Sun's.

Figures (5)

• Figure 1: Dependence of the solutions at the exobase on $\kappa$ for SKD electrons: (a) parameter $y$; (b) ES potential (dashed line marks the Maxwellian limit, $\kappa \rightarrow \infty$, when $\Phi_{E}(r_{0}) \simeq 540$ V); (c) asymptotic (terminal) SW speed $V_{\mathrm{SW}}$. Plotted are the zero-order approximations (dotted lines), the first-order approximations (solid lines), and the exact numerical results (orange squares). The greenish range in panel (c) delimits the observed limits of the SW speed (300–800 km/s).
• Figure 2: Radial profiles for (a) normalized density, (b) ES potential, and (c) electron temperature as a function of distance $r$ (in units of $R_{S}$). The curves of different colors correspond to different values of the parameter $\kappa = 2, 3, 10$. Short lines in panel (b) indicate the ES potential at the exobase $\Phi_E(r_0)$ (boundary value at $r_0=6R_S$). The dotted lines in panel (c) mark the assumed electron temperatures at the exobase (see text).
• Figure 3: The dependence of the (exact) solutions at the exobase on $\kappa$ for RKD electrons, in the same format as Fig. \ref{['fig1']}. Results are plotted for three cutoffs $\alpha = 0.02$ (red), $\alpha = 0.1$ (black) and $\alpha = 0.3$ (blue), and are compared with the results for SKD electrons (orange) from Fig. \ref{['fig1']}. The greenish range in panel (c) indicates observed SW speeds (300–800 km/s).
• Figure 4: Radial profiles for (a) normalized density, (b) ES potential and (c) electron temperature for RKD electrons with $\alpha=0.3$ and different values of $\kappa$. Short lines in panel (b) indicate $\Phi_E(r_0)$ (boundary values) at the exobase $r_0 = 6R_S$). The dotted lines in panel (c) mark the assumed electron temperatures at the exobase (see text).
• Figure 5: Radial profiles of (a) normalized density, (b) ES potential and (c) electron temperature for the model with RKD electrons with $\alpha=0.02$ and different values of $\kappa$. Short lines in panel (b) indicate $\Phi_E(r_0)$ (boundary values) at the exobase $r_0 = 6R_S$). The dotted lines in panel (c) mark the assumed electron temperatures at the exobase (see text).