Statistical Independence Test of the Kappa Parameter as a Physical Variable Constant and Independent of Temperature Wind Plasma and Particle Density in Solar

Abstract

In this study, we developed and applied a methodological and mathematical framework to demonstrate that the Kappa parameter is not merely a fitting parameter. We provide experimental evidence that the isotropic Standard Kappa Distribution (SKD) is capable of deriving all plasma physical properties of the quiet solar wind proton population and satisfies the ideal gas law. This is based on the analytical relationship between the moment ratio and the Kappa parameter, from which κ ≈ 3 was obtained and the plasma temperature accurately predicted. We then moved to phase space to reveal the thermodynamic nature of the Kappa parameter as a physical variable governing the dynamics and expansion of the solar wind. The calculations showed consistency with weakly coupled plasma. The constancy of the Kappa parameter was explained through the dynamical balance between the characteristic times.                                  
By calculating these characteristic times, we were able to determine the travel time of the plasma and of the slow and fast acoustic disturbances to Earth, as well as the acoustic Mach number. The methodology was further supported by a statistical test between (T, κ) and (n, κ), providing evidence for the physical independence of the Kappa parameter along a thermodynamic path. The study recommends extending this methodology to time-series data from the Parker Solar Probe using the anisotropic Standard Kappa Distribution (SKD), accounting for magnetic-field effects, as well as the Regularized Kappa Distribution (RKD), and applying it to other plasma environments.