Energetic Particle Spectral Shapes in Planetary Magnetospheres; Assessment of the Kappa Function

Abstract:

In assessing the efficacy of the kappa distribution function in space environments, it is useful to follow two paths. First, to what extent do we consider the kappa function (or any function) to represent some kind of universal spectral shape that indicates common physical processes occurring in a wide diversity of space environments? Second, how useful is the kappa function in quantitatively characterizing observed spectral shapes, particularly for the purpose permitting further quantitative analyses of the environment (e. g. wave growth). In this report I evaluate the efficacy of the kappa distribution in representing energetic particle spectral shapes in planetary magnetospheres from both perspectives. In particular, I expand on the extensive treatment provided by Carbary et al. (2014) by taking a more explicit comparative approach between the different planets (Earth, Jupiter, Saturn, Uranus, and Neptune) and also focusing on the most intense (and therefore from my perspective the most interesting) spectra within each of these different planets. There is no question that the “power law tail” represents as close to a universal characteristic of planetary space environments as one could hope to find. Such a universal shape must represent some universality in the energization and/or equilibrating processes. Also, there is no question that such tails must (to be non-divergent) and do roll over to flatter shapes at lower energies. In a number of applications, this basic characteristic has been usefully characterized by the kappa function to extract such parameters of the system as flow velocities. However, at least for the more intense spectra at Earth, Jupiter, Saturn, and Uranus, the kappa function in fact does a relatively poor job in representing the low energy roll-over of energetic particle spectra. Other functional forms have been found to be much more useful for characterizing these spectral shapes over a broad range of energies. And specifically, a very common shape that is found at energies below a power-law spectral component is in fact another power-law component.

Carbary, J. F., M. Kane, B. H. Mauk, and S. M. Krimigis (2014), Using the kappa function to investigate hot plasma in the magnetospheres of the giant planets, J. Geophys. Res. Space Physics, 119, 8426–8447, doi:10.1002/2014JA020324.