by Georgios Nicolaou (MSSL, UCL)
The polytropic equation relates the density and temperature of a fluid through the polytropic index. The polytropic index is a crucial parameter in understanding the physical mechanisms acting on the fluid. In this study, we investigate the large time-scale and the short time-scale fluctuations of the plasma proton density and temperature in order to determine their polytropic index. The large time-scale fluctuations which are associated with the plasma expansion within the heliosphere, follow a polytropic model with a polytropic index ~5/3. The specific behavior is consistent with an adiabatic expanding plasma protons with three degrees of freedom. The radial profile of the density follows in general, the model for a spherical expansion with a constant radial speed (see Figure 1). However, the short time-scale fluctuations, which are associated with plasma turbulence, follow a polytropic model with a polytropic index ~2.7. Interestingly, the short time-scale polytropic index is found to be correlated with the interplanetary magnetic field. We discuss the possibly of a mechanism that supplies/retains energy from the plasma protons in these short time-scales, or a mechanism that restricts the effective degrees of freedom of the protons. We finally highlight the importance of future studies that examine the polytropic index along with the characteristics of the full 3D distributions of the plasma ions and electrons.
Figure 1. Two-dimensional histograms of (top) the proton density and (bottom) the proton temperature as functions of the radial distance for time interval 1. The magenta line in the top panel shows the expected density for an expansion model with constant speed, n ∝ r-2. In the lower panel, the magenta line shows the expected temperature of a polytropic radial expansion model with γ = 5/3 while the blue lines represent expansion models with γ = 2.7. The grey line illustrates the slope determined by Huang et al. 2020 for the parallel proton temperature of fast solar wind observed by SPC.
Please see the paper for full details:
Nicolaou, G., Livadiotis, G., Wicks, R. T., Verscharen, D., Maruca, B. A., (2020). Polytropic Behavior of Solar Wind Protons Observed by Parker Solar Probe. The Astrophysical Journal, 901, 1, https://doi.org/10.3847/1538-4357/abaaae.