Electron-Ion equilibration in CME-driven shocks

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1st Author:	John RAYMOND
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Published:	August 3, 2026
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Introduction

Coronal mass ejections (CMEs) drive shock waves into regions of very low collisionality. The jumps in density, pressure and temperature at a shock wave in dense gas are mediated by particle collisions, and that leads to thermal equilibrium: equal temperatures of all particle species and a Maxwellian velocity distribution for each species. In a low density plasma, on the other hand, the collision lengths are large, and the shock jump must therefore be mediated by electromagnetic fields and plasma waves. That can lead to non-Maxwellian velocity distributions, such as Solar Energetic Particles (SEPs), and to differing electron and ion temperatures.

In the solar wind, postshock electron temperatures are generally less than proton temperatures (e.g., Ref. [1]) though there is considerable scatter. Shocks in supernova remnants reach higher Mach numbers, and they show a trend of decreasing electron-to-ion temperature ratio with increasing shock speed or Mach number (Ref. [2]). CME-driven shocks In the solar corona are more difficult to study, but they are observed as type II radio bursts and as faint emission in UV, EUV and white light coronagraph spectra and images (e.g., Ref. [3]).

How do we infer plasma temperatures?

In some cases, it is possible to infer the electron temperature behind a coronal shock by comparing extreme ultraviolet images from AIA in different bands. When the electrons are suddenly heated in a shock, the iron ions are successively ionized from Fe X to Fe XII to Fe XIV to Fe XVI (The AIA 171, 193, 211 and 335 Å bands). If the density is known from type II radio emission or from a global MHD model of the corona, the lags between the appearance of the shock in the different bands indicate the electron temperature (Refs. [4,5]). Figure 1 shows a CME-driven shock observed on 2010 June 13, with the 3D structure inferred from AIA and STEREO images (Ref. [5]). Figure 2 shows the dimensionless parameter ΔT_e at different positions along the shock front, where ΔT_e = 0 corresponds to equal electron and proton temperatures and ΔT_e = 1 corresponds to no electron heating. The intermediate values seen in Figure 2 show that these 500-700 km/s shocks heat the electrons about half as efficiently as the ions.

Figure 1: SDO/AIA 193 Å running difference images at three different times of the 13 June 2010 CME-driven shock wave. The blue line shows the outline of the geometric model - here, the data were binned by a factor of 8 to increase the S/N when fitting the model to the data. The software captures the irregular shape of the shock, accounting for angle-dependent acceleration. The shock can be identified as the bright outer ring of the structure, while the erupting prominence driving the shock is clearly identified as the bright inner ring structure. Bottom: Corresponding STEREO-A EUVI 195 Å difference images, with the geometric model plotted in blue. Right: Labeled reference of different portions of the shock structure.

Figure 2: A schematic map of the shock, with separate regions highlighted in yellow, magenta, and/or cyan based on the performance of each model based on the time of the peaks and the intensities of the peaks. Panels showing the combined color maps use a CMY subtractive color model to accurately reflect where the data is unable to differentiate between the models. The color wheel at the top-right serves as an approximate guide, where the color changes depending on the separation from the loci for each model. The solid blue hexagon, for instance, represents good agreement with both ΔT_e = 0.5 (cyan) and ΔT_e = 0.25 (magenta) models where ΔT_e = 0 for complete equilibration and 1 for no equilibration.

Conclusion

Non-equilibrium plasmas probably dominate the Universe, but they are hard to diagnose via remote-sensing techniques. A wealth of plasma physics results from T_e ≠ T_i and anisotropic distribution functions, and large-scale shock waves in the solar corona provide an excellent opportunity to study such effects.