Solar Electron Events

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Number: 51
1st Author: Linghua Wang
2nd Author:
Published: 14 January 2007
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The Sun commonly accelerates electrons to relativistic energies, above 1 MeV. Some of these can then escape and fly into the solar wind in "open" magnetic fields. We then detect some of these bursts of particles by detectors in space near the Earth, or in deep space. In this Nugget we discuss the "impulsive" solar electron events, so-called because the associated soft X-ray burst (when present) is of short duration. Near solar maximum, a thousand such events/month occur over the whole Sun, making these the most common impulsive solar particle acceleration phenomenon. They are almost always accompanied by a solar and interplanetary type III radio bursts, but seldom by hard X-ray bursts.

As the electrons propagate away from the Sun, the magnetic field decreases rapidly (roughly as an inverse square law). Because this slow decrease is adiabatic, the electron velocity vectors must approach the field direction. The angle between the velocity and the field is called the pitch angle and its distribution a PAD ("pitch angle distribution"). The action of the expanding field is to focus the PAD into a field-aligned particle beam. On the other hand, fluctuations in the field may scatter the electrons, reducing the effect of the focusing. Collisions with ambient particles could do this as well, but the solar wind is so tenuous as to make this process unimportant by comparison. If we can measure the pitch-angle distribution we can therefore learn about the presence of these field fluctuations (waves) as well as about the solar origin of the electrons in the first place.

Observed electron pitch-angle distributions

Figure 1 shows a good example of an impulsive electron event. The spectrograms at the bottom descibe the pitch-angle distributions. We obtain these observations from the "3-D Plasma and Energetic Particle (3DP)" instrument on the WIND spacecraft. The spectrograms show that at lower electron energies one has a tight unidirectional beam propagating outwards, but that at higher energies the beam seems more diffuse. We believe that this reveals weak pitch-angle scattering for the higher-energy electrons.

Figure 1: The electron flux-time profile and PAD spectrogram at 1.1 keV (left) and 108 keV (right) for the 2002 October 20 event. The bottom panels show the PAD as maps of intensity vs. time and pitch angle, with 0 degrees along the field (towards the Sun) and 180 degrees away from the Sun. We can use these data to analyze the behavior of the electrons in time and energy. Figure 2 shows the different behavior of low-energy and high-energy electrons: for the low energies, the PAD remains below about 30 degrees in width, limited by the instrumental resolution, for the first hour of the event. It then increases, suggesting that the condition for "scatter-free" propagation has disappeared. At the higher energies the distributions are initially broader and generally increases with time. This suggests some energy-dependent scattering in the solar wind, which we think may be expected because the gyroradii of the electron motions at these energies roughly matches that of the ambient solar-wind protons, which are at much lower energies. This implies the possibility of resonant coupling that would work at the higher energies where this condition is met, but not the lower energies.

Figure 2: The energy and time dependence of the PAD width for the event shown in Figure 1. The left panels show three low-energy channels: 1.1 keV (blue), 1.95 keV (green) and 2.8 keV (red). The right panels show three high-energy channels: 66 keV (blue), 108 keV (green) and 180 keV (red). The peak of electron fluxes at different energies has been shifted to the same time (top panels); naturally the more energetic electrons arrive sooner because of velocity dispersion. Monte-Carlo particle simulation

We model this by a Monte Carlo technique, so named by George Gamow because the celebrated casino there inspired him to think statistically. We sample the physical process with random elements that simulate the statistics (in this case) of the scattering. Based on electron observations at low energies, we assume the injection flux at the Sun to be an isosceles triangular function of time. We also use the peak flux energy spectrum at 1 AU as the source spectrum at the Sun, because the energy of energetic electrons changes negligibly during their propagation. We then consider both magnetic focusing and pitch-angle scattering, and use the Monte-Carlo particle simulation to following the motion of individual electrons from the Sun to 1 AU. Finally, we fit these results to the observations to estimate the electron injection profile at the Sun and the mean free path of their propagation in the solar wind.

Figure 3: The triangular injection profiles at the Sun for the 1998 August 29 event (left) and the 2002 October 20 event (right). Each triangle refers to the model analysis for the electron energy shown on the Y-axis. The red vertical lines show the release times of the associated type III radio bursts, which mark the time of particle acceleration near the Sun. Figure 3 shows that electron injections below ~10-15 keV begin before the type III radio burst (the red dashd lines) and lasts for ~1-2 hours, while electron injections above ~15-20 keV have much shorter durations (~5-30 mins) and are clearly delayed relative to the radio burst. The source of the type III radio burst can thus be identified with low-energy electron injections. These low-energy injections show a hard-soft spectral evolution over a long time interval (~1-2 hours), which argues against a storage/release mechanism in the corona. Thus, they are likely produced by a continuous process. On the other hand, the electron energy spectra fit a double power-law with a downward break at ~40-50 keV, but exhibit a smooth power-law across the transition energy range (~10-15 keV), suggesting low-energy injections may provide the seed electrons for a delayed high-energy injections.

Figure 4: The energy dependence of the electron mean free path for the 1998 August 29 event (black) and the 2002 October 20 event (red). The model allows us to estimate the distance traveled between individual scatterings by an electron of a given energy (the "mean free path"). In Figure 4, we see that the mean free path systematically decreases with energy. It is more than two AU for electrons below 10 keV ("scatter-free" propagation), but ~0.3-0.8 AU for electrons above 30 keV. In comparison, the expected total path length along the Parker spiral should be on the order of 1.1-1.3 AU. This energy dependence is consistent with the results of the PAD study described above.


In the selected impulsive solar electron events, the low-energy and high-energy electrons exhibit different injection and propagation behaviors. At the Sun, the injection of low-energy (0.4-15 keV) electrons is related to the type III radio burst and (surprisingly) has a long duration. The higher-energy electrons (15-300 keV) electrons start later and have shorter event durations. We think that the low-energy electrons may provide the seed population for the acceleration of the delayed high-energy electrons. After the electrons escape into the solar wind, the low energy electrons seem to propagate nearly free of scattering, but the high-energy suffer from some pitch-angle scattering.

Biographical note: Linghua Wang is a graduate student at the Space Sciences Laboratory in Berkeley.

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