ON THE SPECTRAL HARDENING AT ≳300 keV IN SOLAR FLARES

Abstract

It has long been noted that the spectra of observed continuum emissions in many solar flares are consistent with double power laws with a hardening at energies 300 keV. It is now widely believed that at least in electrondominated events, the hardening in the photon spectrum reflects an intrinsic hardening in the source electron spectrum. In this paper, we point out that a power-law spectrum of electrons with a hardening at high energies can be explained by the diffusive shock acceleration of electrons at a termination shock with a finite width. Our suggestion is based on an early analytical work by Drury et al., where the steady-state transport equation at a shock with a tanh profile was solved for a p-independent diffusion coefficient. Numerical simulations with a p-dependent diffusion coefficient show hardenings in the accelerated electron spectrum that are comparable with observations. One necessary condition for our proposed scenario to work is that high-energy electrons resonate with the inertial range of the MHD turbulence and low-energy electrons resonate with the dissipation range of the MHD turbulence at the acceleration site, and the spectrum of the dissipation range ∼k −2.7 . A ∼ k −2.7 dissipation range spectrum is consistent with recent solar wind observations.

A Statistical Study of the Spectral Hardening of Continuum Emission in Solar Flares

“…A further condition is that the turbulence spectrum is in the dissipation range ∼k −2.7 . Li et al (2013) also performed numerical simulations with momentum-dependent diffusion coefficients and showed that the accelerated electron spectrum can develop hardenings comparable to observations. As a continuation of Li et al (2013), we conduct a statistical study of electron-dominated events that show clear spectral hardenings.…”

“…Li et al (2013) also performed numerical simulations with momentum-dependent diffusion coefficients and showed that the accelerated electron spectrum can develop hardenings comparable to observations. As a continuation of Li et al (2013), we conduct a statistical study of electron-dominated events that show clear spectral hardenings. Except for a few events from the literature (see Table 1), most events we considered are time-integrated spectra averaged over the entire flare.…”

“…In our recent study (Li et al 2013), we suggested that hardening in an electron spectrum at high energies can be obtained by the diffusive shock acceleration of electrons at a flare termination shock that has a finite width on the order of an ion inertial length scale. The accelerated electrons are likely the heated electrons during the flare process, but can also be electrons accelerated previously.…”

Review on Current Sheets in CME Development: Theories and Observations

“…Detailed features of the particle acceleration in a CS are still open question, and more effort is needed in further and deeper research (e.g., see Dauphin et al 2007;, 2013a, 2013b. The role of small scale structures due to turbulence of the CS in particle acceleration has recently studied by Nishizuka and Shibata (2013) who found that the interaction of these structures provides an approach to Fermi acceleration for particles.…”

Large gradual solar energetic particle events

“…They found that the acceleration of electrons was extremely efficient. Moreover, Li et al (2013) showed that the physical thickness of the shock-being of the order of the thermal ion gyro-radii, which is much larger than that of suprathermal electrons-can affect the resulting shock-accelerated energy spectrum and may even explain the observed spectral features.…”