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

Abstract

The observed hard X-ray and γ -ray continuum in solar flares is interpreted as Bremsstrahlung emission of accelerated non-thermal electrons. It has been noted for a long time that in many flares the energy spectra show hardening at energies around or above 300 keV. In this paper, we first conduct a survey of spectral hardening events that were previously studied in the literature. We then perform a systematic examination of 185 flares from the Solar Maximum Mission. We identify 23 electron-dominated events whose energy spectra show clear double power laws. A statistical study of these events shows that the spectral index below the break (γ 1 ) anti-correlates with the break energy (ε b ). Furthermore, γ 1 also anti-correlates with Fr, the fraction of photons above the break compared to the total photons. A hardening spectrum, as well as the correlations between (γ 1 , ε b ) and (γ 1 , Fr), provide stringent constraints on the underlying electron acceleration mechanism. Our results support a recent proposal that electrons are being accelerated diffusively at a flare termination shock with a width of the order of an ion inertial length scale.

Relativistic Electrons Produced by Reconnecting Electric Fields in a Laser-Driven Bench-Top Solar Flare

“…So, on one hand, if the two Al-foils are arranged in the same plane as we do for Case 1, magnetic reconnection roughly occurs in a 2-dimensional fashion; on the other hand, if the two Al-foils are not in the same plane, instead an angle exists between the planes where the two Al-foils are located, as we arranged for Case 2, a guid field along the z-axis the is hence created in the system, and magnetic reconnection happens in a 2.5-dimensional fashion (see also discussions by Li & Lin 2012;Zhakova et al 2011;Li et al 2013 ).…”

“…Plasma blobs flowing in a CS developed by a major eruption were reported by Ko et al (2003) for the first time, and were observed in many eruptive events afterwords; the numerical experiments by Forbes & Priest (1983) displayed plasma blobs in the reconnecting CS for the first time, then were confirmed by all the subsequent numerical experiments on the related topic (e.g., see a recent review by for more details). Li & Lin (2012) and Li et al (2013) showed that complex structures inside CS play an important role in governing both trajectories and spectra of energetic particles accelerated in the CS. But it is very hard, if not impossible, to observe this process directly and to perform in situ measurements for the energetic particles near the reconnection region in space, so the necessity to conduct the laboratory experiments is apparent.…”

Diffusive shock acceleration of cosmic rays from two stationary shocks

“…Similarly, spectral hardening has been observed at solar flare termination shocks Li et al The breaking point p b as a function of L (crosses) and u 2 (circles), numerically evaluated using the first derivative of log n(p) with respect to log p. Solid lines are Eq. (15) (2013) and Kong et al (2013). In these previous studies, the finite thickness of the termination shock was considered, and it was concluded that spectral hardening occurs because high-energy electrons can see the full width, while low-energy particles accelerate for only part of the shock width.…”

Gyrosynchrotron Emission Generated by Nonthermal Electrons with the Energy Spectra of a Broken Power Law

“…Existence of such broken-power-law energy distribution of energetic electrons has been demonstrated by the HXR observation showing a broken photon spectrum with a harder spectral component around 300 keV or higher (Suri et al 1975;Yoshimori et al 1985;Shih et al 2009;Kawate et al 2012;Kong et al 2013). The straightforward interpretation of this observation is that the source electrons intrinsically have a hardening energy distribution (Suri et al 1975;Yoshimori et al 1985;Dennis et al 1988).…”

“…For electrons with a broken-power-law distribution (δ 1 = −3.0, δ 2 > δ 1 ), N nth gets larger accordingly (by several percentages to several times). According to the typical δ value of -3 to -5 (in some cases larger than -2, Effenberger et al 2017;Oka et al 2018) and E B value around 1.0 MeV (Kong et al 2013;White et al 2011), in our parameter study we vary the three parameters in the following ranges: Both the size and depth of the source are fixed to be 14 ′′ (∼ 10 9 cm). Two viewing angles have been considered, with θ = 20 • for the quasi-parallel case and θ = 70 • for the quasi-perpendicular case.…”