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5.2 Soft-hard-soft behavior in hard X-rays

The hardness of the non-thermal spectrum changes in the course of a flare, starting soft (steep), getting harder at the peak and softening toward the end (Parks and Winckler, 1969Kane and Anderson, 1970). A few large flares continue to harden after the peak (Frost and Dennis, 1971Krucker et al., 2005b). These flares have been shown to be particularly well associated with solar energetic particle events (Kiplinger, 1995).
View Image

Figure 27: Flux density at 35 keV and power-law index as determined from RHESSI observations of the non-thermal component of flare hard X-ray emission. Colors mark individual subpeaks. The close correlation demonstrates soft-hard-soft behavior in the smallest details (from Grigis and Benz, 2004Jump To The Next Citation Point).

The great majority of flares follows a soft-hard-soft behavior (illustrated in Figure 27View Image). This correlation between (negative) spectral index and flux is generally interpreted as a signature of the acceleration process. A similar relation also holds for peak values of flares with different size, indicating that small flares are on the average softer (Battaglia et al., 2005). Both the time variation and the size variation of the spectral index with flux indicate that intense hard X-ray radiation is not a superposition of many small events. High flux means that the acceleration process is driven more forcefully, resulting in a harder spectrum. It is stringent property of the acceleration process, but alas, many acceleration processes show this behavior.

The soft-hard-soft property has become more relevant recently when it became possible to express the relation between flux and spectral index in a quantitative way that can be compared to models (Grigis and Benz, 2004Jump To The Next Citation Point2005b). The relation appears as a power-law relation between the photon spectral index γ and the flux density F(E0) measured at a given energy E0,

γ = AF (E )−α , (6 ) 0
where A is constant that varies from flare to flare, and α is 0.121±0.009 in the flare rise phase and 0.172±0.012 in the decay phase for E0 = 35 keV (Grigis and Benz, 2004). In this quantitative form, the soft-hard-soft behavior becomes a stringent condition for electron acceleration theories.
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