The great majority of flares follows a soft-hard-soft behavior (illustrated in Figure 27). 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, 2004, 2005b). The relation appears as a power-law relation between the photon spectral index and the flux density F(E0) measured at a given energy E0,A is constant that varies from flare to flare, and is 0.1210.009 in the flare rise phase and 0.1720.012 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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