1. The spectral evolution of impulsive solar X-ray flares
Grigis, P.C. and Benz, A.O.2004, A&A, 426, 1093
Grigis, P.C. and Benz, A.O.2005, A&A, 434, 1173
June, 27, 2005

2. δ N ｔ E ◎ Spectral analysis
The non thermal photons usually follows a power-law distribution in energy.
We can obtain the information of propagating process
by time variation of spectral index. N E ｔ δ
N ; number of particles
E ; energy
Delta ; spectral index
t ; time
The major flare spectrum starts soft, gets harder as the flux rises and softer again after peak time. 　⇒　SHS pattern
However, flares are also observed systematically hardened with time.　 ⇒　SHH pattern

3. Event selection;
13 Feb ～　31 Nov
GOES class M1～X1 because of pile up affect of RHESSI.
more than 3 min. away from any interruption in the data.
without automatic fitting routine failure,,,etc
26 events,
a total 911 fitting for 24 events,
and a total time of 3722 s.

5. ◎　Assess the effect of the fitting routine
Although the absolute values of the parameters are differ, they preserve the temporal variations.
⇒　The fitting routine preserves the time evolution of the observed counts with high precision.

6. ◎　Relation between flux and spectral index
The plot clearly shows the overall SHS trend.
cross-correlation is –0.80 ± 0.03
γ= AF35-α　（A= 4.043,α= 0.197）

7. ◎　Some more detail at the behavior of single flare
Since there are consecutive peaks in F35 with about same height, but having different minimum value of γ.
⇒ A model of a strict functional dependence does not work well for an entire flare.

8. ◎　γ vs F35 plot for three events
Interestingly, in some flare the fitted line is steeper in the decay phases.
αr = ± 0.009
αd = ± 0.012

9. Conclusion
The fitting method eliminates the influence of the thermal component and improves considerably the noise on the derived spectral index.
The SHS behavior appears on short time scale, although SHS was previously considered to be a global property of flares.
The relation between spectral index and flux appears linear in double-logarithmic representation.
The SHS behavior supports the idea that each non-thermal emission peak represents a distinct acceleration event of electrons in the flare.

10. Introduction
The authors give a simple quantitative description of the SHS patterns. Can this systematical trend in the evolution of the HXR photon spectrum be used to put constrains on acceleration mechanisms?
The main piece of information is the relation between the normalization of the non thermal component of the spectrum and its spectral index (assuming to be a power-law ).

11. Acceleration scenarios
Constant productivity scenario
The productivity of accelerator is constant (rate or power) above a threshold energy. But the acceleration process evolves in such a way that flux and index vary.
Stochastic acceleration scenario
Plasma wave accelerate stochastically the electron in plasma slab.

12. Interestingly, stochastic model has the special property that all the spectra cross each other in a very narrow region of the plot.

13. ◎ Comparison with the data
The constant rate and stochastic acceleration models corresponding to the rise and decay phases. In each fit, the model parameters are constant in time.

14. Most of the parameters are concentrated in a relatively narow region, except for about 20～30%.

15. The resulting parameters imply unphysically high electron acceleration rates and energies for 20～30% events.
⇒ more degrees of freedom are necessary for interpretation.
⇒ the mathematical reason of failure is that these model just assume power-law behavior of observed electron distribution above a fixed threshold energy.

16. Conclusion
A simple stochastic acceleration model yields plausible best fit model parameters for about 77% of 141 events consisting of rise and decay phases of individual HXR peaks.
However, it implies unphysically high electron acceleration rate and total energies for others.
Other simple acceleration models such as constant rate of accelerated electrons or constant input power have a similar failure rate.
The cases compatible with a simple stochastic model require typically a few times 10^36 electrons accelerated per second beyond a threshold energy of 18 keV in the rise phase and 24 keV in the decay phase of flare peaks