Wavelet analysis of solar flare hard X-rays

We apply a multiresolution analysis to hard X-ray (HXR) time profiles f(t) of solar flares. This method is based on a wavelet transform (with triangle -shaped wavelets), which yields a dynamic decomposition of the power at dif ferent timescales T, the scalogram P(T, t). For stationary processes, time- averaged power coefficients, the scalegram S(T), can be calculated. We deve lop an algorithm to transform these (multiresolution) scalegrams S(T) into a standard distribution function of physical timescales, N(T). We analyze 6 47 solar flares observed with the Compton Gamma Ray Observatory (CGRO), rec orded at energies greater than or equal to 25 keV with a time resolution of 64 ms over 4 minutes in each flare. The main findings of our wavelet analy sis are: 1. In strong flares, the shortest detected timescales are found in the rang e T-min approximate to 0.1-0.7 s. These minimum timescales are found to cor relate with the flare loop size r (measured from Yohkoh images in 46 flares ), according to the relation T-min(r) approximate to 0.5(r/10(9) cm) s. Mor eover, these minimum timescales are subject to a cutoff, T-min(n(e)) greate r than or similar to T-Defl(n(e)), which corresponds to the electron collis ional deflection time at the loss-cone site of the hare loops (inferred fro m energy-dependent time delays in CGRO data). 2. In smoothly varying flares, the shortest detected timescales are found i n the range T-min approximate to 0.5-5 s. Because these smoothly varying fl ares exhibit also large trap delays, the lack of detected fine structure is likely to be caused by the convolution with trapping times. 3. In weak flares, the shortest detected timescales cover a large range, T- min approximate to 0.5-50 s, mostly affected by Poisson noise. 4. The scalegrams S(T) show a power-law behavior with slopes of beta(max) a pproximate to 1.5-3.2 (for strong hares) over the timescale range of [T-min , T-peak]. Dominant peaks in the timescale distribution N(T) are found in t he range T-peak approximate to 0.5-10(2) s, often coinciding with the upper cutoff of N(T). These observational results indicate that the fastest significant HXR time structures detected with wavelets tin strong flares) are related to physica l parameters of propagation and collision processes. If the minimum timesca le T-min is associated with an Alfvenic crossing time through elementary ac celeration cells, we obtain sizes of r(acc) approximate to 75-750 km, which have a scale-invariant ratio r(acc)/r approximate to 0.03 to flare loops a nd are consistent with cell sizes inferred from the frequency bandwidth of decimetric millisecond spikes.