Electron trapping times and trap densities in solar flare loops measured with Compton and Yohkoh

We measure energy-dependent time delays of approximate to 20-200 keV hard X-ray (HXR) emission from 78 flares observed simultaneously with the Compton Gamma Ray Observatory and Yohkoh. Fast time structures (less than or equal to 1 s) are filtered out, because their time delays have been identified in terms of electron time-of-flight (TOF) differences from directly precipitating electrons (Aschwanden et al.). For the smooth HXR flux, we find systematic time delays in the range of tau(s) = t(50 keV)-t(200 keV) approximate to -(1... 10) s, With a Sign opposite to TOF delays, i.e., the high-energy HXRs lag the low-energy HXRs. We interpret these time delays of the smooth HXR flux in terms of electron trapping, and we fitted a model of the collisional deflection time t(Defl)(E) proportional to E(3/2)n(e)(-1) to the observed HXR delays in order to infer electron densities n(e)(Trap) in the trap. Independently, we determine the electron density n(e)(SXR) in flare loops from soft X-ray (SXR) peak emission measures EM = integral n(e)(2) dh, using loop width (w) measurements to estimate the column depth dh approximate to w. Comparing the two independent density measurements in HXR and SXR, we find a mean ratio of q(e) = n(e)(Trap)/n(e)(SXR) approximate to 1, with a relatively small scatter by a factor of approximate to 2. Generally, it is likely that the SXR-bright hare loops have a higher density than the trapping regions (when q(e) < 1), but they also are subject to filling factors less than unity (when q(e) > 1). Our measurements provide comprehensive evidence that electron trapping in solar flares is governed in the weak-diffusion limit, i.e., that the trapping time corresponds to the collisional deflection time, while pitch-angle scattering by resonant waves seems not to be dominant in the 20-200 keV energy range. The measurements do not support a second-step acceleration scenario for energies less than or equal to 200 keV.