Deconvolution of Directly Precipitating and Trap‐Precipitating Electrons in Solar Flare Hard X‐Rays. II.Compton Gamma Ray ObservatoryData Analysis

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Abstract
Based on the deconvolution method developed in the first paper of this series, we present here the data analysis of 20-200 keV hard X-ray (HXR) data from the Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory (CGRO) recorded during 103 solar flares in 1991-1995. These are all of the flares simultaneously observed by CGRO with high time resolution (64 ms) and by Yohkoh in flare mode. The deconvolution method takes the measured HXR count rates as function of energy and time, I(ε, t), and computes the following self-consistently: the electron injection function n(E, t), the directly precipitating electron flux nprec(E, t), the trapped-precipitating flux ntrap(E, t), the fraction of directly precipitating electrons (qprec), the electron time-of-flight distance (lTOF), and the electron density at the loss cone site of the trap (ne). We find that the electron time-of-flight distances (lTOF = 20.0 ± 7.3 Mm) inferred with the deconvolution method are fully consistent with those obtained earlier using a Fourier filter method. The trap electron densities (ne = 1010.96±0.57 cm-3) obtained from deconvolving the e-folding decay times of HXR pulses (according to the trap model of Melrose & Brown) are found to be statistically a factor of 1.5 lower than those inferred from cross-correlation delays. The fraction qprec of directly precipitating electrons, measured for the first time here, is found to have a mean (and standard deviation) of qprec = 0.42 ± 0.16. Based on this precipitation fraction, we infer loss cone angles of α0 ≈ 20°-70° and magnetic mirror ratios of R = Bloss/Binj ≈ 1.2 - 3 (with a median value of Rmedian = 1.6) between the loss cone site and injection/acceleration site, assuming an isotropic pitch angle distribution at the injection site. The TOF distances and mirror ratios constrain magnetic scale heights in flare loops to λB = 10-150 Mm. The fact that this two-component model (with free-streaming and trapped electrons) satisfactorily fits the energy-dependent time delays in virtually all flares provides strong evidence that electron time-of-flight differences and collisional scattering times dominate the observed HXR timing, while the injection of electrons appears to be synchronized (independent of energy) and does not reveal the timing of the acceleration process.