Electron transport during the 1999 august 20 flare inferred from microwave and hard X-ray observations

We discuss injection and transport of high-energy electrons during a GOES X-ray class M9.8 flare observed in microwaves with the Owens Valley Solar Array (OVSA) and in hard X-rays (HXRs) with the hard X-ray telescope (HXT) on board Yohkoh. Observed at 1 s timescales or better in both wavelength regimes, the event shows (1) a large difference in scale between the microwave source and the HXR source; (2) an unusually hard HXR spectrum (maximum spectral index ∼-1.6), followed by rapid spectral softening; and (3) a microwave light curve containing both impulsive peaks (3 s rise time) simultaneous with those of the HXRs and a long, extended tail with a uniform decay rate (2.3 minutes). We analyze the observations within the framework of the electron trap-and-precipitation model, allowing a time-dependent injection energy spectrum. Assuming thick-target bremsstrahlung for the HXRs, we infer the electron injection function in the form Q(E, t) ∼ (E/E₀)^-δ(t), where the timescale for δ(t) to change by unity is ∼7 s. This injection function can account for the characteristics of the impulsive part of the microwave burst by considering the bulk of the electrons to be directly precipitating without trapping. The same injection function also accounts for the gradual part of the microwave emission by convolving the injection function with a kernel representing the trapping process, which at late times gives N(E, t) ∼ e^-vt (E/E₀)^-b. We require b ∼ 1.4 and v ∼ 6 × 10^-3β s^-1, where β is the electron speed divided by the speed of light. Therefore, the derived form of the precipitation rate ν itself indicates strong pitch-angle diffusion, but the slow decay of the microwave radiation requires a small loss cone (∼4°) and a low ambient density in the coronal trap. Also, the numbers of electrons needed to account for the two components of the microwave emission differ by an order of magnitude. We estimate that the ≥100 keV number of the directly precipitating electrons is ∼10³³, while the trapped population requires ∼10³² electrons. This leads us to a model of two interacting loops, the larger of which serves as an efficient trap while the smaller provides the impulsive source. These characteristics are consistent with the spatially resolved observations.