ELECTRON TIME-OF-FLIGHT DIFFERENCES IN SOLAR-FLARES

In the thick-target model for hard X-ray (HXR) emission in solar flares, electron acceleration is assumed to occur in flaring loops at coronal heights, while HXR bremsstrahlung emission is produced in the chromosphere. Under this assumption, the velocity spectrum of the accelerated electrons causes time-of-flight differences that are expected to result in the lower energy HXRs to be delayed with respect to the higher energies. Here we report on the first observational evidence for such a delay. The electron time-of-flight differences between electrons that produce 25-50 keV and 50-100 keV HXR emission are found to have a distribution with a mean of tau = 16.7 +/- 1.9 ms and a standard deviation of sigma(tau) = 16.8 ms. This result is based on the statistics of 5430 HXR pulses detected during 640 solar flares, recorded in the Discriminator Science Data (DISCSC) burst trigger mode with a time resolution of 64 ms by the Burst and Transient Source Experiment (BATSE) onboard the Compton Gamma Ray Observatory (CGRO). From the time-of-flight differences we infer a mean altitude of the acceleration site of H = 7300 +/- 800 km (with a standard deviation of sigma(H) = 7300 km) above the level at which the electrons lose their energy. This derived mean loop height should be considered as a lower limit because it is based on the predominance of time-of-light effects over opposite delay effects caused by pitch-angle scattering or trapping. For the electron density in the flare loops we find an upper limit of n(e) less than or equal to 4 x 10(12) cm(-3), based on the requirement that the electron travel time has to be shorter than the collision time. The relatively small time-of-flight differences correspond typically to only approximate to 3% of the HXR pulse duration, and, therefore, no rapid variation in the spectral slope of the observed HXR spectrum is expected.