A.V.R. Silva¹, V.F. Melnikov^1,2, and M. Valente³

1 CRAAE, Mackenzie, R. da Consolação, 896, Sáo, Paulo, SP 01302-000, Brazil

2 Radiophysical Research Institute, B. Pecherskaya St. 25,603600,Nizhnii Novgorod, Russia

3 Instituto de Fisica Gleb Wataghin, UNICAMP, Campinas, SP,13083-970, Brasil

We have performed a statistical study on the duration of hard X-ray bursts and its dependence on the energy of emission. A large number of bursts were analyzed, and their spectra fit by power-laws. These flares were observed by the BATSE Large Area Detector on the Compton Gamma Ray Observatory in 16 energy channels from 15 to 8000 keV. The time profile of each burst in all energy channels were fit as Gaussian F(E,t)~exp[-((t-t_m)/Dt(E))²], where t_m is the time of maximum emission. We then averaged the duration of all flares at a certain energy, and found that the mean duration, Dt, of bursts decreases logarithmically with energy, E, as Dt(E) = A - B lnE (with a correlation coefficient of 0.95). Qualitatively the dependence found is consistent with the commonly observed ``soft-hard-soft" temporal behavior of hard X-ray spectra during impulsive flares. However, this quite good linear dependence allows us to get some interesting information about a quantitative law of temporal behavior of hard X-ray spectral index. We show that the spectral index is a parabolic function in time with parameters derived from A and B. Studies of the temporal evolution of the spectra for individual flares were also performed. The empirical laws obtained can serve as useful constrains when studying the dynamics of electron acceleration in impulsive hard X-ray flares.