CENTER-TO-LIMB VARIATIONS OF CHARACTERISTICS OF SOLAR-FLARE HARD X-RAY AND GAMMA-RAY EMISSION

The observed distribution of fluxes and spectral indices of flares at X-ray and gamma-ray range are analyzed with particular attention to variation with heliocentric longitude of these distributions and their moments. It is shown how these distributions can be used to set constraints on the distribution and average values of model parameters describing the characteristics of the accelerated electrons and flare plasma. The models assumed are the nonthermal thick target models, whereby accelerated electrons with power-law spectra and Gaussian pitch angle distribution are injected at the top of a coronal loop with two kinds of converging field geometries. The basic distributions are derived from data on all flares, irrespective of their position on the sun, at low energies (hard X-rays) where the angular dependence of the parameters is negligible. Comparison of X-ray and gamma-ray spectral indices show that the spectrum of the accelerated electrons must flatten at higher energies. From comparison of observed and predicted angular variation of (1) the number of flares at different photon energy ranges (especially above 10 MeV), (2) the average gamma-ray spectral index, and (3) the gamma-ray-to-X-ray flux ratio constraints have been set on model parameters. In particular the range of the Gaussian width of the pitch angle distribution of electrons beamed along the field lines and the convergence rate of the magnetic field are delimited. Isotropic pitch angle distributions or distributions peaking perpendicular to the field lines, and field convergence rate with more than a fivefold increase in the magnetic field from corona to the photosphere can be ruled out.