Asaf Pe'er, Felix Ryde, Ralph A. M. J. Wijers, Peter Mészáros, Martin J. Rees
Abstract
In recent years increasing evidence has emerged for a thermal component in the gamma- and X-ray spectrum of the prompt emission phase in gamma-ray bursts. The temperature and flux of the thermal component show a characteristic break in the temporal behavior after a few seconds. We show here, that measurements of the temperature and flux of the thermal component at early times (before the break) allow the determination of the values of two of the least restricted fireball model parameters: the size at the base of the flow and the outflow bulk Lorentz factor. Relying on the thermal emission component only, this measurement is insensitive to the inherent uncertainties of previous estimates of the bulk motion Lorentz factor. We give specific examples of the use of this method: for GRB970828 at redshift z=0.9578, we show that the physical size at the base of the flow is r₀ = (2.9+-1.8)*10⁸ Y₀^-3/2 cm and the Lorentz factor of the flow is Gamma = (305\+-28) Y₀¹/4, and for GRB990510 at z=1.619, r₀=(1.7+-1.7)*10⁸ Y₀^-3/2 cm and Gamma=(384+-71) Y₀¹/4, where Y = 1 Y₀ is the ratio between the total fireball energy and the energy emitted in gamma- rays.