A New Method of Determining the Initial Size and Lorentz Factor of Gamma-Ray Burst Fireballs Using a Thermal Emission Component

In recent years increasing evidence has emerged for a thermal component inthe 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 breakin the temporal behavior after a few seconds. We show here, that measurementsof the temperature and flux of the thermal component at early times (before thebreak) allow the determination of the values of two of the least restrictedfireball model parameters: the size at the base of the flow and the outflowbulk Lorentz factor. Relying on the thermal emission component only, thismeasurement is insensitive to the inherent uncertainties of previous estimatesof the bulk motion Lorentz factor. We give specific examples of the use of thismethod: for GRB970828 at redshift z=0.9578, we show that the physical size atthe base of the flow is r_0 = (2.9+-1.8)*10^8 Y_0^{-3/2} cm and the Lorentzfactor of the flow is Gamma = (305\+-28) Y_0^{1/4}, and for GRB990510 atz=1.619, r_0=(1.7+-1.7)*10^8 Y_0^{-3/2} cm and Gamma=(384+-71) Y_0^{1/4}, whereY = 1 Y_0 is the ratio between the total fireball energy and the energy emittedin gamma- rays.Comment: Discussion added on gamma-ray emission efficiency. Accepted for publication in Ap.J. Let