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 in the γ- 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 GRB 970828 at redshift z = 0.9578, we show that the physical size at the base of the flow is r 0 = (2.9 ± 1.8) × 10 8 Y cm and the Lorentz factor of the flow is Γ = (305 ± 28) Y , and for GRB 990510 at z = 1.619, r 0 = (1.7 ± 1.7) × 10 8 Y cm and Γ = (384 ± 71) Y , where Y = 1 Y 0 is the ratio between the total fireball energy and the energy emitted in γ-rays.