Hydrodynamic properties of gamma-ray bursts outflows deduced from thermal component

We study the properties of a significant thermal emission component that was identified in 47 GRBs observed by different instruments. Within the framework of the "fireball" model, we deduce the values of the Lorentz factor Gamma, and the acceleration radius, r_0, for these bursts. We find that all the values of Gamma in our sample are in the range 10^2 <= Gamma <= 10^3, with <Gamma> = 370. We find a very weak dependence of Gamma on the acceleration radius r_0, Gamma ~ r_0^alpha with alpha = -0.10 +- 0.09 at sigma = 2.1 confidence level. The values of r_0 span a wide range, 10^6.5 <= r_0 <= 10^{9.5} cm, with mean value <r_0>~10^{8} cm. This is higher than the gravitational radius of a 10 M_sun black hole by a factor ~30. We argue that this result provides indirect evidence for jet propagation inside a massive star, and suggests the existence of recollimation shocks that take place close to this radius.