The early X-ray afterglow for a significant number of gamma-ray bursts detected by the Swift satellite is observed to have a phase of very slow flux decline with time ( F _ { \nu } \propto t ^ { - \alpha } with 0.2 \lesssim \alpha \lesssim 0.8 ) for 10 ^ { 2.5 } { s } \lesssim t \lesssim 10 ^ { 4 } s , while the subsequent decline is the usual 1 \lesssim \alpha _ { 3 } \lesssim 1.5 behavior , that was seen in the pre- Swift era .
We show that this behavior is a natural consequence of a small spread in the Lorentz factor of the ejecta , by a factor of \sim 2 - 4 , where the slower ejecta gradually catch-up with the shocked external medium , thus increasing the energy of forward shock and delaying its deceleration .
The end of the “ shallow ” flux decay stage marks the beginning of the Blandford-McKee self similar external shock evolution .
This suggests that most of the energy in the relativistic outflow is in material with a Lorentz factor of \sim 30 - 50 .