Lorentz Factor Evolution Patterns within Relativistic Jets of GRBs and AGNs

The Lorentz factor (Γ) is an important parameter related to the relativistic jet physics. We study the evolution patterns of Γ within gamma-ray burst (GRB) and active galactic nuclear jets for individual GRB 090168, GRB 140508A, and 3C 454.3. By estimating the Γ values for well-separated pulses in GRBs 090618 and 140508A with an empirical relation derived from typical GRBs, we find that the Γ evolution pattern in the two GRBs are different. The increasing-to-coasting evolution pattern of Γ in GRB 090618 likely indicates that the GRB fireball is still being accelerated in the prompt phase. The clear decrease evolution pattern of Γ in GRB 140508A suggests the deceleration of the fireball components. By deriving the Γ value through fitting their spectral energy distribution in different flares of 3C 454.3, a pattern of Γ-tracking-γ-ray flux is clearly found, likely indicating that the observed gamma-ray flares are being due to the Doppler boosting effect to the jet emission.