Jets in a Gamma-Ray Burst During its Prompt Emission: Evolution of Lorentz Factor

Knowledge about the Lorentz factor and its evolution of relativistic jets in gamma-ray bursts (GRBs) is crucial to understand their physics. An exact value of bulk Lorentz factor can be estimated based on a high-energy spectral cutoff, which may appear in GRBs' prompt emission owing to the absorption of photon-photon pair production. In this work, we focus on the investigation of the bulk Lorentz factor evolution of jets in an individual burst. Based on \textsl{Fermi} observations, we search for the bursts with multiple $\gamma$-ray pulses characterized by a high-energy spectral cutoff, and nine GRBs are obtained. Together with the estimation of the pulse duration and radiation spectrum, the Lorentz factor of jets corresponding to different pulses in an individual GRB are estimated. It is shown that the Lorentz factor of jets in an individual GRB fluctuates within a certain range and without a general trend in these nine GRBs. In addition, the Lorentz factors of the jets in GRBs~130821A, 160509A and 160625B seem to increase with time. We also study the relations among $L_{\rm iso }$, $E_{\rm p,z}$, and $\Gamma$ for the pulses in our sample, which is found to be consistent with that found in previous works.