标题： 一种广义方法测量伽马射线暴光球辐射的洛伦兹因子 显示英文标题

标题： A generalized method to measure the Lorentz factor from gamma-ray burst photospheric emission

摘要： 伽马射线暴（GRBs）的观测性质依赖于整体洛伦兹因子 $\Gamma$ 的值。因此，准确估计它是重要的目标。在这项工作中，我们提出了一种基于观测光球辐射测量 $\Gamma$ 的方法，该方法也可用于可能导致非热谱形状的高度耗散流。为了使该方法适用，需要满足两个条件：喷流后期光子数应守恒，且原始光子温度必须从数据中推断出来。详细讨论了通过亚光球激波耗散的情况，并表明当识别出低能谱断点时，该方法特别有效。我们通过将其应用于两个不同的GRB谱线来展示该方法的能力。从其中一个谱线中，我们得到了 $\Gamma$ 的值，统计不确定性仅为 \($\sim 15$\% \)，而对另一个谱线我们只得到上限。 显示英文摘要

摘要： The properties of gamma-ray bursts (GRBs) that are inferred from observations depend on the value of the bulk Lorentz factor, $\Gamma$. Consequently, accurately estimating it is an important aim. In this work, we present a method of measuring $\Gamma$ based on observed photospheric emission, which can also be used for highly dissipative flows that may lead to non-thermal spectral shapes. For the method to be applicable, two conditions need to be met: the photon number should be conserved in the later stages of the jet, and the original photon temperature must be inferred from the data. The case of dissipation via subphotospheric shocks is discussed in detail, and we show that the method is particularly efficient when a low-energy spectral break is identified. We demonstrate the capabilities of the method by applying it to two different GRB spectra. From one of the spectra, we obtain a value for $\Gamma$ with statistical uncertainties of only $\sim 15$\%, while for the other spectrum we only obtain an upper limit.