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

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.