Photospheric Emission in Gamma-ray Bursts: Variability

It is generally believed that the variability of photospheric emission in gamma-ray bursts (GRBs) traces that of the jet power. This work further investigates the variability of photospheric emission in a variable jet. By setting a constant $\eta$ (dimensionless entropy of the jet), we find that the light curve of the photospheric emission shows a ``tracking'' pattern on the time profile of jet power. However, the relative variability is significantly low in the photospheric emission compared with that in the jet power. If the $\eta$ is genetic variable, the variability of the photospheric emission is not only limited by the jet power but also affected by $\eta$ strongly. It becomes complex and is generally different from that of the jet power. Moreover, the opposite phase may stand in the variabilities of the photospheric emission at different photon energies. We also find that the relative variability does not remain constant over the photon energies with an obvious reduction at a certain energy. This is consistent with the analysis of GRB 090902B in which an appreciable thermal component has been detected in a wide energy range. For several other GRBs coupling with the thermal component, we conservatively evaluate the variability of the thermal and non-thermal emission, respectively. Our results show that the relative variability of the thermal emission is likely comparable to that of the non-thermal emission for these bursts. In addition, the analysis of GRB~120323A reveals that the variability of the photospheric emission may be of the opposite phase from that of the non-thermal emission.