The time-resolved spectra of photospheric emission from a structured jet for gamma-ray bursts

The quasi-thermal components found in many Fermi gamma-ray bursts (GRBs) imply that the photosphere emission indeed contributes to the prompt emission of many GRBs. But whether the observed spectra empirically fitted by the Band function or cutoff power law, especially the spectral and peak energy ($E_{p}$) evolutions can be explained by the photosphere emission model alone needs further discussion. In this work, we investigate in detail the time-resolved spectra and $E_{p}$ evolutions of photospheric emission from a structured jet, with an inner-constant and outer-decreasing angular Lorentz factor profile. Also, a continuous wind with a time-dependent wind luminosity has been considered. We show that the photosphere spectrum near the peak luminosity is similar to the cutoff power-law spectrum. The spectrum can have the observed average low-energy spectral index $\alpha $ $ \sim -1$, and the distribution of the low-energy spectral index in our photosphere model is similar to that observed ($-2\lesssim $ $\alpha \lesssim 0$). Furthermore, the two kinds of spectral evolutions during the decay phase, separated by the width of the core ($\theta _{c}$), are consistent with the time-resolved spectral analysis results of several Fermi multi-pulse GRBs and single-pulse GRBs, respectively. Also, for this photosphere model we can reproduce the two kinds of observed $E_{p}$ evolution patterns rather well. Thus, by considering the photospheric emission from a structured jet, we reproduce the observations well for the GRBs best fitted by the cutoff power-law model for the peak-flux spectrum or the time-integrated spectrum.