Interpreting the spectral lags of single-pulsed gamma-ray bursts via the photosphere in the jet model

The prompt emission of gamma-ray bursts (GRBs) is a long-standing problem. The spectral-lag phenomenon can provide us with some clues about the emission mechanism. By analogy with the spectral lag of blazars at radio frequencies, we propose using the photosphere in the jet model to interpret the spectral lag of GRBs. Assuming a canonical jet and respecting the scaling laws of both the magnetic field and the number density of radiative particles, the radius of the photosphere and the magnetic field can be predicted. Five long bursts with known redshifts are studied. The prompt emitting regions of these bursts are located at about one or several astronomical units from the jet base. Without strictly constrained parameters, the magnetic fields at the photosphere radius are not well constrained. Taking the median values, the magnetic field is distributed in the range of 10(4)similar to 10(7) G, which has no conflicts with the constraints obtained from the synchrotron cooling time.