Broadening of the thermal component of the prompt GRB emission due to rapid temperature evolution

The observations of the prompt emission of gamma ray bursts (GRB) by GLAST Burst Monitor (GBM), on board Fermi Gamma-ray Space Telescope, suggest the presence of a significant thermal spectral component, whose origin is not well understood. Recently, it has been shown that for long duration GRBs, the spectral width as defined as the logarithm of the ratio of the energies at which the spectrum falls to half its peak value, lie in the range of 0.84-1.3 with a median value of 1.07. Thus, while most of the GRB spectra are found to be too narrow to be explained by synchrotron emission from an electron distribution, they are also significantly broader than a blackbody spectrum whose width should be 0.54. Here, we consider the possibility that an intrinsic thermal spectrum from a fire-ball like model, may be observed to be broadened if the system undergoes a rapid temperature evolution. We construct a toy-model to show that for bursts with durations in the range 5-70 s, the widths of their 1 second time-averaged spectra can be at the most ≲ 0.557. Thus, while rapid temperature variation can broaden the detected spectral shape, the observed median value of ∼ 1.07 requires that there must be significant sub-photospheric emission and/or an anisotropic explosion to explain the broadening for most GRB spectra.