Model Limitation of Break Power-Law Fitting of the Fermi GRB Time-Resolved Spectra

We use the models SBPL (smooth break power-law), BPL (power-law connecting broken line) and Band to fit 8 Fermi bright bursts to get 165 best model fitting spectra. Then based on the energy flux Fluence of these 165 spectra, the range of the three model fitting data and some conclusions are obtained. Obtaining BPL can fit darker bursts well (F_e < 5×10^-5 erg·cm^-2), while brighter bursts can get better fit with Band (5×10^-5 erg·cm^-2 < F_e < 2.0×10^-4 erg·cm^-2) and SBPL (2.0×10^-4 erg·cm^-2 < F_e < 3.8×10^-4 erg·cm^-2). Nearly half of the spectra in the sample is fitted well by BPL, indicating that the spectral shape of some dark bursts is close to the shape of the polyline, that is, the spectral inflection is sharper. Although the best fitting model in most spectra is BPL, Band and SBPL also get acceptable fits, and there are so few high-energy photons that the existing data cannot well exclude some energy spectrum models. In addition, the current fitting may be affected by the response matrix of the instrument, and it is not possible to determine the true physical model very well, that is, the GRB spectrum may be explained by the model, but it may not be true.