A Consistency Check of Synchrotron Radiation with Fermi GRB Spectra

We define a new quantity, the curvature width, to check the consistency of the synchrotron model with the spectra of gamma-ray bursts (GRBs). This quantity measures the spectral break sharpness at the emission energy spectral ( vFv, v is frequency and F v is energy flux as a function of v) peak in GRBs. Using this quantity, we check the consistency between the theoretical synchrotron model and the observed GRB spectra. We first calculate the curvaturewidths of several typical synchrotron models including the mono-energetic, single power-law and broken power-law electron synchrotron models. Then we choose a GRB sample including a total of 1198 spectra from the Fermi/GBM (Gamma-ray Burst Monitor) long GRB time-resolved spectra catalog, fit the spectra with commonly used empirical models and compute the spectral curvature widths of best-fit models. By comparing the two curvature widths, we find most of the sample are incompatible with the synchrotron models, because the spectral breaks of the synchrotron models are much smoother than those of the data. Our results suggest that the synchrotron models are hard to accommodate most of the observed GRB spectra. Further, a tight anti-correlation between the photon flux and curvature width is found within a pulse of a burst, which suggests the higher flux, the sharper spectral break or the more deviating from the synchrotron models.