The Synchrotron Shock Model Confronts a `Line of Death' in the BATSE   Gamma-Ray Burst Data
  The synchrotron shock model (SSM) for gamma-ray burst emission makes a testable prediction: that the observed low-energy power-law photon number spectral index cannot exceed -2/3 (where the photon model is defined with a positive index: dN/dE is proportional to E^alpha). We have collected time-resolved spectral fit parameters for over 100 bright bursts observed by the Burst And Transient Source Experiment on board the Compton Gamma Ray Observatory. Using this database, we find 23 bursts in which the spectral index limit of the SSM is violated. We discuss elements of the analysis methodology that affect the robustness of this result, as well as some of the escape hatches left for the SSM by theory. 
R. D. Preece, M. S. Briggs, R. S. Mallozzi, G. N. Pendleton, and W. S.   Paciesas (UAH) and D. L. Band (CASS/UCSD)