Spectral Tests Using BATSE GRB Data Result in a Failing Grade for the Synchrotron Shock Model

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. We have collected time-resolved spectral fit parameters for 137 bright bursts observed by BATSE. Using this database, we find 23 bursts in which the spectral index limit of the SSM is violated. Out of nearly 4000 individual spectra, there are 312 that have power-law indices that are significantly greater than the SSM limit, which may be compared with only 8 expected from simulated error distributions at the same significance (> 2.4 sigma).