Synchrotron Radiation as the Source of Gamma‐Ray Burst Spectra

We investigate synchrotron emission models as the source of gamma-ray burstspectra. We show that including the possibility for synchrotronself-absorption, a ``smooth cutoff'' to the electron energy distribution, andan anisotropic distribution for the electron pitch angles produces a wholerange of low energy spectral behavior. In addition, we show that the procedureof spectral fitting to GRB data over a finite bandwidth can introduce aspurious correlation between spectral parameters - in particular, the value ofthe peak of the nu F_nu spectrum, E_p, and the low energy photon spectral indexalpha (the lower E_p is, the lower (softer) the fitted value of alpha will be). From this correlation and knowledge of the E_p distribution, we show how toderive the expected distribution of alpha. We show that optically thinsynchrotron models with an isotropic electron pitch angle distribution canexplain the distribution of alpha below alpha=-2/3. This agreement is achievedif we relax the unrealistic assumption of the presence of a sharp low energycutoff in the spectrum of accelerated electrons, and allow for a more gradualbreak. We show that this low energy portion of the electron spectrum can be atmost flat. We also show that optically thin synchrotron models with ananisotropic electron pitch angle distribution can explain all bursts with -2/3< alpha <= 0$. The very few bursts with low energy spectral indices that fallabove alpha=0 may be due the presence of a the synchrotron self-absorptionfrequency entering the lower end of the BATSE window. Our results also predicta particular relationship between alpha and E_p during the temporal evolutionof a GRB. We give examples of spectral evolution in GRBs and discuss how thebehavior are consistent with the above models.Comment: 21 pages, including 10 postscript figures. To appear in the December 10, 2000 issue of Ap