5 Summary

We find that the most natural explanation of the evolution of the Band photon index $\alpha$ is that of optical thinning. The very high initial $\alpha$ plus the Liang-Kargatis decay law found in many pulses are in favor of the saturated Compton cooling model. In such a model all of the physical parameters of the gamma-ray emitting ejecta shell in the comoving frame are uniquely determined or tightly constrained by the source distance d, Thomson depth $\tau_{\rm T}$, the LK decay constant $\Phi_{\rm o}$ plus the pulse rise time. These parameters then predict the afterglow behaviors from first principles once the ISM or CBM density plus proton loading is specified. Future observations should be able to test such predictions.

Acknowledgements

This work is supported by NASA grant NAG5-3824.