The Unique Signature of Shell Curvature in Gamma-Ray Bursts

As a result of spherical kinematics, temporal evolution of received gammaray emission should demonstrate signatures of curvature from the emitting shell. Specifically, the shape of the pulse decay must bear a strict dependence on the degree of curvature of the gamma-ray emitting surface. We compare the spectral evolution of the decay of individual GRB pulses to the evolution as expected from curvature. In particular, we examine the relationship between photon flux intensity (I) and the peak of the νFν distribution (Epeak) as predicted by colliding shells. Kinematics necessitate that Epeak demonstrate a power-law relationship with I described roughly as: I = E (1−ζ) peak where ζ represents a weighted average of the low and high energy spectral indices. Data analyses of 24 observed gamma-ray burst pulses provide evidence that there exists a robust relationship between Epeak and I in the decay phase. Simulation results, however, show that a sizable fraction of observed pulses evolve faster than kinematics allow. Regardless of kinematic parameters, we found that the existence of curvature demands that the I − Epeak function decay be defined by ∼ (1 − ζ). Efforts were employed to break this curvature dependency within simulations through a number of scenarios such as anisotropic emission (jets) with angular dependencies, thickness values for the colliding shells, and various cooling mechanisms. Of these, the only method successful in dominating curvature effects was a slow cooling model. As a result, GRB models must confront the fact that observed pulses do not evolve in the manner which curvature demands.