Closure relations for e^± pair signatures in gamma-ray bursts

We present recipes to diagnose the fireball of gamma-ray bursts (GRBs) by combining observations of e^± pair signatures (the pair annihilation line and the cutoff energy due to the pair creation process). Our recipes are largely model-independent and extract information even from the nondetection of either pair signature. We evaluate physical quantities such as the Lorentz factor, optical depth, and pair-to-baryon ratio only from the observable quantities. In particular, we can test whether the prompt emission of GRBs comes from the pair/baryonic photosphere or not. The future Gamma-Ray Large Area Space Telescope (GLAST) satellite will provide us with good chances to use our recipes via either detection or nondetection of pair signatures.