Closure Relations for Electron-Positron Pair-Signatures in Gamma-Ray Bursts

We present recipes to diagnose the fireball of gamma-ray bursts (GRBs) by combining observations of electron-positron 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 non-detection 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-coming Gamma-Ray Large Area Space Telescope (GLAST) satellite will provide us with good chances to use our recipes by detecting or non-detecting pair-signatures.