E peak ESTIMATOR FOR GAMMA-RAY BURSTS OBSERVED BY THE SWIFT BURST ALERT TELESCOPE

We report a correlation based on a spectral simulation study of the prompt emission spectra of gamma-ray bursts (GRBs) detected by the Swift Burst Alert Telescope (BAT). The correlation is between the E peak energy, which is the peak energy in the νFν spectrum, and the photon index (Γ) derived from a simple power-law (PL) model. The E peak-Γ relation, assuming the typical smoothly broken PL spectrum of GRBs, is log E peak = 3.258 - 0.829 Γ (1.3 ≤ Γ ≤ 2.3). We take into account not only a range of E peak energies and fluences, but also distributions for both the low-energy photon index and the high-energy photon index in the smoothly broken PL model. The distribution of burst durations in the BAT GRB sample is also included in the simulation. Our correlation is consistent with the index observed by BAT and E peak measured by the BAT, and by other GRB instruments. Since about 85% of GRBs observed by the BAT are acceptably fit with the simple PL model because of the relatively narrow energy range of the BAT, this relationship can be used to estimate E peak when it is located within the BAT energy range.