Hardness as a Spectral Peak Estimator for Gamma-Ray Bursts.

Simple hardness ratios are found to be a good estimator for the spectral peak energy in Gamma-Ray Bursts (GRBs). Specifically, a high correlation strength is found between the $\nu F_{\nu}$ peak in the spectrum of BATSE GRBs, $\epo$, and the hardness of GRBs, $\hr$, as defined by the fluences in channels 3 and 4, divided by the combined fluences in channels 1 and 2 of the BATSE Large Area Detectors. The correlation is independent of the type of the burst, whether Long-duration GRB (LGRB) or Short-duration (SGRB) and remains almost linear over the wide range of the BATSE energy window (20-2000 KeV). Based on Bayes theorem and Markov Chain Monte Carlo techniques, we also present multivariate analyses of the observational data while accounting for data truncation and sample-incompleteness. Prediction intervals for the proposed \hrep ~relation are derived. Results and further simulations are used to compute $\epo$ estimates for nearly the entire BATSE catalog: 2130 GRBs. These results may be useful for investigating the cosmological utility of the spectral peak in GRBs intrinsic luminosity estimates.