2000ApJ...534..227L

We present results of correlation studies, examining the association between the peak of the νF_ν spectrum of gamma-ray bursts, E_p, with the burst's energy fluence and photon peak flux. We discuss methods of accounting for data truncation in E_p and fluence or flux when performing the correlation analyses. However, because bursts near the detector threshold are not usually able to provide reliable spectral parameters, we focus on results for the brightest bursts, in which we can better understand the selection effects relevant to E_p and burst strength. We find that there is a strong correlation between total fluence and E_p. We discuss these results in terms of both cosmological and intrinsic effects. In particular, we show that for realistic distributions of the burst parameters, cosmological expansion alone cannot account for the correlation between E_p and total fluence: the observed correlation is likely the result of an intrinsic relation between the burst rest-frame peak energy and the total radiated energy. We investigate this latter scenario in the context of synchrotron radiation from external and internal shock models of GRBs. We find that the internal shock model is consistent with our interpretation of the correlation, while the external shock model cannot as easily explain this intrinsic relation between peak energy and burst-radiated energy.