Variation of the Amati Relation with the Cosmological Redshift: a Selection Effect or an Evolution Effect?

Because of the limit in the number of gamma-ray bursts (GRBs) with available redshifts and spectra, all current investigations on the correlation among GRB variables use burst samples with redshifts that span a very large range. The evolution and selection effects have thus been ignored, which might have important influence on the results. In this Letter, we divide the 48 long-duration GRBs in Amati (2006, 2007) into four groups with redshift from low to high, each group contains 12 GRBs. Then we fit each group with the Amati relation $\log E_{\text{iso}}=a+b\log E_{\text{p}}$, and check if the parameters $a$ and $b$ evolve with the GRB redshift. We find that $a$ and $b$ vary with the mean redshift of the GRBs in each group systematically and significantly. Monte-Carlo simulations show that there is only $\sim 4$ percent of chance that the variation is caused by the selection effect arising from the fluence limit. Hence, our results may indicate that GRBs evolve strongly with the cosmological redshift.