Reconciling low and high redshift GRB luminosity correlations

Abstract: The correlation between the peak spectra energy ($E_p$) and the equivalent isotropic energy ($E_{\rm iso}$) of long gamma-ray bursts (GRBs), the so-called Amati relation, is often used to constrain the high-redshift Hubble diagram. Assuming Lambda cold dark matter ($\Lambda$CDM) cosmology, Wang et al. found a $\gtrsim 3\sigma$ tension in the data-calibrated Amati coefficients between low- and high-redshift GRB samples. To reduce the impact of fiducial cosmology, we use the Parameterization based on cosmic Age (PAge), an almost model-independent framework to trace the cosmological expansion history. We find that the low- and high-redshift tension in Amati coefficients stays almost the same for the broad class of models covered by PAge, indicating that the cosmological assumption is not the dominant driver of the redshift evolution of GRB luminosity correlation. Next, we analyze the selection effect due to flux limits in observations. We find Amati relation evolves much more significantly across energy scales of $E_{\rm iso}$. We debias the GRB data by selectively discarding samples to match low-$z$ and high-$z$ $E_{\rm iso}$ distributions. After debiasing, the Amati coefficients agree well between low-$z$ and high-$z$ data groups, whereas the evidence of $E_{\rm iso}$-dependence of Amati relation remains to be strong. Thus, the redshift evolution of GRB luminosity correlation can be fully interpreted as a selection bias, and does not imply cosmological evolution of GRBs.