Can GRB Empirical Correlations Be Used for Population Studies?

TL;DR

This study critically evaluates the use of empirical correlations in gamma-ray bursts for population studies, finding they are unreliable for constraining GRB rates due to inherent limitations.

Contribution

The paper demonstrates that empirical GRB correlations cannot reliably serve as distance indicators for population studies, even under idealized conditions.

Findings

Empirical correlations do not accurately constrain GRB rate $\\Psi_{GRB}$.

Redshift solutions from these correlations are unreliable for population analysis.

Selection biases further undermine the utility of empirical correlations.

Abstract

Only a small fraction of Gamma-ray bursts (GRBs) have independent redshift measurements, which are essential for understanding their intrinsic properties. For this reason, empirical correlations of GRBs have often been touted as useful distance indicators, for both individual GRBs as well as population studies. Building upon our previous work, we test the ability of the Yonetoku, 3D Dainotti, and the L-T-E correlation to adequately constrain the GRB rate, $\Psi_{GRB}$. Our analysis demonstrates that, even under idealized conditions that neglect substantial uncertainties, the derived redshift solutions cannot accurately constrain $\Psi_{GRB}$, regardless of the intrinsic distribution's characteristic width. We thus demonstrate unequivocally that -- notwithstanding the questionable assumption of no selection biases -- empirical GRB correlations alone cannot serve as reliable distance indicators at either the individual or population level.