A test of Amati relation using HII galaxy distances

TL;DR

This work tackles the circularity of the Amati relation for gamma-ray bursts by calibrating GRB distances with model-independent luminosity distances from HII galaxies. An ANN-based interpolation is used to reconstruct the GRB luminosity distance $D_L$ at GRB redshifts, enabling computation of $E_{iso}$ without assuming a cosmology. Bayesian regression on two GRB datasets yields consistent Amati slopes ($a\approx 0.54$ for A220 and $a\approx 0.40$ for D17) but with substantial intrinsic scatter (~28–35%), indicating that Amati relation with HII anchors is not yet a precision cosmology probe. The results highlight limitations due to scatter and possible $L-\sigma$ evolution, while future missions like SVOM and THESEUS may offer tighter constraints and improve the utility of GRBs for cosmology.

Abstract

We use model-independent luminosity distances of 186 HII galaxy observations to address the circularity problem in the Amati relation for Gamma-ray Bursts (GRBs). For this purpose, we used Artificial Neural Network based interpolation to reconstruct the luminosity distance corresponding to the GRB redshift. We then use two independent GRB datasets to test the robustness of the Amati relation at redshifts below $z=2.6$. Our best-fit Amati relation parameters are consistent for the same datasets to within $1σ$. The intrinsic scatters which we obtain for the two datasets of about 28\% and 35\%, are comparatively larger. This implies that the Amati relation using HII galaxies as distance anchors cannot be used as a probe of precision cosmology.

Figures (5)

• Figure S1: Non-Parametric reconstruction of $D_L$ using ANN-based regression from HII Galaxy measurements upto $z$ of 2.6. The blue shaded region shows the 68% allowed region.
• Figure S2: Marginalized 68% and 95% credible intervals for $a$, $b$, and $\ln \sigma_s$ (cf. Eq. \ref{['eq:amati']}) for the subset of D17 GRBs having $z<2.6$. The dashed vertical line in the marginalized plots for each parameter shows the 68% uncertainty.
• Figure S3: Marginalized 68% and 95% credible intervals for $a$, $b$, and $\ln \sigma_s$ (cf. Eq. \ref{['eq:amati']}) for the subset of A220 GRBs having $z<2.6$. The dashed vertical line in the marginalized plots for each parameter shows the 68% uncertainty.
• Figure S4: The best-fit regression line (red line) and the $1\sigma$ confidence interval (shaded region), derived from the MCMC posterior samples along with the data for A220 dataset having $z<2.6$. The mean and standard deviation are computed at each $x$-coordinate from the ensemble of all posterior regression lines.
• Figure S5: The best-fit regression line (red line) and the $1\sigma$ confidence interval (shaded region), derived from the MCMC posterior samples along with the data for D17 dataset having $z<2.6$. The mean and standard deviation are computed at each $x$-coordinate from the ensemble of all posterior regression lines.