TITLE:
Do the Amati and Yonetoku Relations Evolve with Redshift for Swift GRBs?
AUTHORS:
Ali M. Hasan, Walid J. Azzam
KEYWORDS:
Gamma-Ray Bursts, Spectral Correlations, Redshift Evolution, Cosmological Probes
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.3,
March
9,
2026
ABSTRACT: Gamma-ray bursts (GRBs) are extremely powerful stellar explosions that have been observed to huge distances with redshifts exceeding 9. Although GRBs are not standard candles, one may “standardize” them by calibrating certain correlations that link an intrinsic parameter to an observed one. Two such correlations that have been discovered are the Amati relation and the Yonetoku relation. The former is a correlation between a burst’s equivalent isotropic energy, Eiso, and its intrinsic peak spectral energy Ep,i, while the latter is a correlation between a burst’s peak isotropic luminosity, Liso, and Ep,i. In this paper, we compiled a large sample of 241 Swift long GRBs for the purpose of examining whether the Amati and Yonetoku relations are immune to redshift evolution. Our methodology encompasses two approaches: the first involves binning the data by redshift and fitting the two relations for each bin, then checking whether the fitting parameters evolve with redshift; the second approach involves using a redshift cutoff to divide the data into a low-redshift group and a high-redshift group, then checking whether the fitting parameters for the two relations are consistent with one another. Our results indicate that the Amati and Yonetoku relations are robust in the sense that they do not show any systematic or significant redshift evolution. Moreover, our results indicate that the high redshift bins show better fits compared to the low redshift bins, which indicates that the Amati and Yonetoku relations are more reliable as “standard candles” for high redshift and hence are promising cosmological probes.