Redshift evolution of the Amati relation: Calibrated results from the Hubble diagram of quasars at high redshifts

Abstract

Gamma-ray bursts (GRBs) have long been proposed as a complementary probe to type Ia supernovae (SNe Ia) and the cosmic microwave background to explore the expansion history of the high-redshift universe, mainly because they are bright enough to be detected at greater distances. Although they lack definite physical explanations, many empirical correlations between GRB isotropic energy or luminosity and some directly detectable spectral or temporal properties have been proposed to make GRBs standard candles. Since the observed GRB rate falls off rapidly at low redshifts, this thus prevents a cosmology independent calibration of these correlations. In order to avoid the circularity problem, SN Ia data are usually used to calibrate the luminosity relations of GRBs in the low redshift region (limited by the redshift range for SN Ia sample), and then they are extrapolate the luminosity relations to the high redshift region. This approach is based on the assumption of no redshift evolution for GRB luminosity relations. In this work, we suggest the use of a complete quasar sample in the redshift range of 0.5 < z < 5.5 to test such an assumption. We divided the quasar sample into several subsamples with different redshift bins, and used each subsample to calibrate the isotropic γ-ray equivalent energy of GRBs in relevant redshift bins. By fitting the newly calibrated data, we find strong evidence that the most commonly used Amati relation between spectral peak energy and isotropic-equivalent radiated energy shows no, or marginal, evolution with redshift. Indeed, at different redshifts, the coefficients in the Amati relation could have a maximum variation of 0.93% at different redshifts, and there could be no coincidence in the range of 1σ.

E iso–Ep correlation of gamma-ray bursts: calibration and cosmological applications

“…Therefore, the 𝐸 iso − 𝐸 p correlation is consistent for all redshift ranges. The correlation shows no significant evolution with redshifts, which is in line with Wang et al (2011) and Dai et al (2021). If the correlation evolves with evolution, the method mentioned in Dainotti et al (2022b) can be used to fit the evolutionary function.…”

Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae

“…More recently, Khadka et al (2021) found that the Amati relation is independent of redshift within the error bars with the A220 GRB data set. Dai et al (2021) found strong evidence that the Amati relation shows no, or marginal, evolution with redshift. Tang et al (2021) found that the intercept and slope of the Amati relation for the low-z subsample and high-z subsample differ at more than 2δ.…”

The Cosmic History of Long Gamma-Ray Bursts

“…LGRBs follow the E p − L iso (Yonetoku et al 2004) correlation, where E p is the peak energy of the ν F ν spectrum and the E p − E iso correlation (Amati & Frontera 2002) links the peak energy with the isotropic energy E iso . It has been proved (Nava et al 2012;Dai et al 2021) that these correlations do not evolve with redshift. Following Ghirlanda et al (2015), in our simulation we sample Equation (1), extracting a redshift, and we independently assign an E p value sampling a broken power law.…”