The rest-frame Golenetskii correlation via a hierarchical Bayesian analysis

Abstract

Gamma-ray bursts (GRBs) are characterised by a strong correlation between the instantaneous luminosity and the spectral peak energy within a burst. This correlation, which is known as the hardness-intensity correlation or the Golenetskii correlation, not only holds important clues to the physics of GRBs but is thought to have the potential to determine redshifts of bursts. In this paper, I use a hierarchical Bayesian model to study the universality of the rest-frame Golenetskii correlation and in particular I assess its use as a redshift estimator for GRBs. I find that, using a power-law prescription of the correlation, the power-law indices cluster near a common value, but have a broader variance than previously reported (∼ 1 − 2). Furthermore, I find evidence that there is spread in intrinsic rest-frame correlation normalizations for the GRBs in our sample (∼ 10 51 − 10 53 erg s −1 ). This points towards variable physical settings of the emission (magnetic field strength, number of emitting electrons, photospheric radius, viewing angle, etc.). Subsequently, these results eliminate the Golenetskii correlation as a useful tool for redshift determination and hence a cosmological probe. Nevertheless, the Bayesian method introduced in this paper allows for a better determination of the rest frame properties of the correlation, which in turn allows for more stringent limitations for physical models of the emission to be set.

“Double-tracking” Characteristics of the Spectral Evolution of GRB 131231A: Synchrotron Origin?

“…The relation between the energy flux F and E p , i.e., the Golenetskill E p -F relation (Golenetskii et al 1983;Burgess 2019), for the time-resolved spectra of GRB 131231A is shown in Figure 4a. Previous analyses (e.g., Borgonovo & Ryde 2001;Firmani et al 2009;Ghirlanda et al 2010;Yu et al 2018) have revealed that the Golenetskill E p -F relation shows three main types of behavior: a non-monotonic relation (containing positive and negative power-law segments, with a distinct break typically at the peak flux), a monotonic relation (described by a single power law), and no clear trend.…”

GRB Prompt Emission: Observed Correlations and Their Interpretations

“…The power-law slopes for the relationships obtained by Lu et al [179] and Guiriec et al [39] are slightly different from one another, which shows that the rest frame correlation is not well constrained. Burgess [180] used statistical methods to show that the current formulation of the Golenetskii relationship is not well constraining, at least in the context of using the relationship to detemine the redshifts of GRBs. They suggest adding terms to the relationship that can account for other physical parameters of GRBs such as the opening angle to make this relationship more universal among all GRBs.…”

“…Theories predicting and explaining the Golenetskii relation are still in development [126,180], but there are a few results that have been obtained under each prompt emission model.…”