The Closure Relations in Optical Afterglow of Gamma-Ray Bursts

Abstract

Gamma-ray bursts (GRBs) are extremely high-energy events that can be observed at very high redshift. In addition to γ rays, they can emit in X-ray, optical, and sometimes radio wavelengths. Here, following the approach in Srinivasaragavan et al.; Dainotti et al.; and Dainotti et al., we consider 82 GRBs from Dainotti et al. that have been observed in optical wavelengths and fitted with a broken power law. We consider the relations between the spectral and temporal indices (closure relations; CRs) according to the synchrotron forward-shock model evolving in the constant-density interstellar medium (ISM; k = 0) and the stellar wind environment (k = 2) in both slow- and fast-cooling regimes, where the density profile is defined as n ∝ r −k . We find the ν > max { ν c , ν m } regime is most favored, where ν c and ν m are the cooling and characteristic frequencies, respectively. Finally, we test the 2D Dainotti correlation between the rest-frame end time of the plateau and the luminosity at that time on GRBs that fulfill the most-favored CRs. When we compare the intrinsic scatter σ int of those 2D correlations to the scatter presented in Dainotti et al., we see the scatters of our correlations generally agree with the previous values within 1σ, both before and after correction for selection bias. This new information has helped us to pinpoint subsamples of GRBs with features that could drive the GRB emission mechanism, and eventually allow for GRBs to be used as standard candles.

From the gravitational waves to the exoplanets: the Research Highlights

“…It is crucial to note that the magnetar model is only one of the different ways to explain the plateau emission. However, additional work has been done to explain the plateau phase within the standard fireball model in multiwavelengths, namely, in X-rays [35,36], 𝛾-rays [37][38][39], optical [40], and radio [41]. Indeed, the luminosity-time relation is also viable in optical [19] and in radio [42].…”

A Stochastic Approach to Reconstruct Gamma-Ray-burst Light Curves

“…However, some degree of degeneracy inherent to the model will still remain unavoidable. Here, we recall that this LCR will be approached as a first step, but it can also be extended in high-energy γ-rays, optical, and radio wavelengths for the determination of the closure relation in these respective energy bands (Dainotti et al 2021d(Dainotti et al , 2022c(Dainotti et al , 2023aLevine et al 2023).…”

“…In addition, the plateau emission has been the object of investigation concerning the closure relations (the relations between the temporal and spectral index during or after the plateau region), which allows us to test the viability of the standard fireball model for the observations carrying plateau emission in high-energy γ-rays, X-rays, or optical wavelengths (Willingale et al 2007;Evans et al 2009;Racusin et al 2009;Kumar & Barniol Duran 2010;Oates et al 2012;Gao et al 2013;Wang et al 2015;Tak et al 2019;Srinivasaragavan et al 2020;Fraija et al 2020;Ryan et al 2020;Dainotti et al 2021bDainotti et al , 2021dDainotti et al , 2022cDainotti et al , 2023aMisra et al 2021;Levine et al 2023). Although closure relations are a quick way to test the standard fireball model, a more precise characterization of the decay index after the plateau emission would allow for better precision in determining these relations.…”