The Closure Relations in Optical Afterglow of Gamma-Ray Bursts

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{νc,νm} 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.