Statistical study of gamma-ray bursts with jet break feature in multi-wavelength afterglow emissions

Abstract

It is generally supposed that a transition from the normal decay phase (decay slope $\sim -1$) to a steeper phase (decay slope $\sim -2$) could be suggested as a jet break. The jet opening angle ${\theta }_{\mathrm{jet}}$ is then calculated from the jet break time of the afterglow light curve. This allows the derivation of the collimation-corrected energy $E_{\mathrm{jet}}$ of those GRBs. We extensively searched for the GRBs with jet break features from multi-wavelength afterglow light curves, and 138 GRBs with significant breaks were collected. The jet break times of those GRBs mainly range from 1000 s to $10^6$ s, and the distribution of the collimation-corrected energy $E_{\mathrm{jet}}$ peaks at $\sim 10^{50}$ erg. We also confirmed the $E_{\gamma ,\mathrm{iso}}-E_{\mathrm{p},\mathrm{i}}$, $E_{\mathrm{jet}}-E_{\mathrm{p},\mathrm{i}}$ and $E_{\gamma ,\mathrm{iso}}-{\theta }_{\mathrm{jet}}$ relations, and found $E_{\gamma ,\mathrm{iso}}-T_{\mathrm{j},\mathrm{z}}-E_{\mathrm{p},\mathrm{i}}$ relation remains tight with more multi-wavelength data. This tight $E_{\gamma ,\mathrm{iso}}-T_{\mathrm{j},\mathrm{z}}-E_{\mathrm{p},\mathrm{i}}$ relation is also conformed by different groups of our selected GRBs in the paper. In addition, another two new and tighter correlations among $E_{\mathrm{jet}}-T_{\mathrm{j},\mathrm{z}}-E_{\mathrm{p},\mathrm{i}}$ are well confirmed for different circumburst mediums in this paper. We suggest that those tight three-parameter correlations are more physical, and could be widely applied to constrain the cosmological parameters.

11 pages, 4 figures and 2 tables; final version published in ApJ

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