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

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 $\theta_{\rm jet}$ is then calculated from the jet break time of the afterglow light curve. This allows the derivation of the collimation-corrected energy $E_{\rm jet}$ 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 $E_{\rm jet}$ peaks at $\sim10^{50}$ erg. We also confirmed the $E_{\rm \gamma,iso}-E_{\rm p,i}$, $E_{\rm jet}-E_{\rm p,i}$ and $E_{\rm \gamma,iso}-\theta_{\rm jet}$ relations, and found $E_{\rm \gamma,iso}-T_{\rm j,z}-E_{\rm p,i}$ relation remains tight with more multi-wavelength data. This tight $E_{\rm \gamma,iso}-T_{\rm j,z}-E_{\rm p,i}$ relation is also conformed by different groups of our selected GRBs in the paper. In addition, another two new and tighter correlations among $E_{\rm jet}-T_{\rm j,z}-E_{\rm p,i}$ 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.