Revisiting the Correlations of Peak Luminosity with Spectral Lag and Peak Energy of the Observed Gamma-ray Bursts

An analysis of light curves and spectra of observed gamma-ray bursts in gamma-ray ranges is frequently demanded\udbecause the prompt emission contains immediate details regarding the central engine of gamma-ray bursts (GRBs). We\udhave revisited the relationship between the collimation-corrected peak luminosity and the spectral lag, investigating\udthe lag-luminosity relationships in great detail by focusing on spectral lags resulting from all possible combinations of\udchannels. Firstly, we compiled the opening angle data and demonstrated that the distribution of opening angles of 205 long\udGRBs is represented by a double Gaussian function having maxima at ~ 0.1 and ~ 0.3 radians. We confirmed that the peak\udluminosity and the spectral lag are anti-correlated, both in the observer frame and in the source frame. We found that, in\udagreement with our previous conclusion, the correlation coefficient improves significantly in the source frame. It should\udbe noted that spectral lags involving channel 2 (25-50 keV) yield high correlation coefficients, where Swift/Burst Alert\udTelescope (BAT) has four energy channels (channel 1: 15-25 keV, channel 2: 25-50 keV, channel 3: 50-100 keV, channel 4:\ud100-200 keV). We also found that peak luminosity is positively correlated with peak energy