Luminosity-time and luminosity-luminosity correlations for GRB prompt and afterglow plateau emissions

We present an analysis of 123 gamma-ray bursts (GRBs) with known redshifts possessing an afterglow plateau phase. We reveal that La-T∗a correlation between the X-ray luminosity La at the end of the plateau phase and the plateau duration, T∗a, in the GRB rest frame has a power-law slope different, within more than 2σ, from the slope of the prompt Lf-T∗f correlation between the isotropic pulse peak luminosity, Lf, and the pulse duration, T∗f, from the time since the GRB ejection. Analogously, we show differences between the prompt and plateau phases in the energy duration distributions with the afterglow emitted energy being on average 10 per cent of the prompt emission. Moreover, the distribution of prompt pulse versus afterglow spectral indexes does not show any correlation. In the further analysis we demonstrate that the Lpeak–La distribution, where Lpeak is the peak luminosity from the start of the burst, is characterized with a considerably higher Spearman correlation coefficient, ρ = 0.79, than the one involving the averaged prompt luminosity, Lprompt–La, for the same GRB sample, yielding ρ = 0.60. Since some of this correlation could result from the redshift dependences of the luminosities, namely from their cosmological evolution we use the Efron–Petrosian method to reveal the intrinsic nature of this correlation. We find that a substantial part of the correlation is intrinsic. We apply a partial correlation coefficient to the new de-evolved luminosities showing that the intrinsic correlation exists