Statistical properties of the X-ray afterglow shallow decay phase and their relationships with the prompt gamma-ray emission of gamma-ray bursts

Abstract

We systematically analyze the properties of the X-ray shallow decay phase in Swift GRBs observed from 2004 December to 2021 March. These events have at least the three obvious emission phases: the steep decay, shallow decay and the following decay. We find that the distributions of the characteristic properties of the shallow decay phase are basically lognormal or normal. We also find that the luminosities at the beginning time and the end time of the X-ray shallow decay phase are correlated with the peak luminosity and isotropic energy of the prompt gamma-ray phase, and are also correlated with the corresponding beginning/end time and the total energy of the X-ray shallow decay phase. There is a tighter correlation between the total energy of the shallow decay phase and the isotropic energy of the prompt phase, i.e, $E_{\gamma ,\mathit{iso}} \propto E_{X,\mathit{iso}}^{0.89 \pm 0.06}$. In addition, we also find that the three-parameter $L-T-E$ and $L-T-L$ correlations still exist for our sample. At the same time, there are similar three-parameter correlations for the parameters at the beginning time of the shallow decay phase, i.e., $L_{X,b} \propto T_{b,z}^{-1.58 \pm 0.11}E_{\gamma ,\mathit{iso}}^{0.83 \pm 0.05}$ and $L_{X,b} \propto T_{b,z}^{-1.69 \pm 0.16}L_{p}^{0.49 \pm 0.06}$. The subsamples of short GRBs, GRBs with the internal plateau and GRBs with the early tail emission all follow the same correlations with other events. Our results show that the emission of the X-ray shallow decay phase is highly correlated with the prompt emission, supporting the re-activity of the long-lived central engine.