2025ApJ...979..186Z

The X-ray afterglow of a certain fraction of gamma-ray bursts (GRBs) comprises a phase of shallow decay. However, the origin of the shallow decay segment is still a mystery. In this paper, we select 103 GRBs that exhibit a shallow decay segment, based on Swift/XRT data prior to 2023 June. We apply the fallback accretion energy external dissipation model to the shallow decay segment in our sample, and find the model can interpret the shallow decay segment within a reasonable range of parameter space. The fallback rate of the progenitor envelope materials onto the accretion disk can reach a peak of 10^–7-0.1 M_⊙ s^–1 within a time frame of 10-10⁵ s, which is consistent with the typical density profile and spin profile of the progenitor of a GRB. During the fallback process of progenitor envelope materials, progenitor stars of most GRBs have the highest fallback rate at a radius ∼10¹⁰ cm, which is consistent with the typical radius of a Wolf-Rayet star. The production of shallow decay segments of most GRBs in our sample requires injecting Blandford-Znajek (BZ) energy equal to 10-100 times the kinetic energy of the initial GRB blast wave into the blast wave. However, the shallow decay segment of a few GRBs requires the injected energy to be comparable to the kinetic energy of the blast wave, which means that even if less energy is injected into a GRB blast wave, it is still possible to produce a shallow decay segment. In addition, the peak time of the fallback rate of the progenitor envelope materials is close to the time when BZ energy is injected into the blast wave, which means that the fallback accretion is more active in the initial phase. In summary, our research results provide further support to an external origin for the shallow decay segment in GRBs.