Study on the X-ray Flare of Gamma-Ray Burst Based on the Fallback Accretion Model

Approximately half of Swift gamma-ray bursts (GRBs) consists the X-ray flare in their X-ray afterglows. Up to now, the physical origin of X-ray flares remains a mystery. In this paper, we present a theoretical model to interpret the X-ray flares observed in long GRBs. In this model, the shockwave from a supernova explosion may break up outer materials of the progenitor stars into many clumps. The clumpy material with insufficient kinetic energy would fall back onto the black hole(BH) accretion disk at later times and releases energy through the Blandford-Znajek (BZ) mechanism. This energy contributes to the X-ray flare emission of GRBs through internal dissipation processes. Based on Swift/XRT observational data up to December 2024, we selected 66 long GRBs with X-ray flares. By applying our model to this sample, we find that the model can effectively interpret the X-ray flares within the framework of the progenitor star’s density profile. According to the fitting results, it can be inferred that the X-ray flares may originate from the clumpy material with peak densities of 10−4 – 104 g cm−3 and radii spanning 109 – 1011 cm. This radial range aligns with the typical radii of Wolf-Rayet stars. The mass of the clumpy material that produces the X-ray flare segment is ∼10−4M⊙ − M⊙, consistent with the observations ejecta mass of GRB-SNe. Furthermore, our analysis reveals that the ratio of the angular velocity to the local Keplerian angular velocity, fΩ, is as low as ∼0.2, which indicates that the progenitor star of long GRB was rotating slowly in the final moment before collapse. In summary, our results provide additional support for the origin of long GRBs from the collapse of massive stars.