The Intrinsic Correlations between Prompt Emission and X-ray Flares of Gamma-Ray Bursts

X-ray flare (XRF) is a common phenomenon in the X-ray afterglow of gamma-ray bursts (GRBs). Although it is commonly believed that XRFs may share a common origin with prompt emission, i.e., the “internal” origin, the origin of XRFs is still unknown. In this work, we compile a GRB sample containing 31 GRBs with a single XRF, a well-measured spectrum, and a redshift, and investigate the intrinsic properties and correlations between prompt emission and the XRFs of these events. We find that the distributions of main physical parameters of prompt emission and XRFs are basically log-normal. The median value of the rise time is shorter than the decay time for all flares, with a ratio of about 1:2, which is similar to the fast rise and exponential decay structure of prompt emission pulses. We also find that the prompt emission energy (Eiso) and peak luminosity (Liso) have tight correlations with XRF energy (EX,iso) and peak luminosity (LX,p), Eiso∝EX,iso0.74 (LX,p0.62) and Liso∝EX,iso0.85 (LX,p0.68). However, the durations of prompt emissions are independent of the temporal properties of XRFs. Furthermore, we also analyze the three-parameter correlations between prompt emissions and XRFs, and find that there are tight correlations among the XRF peak time (Tp,z), LX,p, and Eiso/Liso, LX,p∝Tp,z−1.08Eiso0.84 and LX,p∝Tp,z−1.09Liso0.71. Interestingly, these results are very similar to the properties of an X-ray plateau in GRBs, which indicates that X-ray flares and plateaus may have the same physical origin, and strongly supports that the two emission components originate from the late-time activity of the central engine.