Abstract
Gamma-ray burst (GRB) X-ray flares are believed to mark the late-time activity of the central engine. We compute the temporal evolution of the average flare luminosity 〈L〉 in the common rest-frame energy band of 44 GRBs taken from the large Swift 5-yr data base. Our work highlights the importance of a proper consideration of the threshold of detection of flares against the contemporaneous continuous X-ray emission. In the time-interval 30 < t < 1000 s, we find 〈L〉∝t
−2.7±0.1; this implies that the flare isotropic energy scaling is E
iso,flare∝t
−1.7. The decay of the continuum underlying the flare emission closely tracks the average flare luminosity evolution, with a typical flare-to-steep-decay luminosity ratio L
flare/L
steep= 4.7. This suggests that flares and continuum emission are deeply related to one another. We infer on the progenitor properties considering different models. According to the hyperaccreting black hole scenario, the average flare luminosity scaling can be obtained in the case of rapid accretion (t
acc≪t) or when the last ∼0.5 M⊙ of the original 14 -M⊙ progenitor star is accreted. Alternatively, the steep ∝t
−2.7 behaviour could be triggered by a rapid outward expansion of an accretion shock in the material feeding a convective disc. If instead we assume the engine to be a rapidly spinning magnetar, then its rotational energy can be extracted to power a jet whose luminosity is likely to be between the monopole (L∝ e−2t
) and dipole (L∝t
−2) cases. In both scenarios, we suggest the variability, which is the main signature of the flaring activity, to be established as a consequence of different kinds of instabilities.