Testing the curvature effect and internal origin of gamma-ray burst prompt emissions and X-ray flares with Swift data

The X-ray light curves of many GRBs have a steep tail following the gamma-rays and have some erratic flares. We assume that these tails and flares are of internal origin and that their decline behaviors are dominated by the curvature effect. This effect suggests that the decay slope of the late steep decay part of the light curves is alpha = 2 + beta, where beta is the X-ray spectral index. We present a self-consistency test for this scenario with a sample of 36 prompt emission tails/flares in 22 light curves observed by the Swift XRT. We derive the zero time (t(0)) for each steep decay component by fitting the light curves with the constraint of alpha = 2 + beta. Our results show that the t(0) values of the prompt emission tails and the tails of well-separated flares are self-consistent with the expectation of the internal dissipation models, indicating that each X-ray flare forms a distinct episode of the central engine activity and the central engine remains active after the prompt emission is over, sometimes up to similar to 1 day after the GRB trigger. This challenges the conventional models and calls for new ideas to restart the central engine. We further show that the onset time of the late central engine activity does not depend on the GRB duration. We also identify a minority group of GRBs whose combined BAT-XRT light curves are smoothly connected, without an abrupt transition between the prompt emission and the afterglow. These GRBs may have an external origin for both the prompt emission and the afterglow.