Fallback accretion on to a newborn magnetar: long GRBs with giant X-ray flares

Flares in the X-ray afterglow of gamma-ray bursts (GRBs) share more characteristics with the prompt emission than the afterglow, such as pulse profile and contained fluence. As a result, they are believed to originate from late-time activity of the central engine and can be used to constrain the overall energy budget. In this paper, we collect a sample of 19 long GRBs observed by Swift-XRT that contain giant flares in their X-ray afterglows. We fit this sample with a version of the magnetar propeller model, modified to include fallback accretion. This model has already successfully reproduced extended emission in short GRBs. Our best-fittings provide a reasonable morphological match to the light curves. However, 16 out of 19 of the fits require efficiencies for the propeller mechanism that approach 100 per cent. The high-efficiency parameters are a direct result of the high energy contained in the flares and the extreme duration of the dipole component, which forces either slow spin periods or low-magnetic fields. We find that even with the inclusion of significant fallback accretion, in all but a few cases it is energetically challenging to produce prompt emission, afterglow, and giant flares within the constraints of the rotational energy budget of a magnetar.