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Some models of gamma-ray bursts (GRBs) invoke nascent millisecond magnetarsas the central engine and address the X-ray afterglows with the interaction ofmagnetar magnetospheres with fallback discs. We study the evolution of fallbackdiscs interacting with the millisecond magnetars. Initially, the accretion ratein the fallback disc is very high, well above the rate required for theEddington limit. The inner parts of such a disc, even if it is cooling by theneutrino emission, get spherical due to the radiation pressure, which regulatesthe mass accretion rate within the spherization radius. Such a disc can notpenetrate the light cylinder radius for the typical magnetic fields, and theinitial spin frequencies invoked for the magnetars. As a result of theauto-regulation of the accretion flow, the fallback disc can not interactdirectly with the magnetar's magnetosphere within the first few days. This hasimplications for the fallback disc models of GRB afterglows since the accretionand propeller luminosities, in the presence of radiation pressure, are too lowto address the typical luminosities of X-ray afterglows.

Evolution of fallback discs around millisecond magnetars: effect of supercritical accretion on GRB afterglows