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

Some models of gamma-ray bursts (GRBs) invoke nascent millisecond magnetars as the central engine and address the X-ray afterglows with the interaction of magnetar magnetospheres with fallback discs. We study the evolution of fallback discs interacting with the millisecond magnetars. Initially, the accretion rate in the fallback disc is very high, well above the rate required for the Eddington limit. The inner parts of such a disc, even if it is cooling by the neutrino emission, get spherical due to the radiation pressure, which regulates the mass-accretion rate within the spherization radius. Such a disc can not penetrate the light cylinder radius for the typical magnetic fields, and the initial spin frequencies invoked for the magnetars. As a result of the autoregulation of the accretion flow, the fallback disc can not interact directly with the magnetar's magnetosphere within the first few days. This has implications for the fallback disc models of GRB afterglows since the accretion and propeller luminosities, in the presence of radiation pressure, are too low to address the typical luminosities of X-ray afterglows.