In the present work we study self-gravity effects on the vertical structure of a magnetized neutrino-dominated accretion disk as a central engine for gamma-ray bursts (GRBs). Some of the disk physical timescales that are supposed to play a pivotal role in the late-time evolutions of the disk, such as viscous, cooling, and diffusion timescales, have been studied. We are interested in investigating the possibility of the occurrence of X-ray flares, observed in late-time GRBs’ extended emission through the “magnetic barrier” and “fragmentation” processes in our model. The results lead us to interpret self-gravity as an amplifier for Blandford–Payne luminosity (BP power) and the generated magnetic field, but a suppressor for neutrino luminosity and magnetic barrier processes via highlighting the fragmentation mechanism in the outer disk, especially for the higher mass accretion rates.

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