Self-gravitating collapsing star and black hole spin-up in long gamma ray bursts
Authors: Janiuk Agnieszka , Shahamat Dehsorkh Narjes , Król Dominika Ł. 
Published: June 2023

Context. Long gamma ray bursts (GRBs) originate from the collapse of massive, rotating stars. Some of the GRBs exhibit much stronger variability patterns in the prompt GRB emission than the usual stochastic variations. We discuss the mechanisms able to account for this effect.
Aims We aim to model the process of stellar collapse in the scenario of a self-gravitating collapsing star. We account for the changes in Kerr metric induced by the growth of the black hole; accretion of angular momentum; and the self-gravity effect due to a large mass of the collapsing stellar core falling onto black hole in a very short time. We also investigate the existence of accretion shocks in the collapsar, and the role of magnetic field in their propagation.
Methods. We compute the time-dependent axially symmetric general relativistic magnetohydrodynamic model of a collapsing stellar core in the dynamical Kerr metric. We explore the influence of self-gravity in such a star, where the newly formed black hole is increasing the mass and changing its spin. The Kerr metric evolves according to the mass and angular momentum changes during the collapse. We parameterize the rotation inside the star, and account for the presence of large-scale poloidal magnetic field. For the set of the global parameters, such as the initial black hole spin and the initial content of specific angular momentum in the stellar envelope, we determine the evolution of black hole parameters (mass and spin) and quantify the strength of the gravitational instability. We then estimate the variability timescales and amplitudes.
Results. We find that the role of the gravitational instability measured by the value of the Toomre parameter is relatively important in the innermost regions of the collapsing star. The character of accretion rate variability strongly depends on the assumption of self-gravity in the model, and is also affected by the magnetic field. Additional factors are initial spin and rotation of the stellar core. We find that for subcritical rotation of the precollapsed star, a centrifugally supported mini-disc is present at the equatorial plane, and it may be subject to fragmentation due to self-gravitating instability. We also find that self-gravity may play a role in the angular momentum transport and that it generally lowers the final mass and spin of the black hole, while the accretion-rate variability amplitude is much larger in self-gravitating objects. The effect of magnetic field is rather weak, while it seems to decrease the strength of accretion shocks. The magnetisation affects the global properties of the flow in a non-linear way, and is manifested mostly in models with moderate initial black hole spins but supercritical rotation of the collapsing star.
Conclusions. Our computations confirm that gravitational instability can account for flaring activity in GRBs and the variations in their prompt emission. Rapid variability detected in the brightest GRBs (most likely powered by rapidly spinning black holes) is consistent with the self-gravitating collapsar model, where the transonic shocks are formed. The effect should be weakened by magnetic field.