Transition from Regular to Chaotic Circulation in Magnetized Coronae near Compact Objects

TL;DR

This paper investigates how charged particle motion in the magnetized coronae around black holes and stars transitions from regular to chaotic, using recurrence analysis to identify chaos onset and examining the influence of black hole spin.

Contribution

It introduces the use of Recurrence Quantification Analysis to detect chaos in particle trajectories near compact objects, revealing complex effects of black hole spin on chaotic behavior.

Findings

Recurrence analysis effectively detects chaos onset in particle motion.

Chaos occurs at high energy levels when particles cross the equatorial plane.

Black hole spin influences chaos in a more complex way than previously assumed.

Abstract

Accretion onto black holes and compact stars brings material in a zone of strong gravitational and electromagnetic fields. We study dynamical properties of motion of electrically charged particles forming a highly diluted medium (a corona) in the regime of strong gravity and large-scale (ordered) magnetic field. We start our work from a system that allows regular motion, then we focus on the onset of chaos. To this end, we investigate the case of a rotating black hole immersed in a weak, asymptotically uniform magnetic field. We also consider a magnetic star, approximated by the Schwarzschild metric and a test magnetic field of a rotating dipole. These are two model examples of systems permitting energetically bound, off-equatorial motion of matter confined to the halo lobes that encircle the central body. Our approach allows us to address the question of whether the spin parameter of the black hole plays any major role in determining the degree of the chaoticness. To characterize the motion, we construct the Recurrence Plots (RP) and we compare them with Poincar\'e surfaces of section. We describe the Recurrence Plots in terms of the Recurrence Quantification Analysis (RQA), which allows us to identify the transition between different dynamical regimes. We demonstrate that this new technique is able to detect the chaos onset very efficiently, and to provide its quantitative measure. The chaos typically occurs when the conserved energy is raised to a sufficiently high level that allows the particles to traverse the equatorial plane. We find that the role of the black-hole spin in setting the chaos is more complicated than initially thought.