Transition From Regular to Chaotic Circulation in Magnetized Coronae Near Compact Objects

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 Poincaré 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.

Inducing Chaos by Breaking Axial Symmetry in a Black Hole Magnetosphere

“…Since both of these systems were found to be nonintegrable, in which case the chaotic dynamics emerges, we subsequently focused on the dynamic properties of these orbits, trying to identify which parameters of the system trigger chaos. We found that within the off-equatorial lobes, the dynamics are mostly regular and chaos typically appears only when the energy of the particle is sufficiently increased to the level that corresponds to cross-equatorial confinements (Kopáček et al 2010a).…”

“…This work represents a natural extension of our previous studies (Kopáček et al 2010a;Kovář et al 2008Kovář et al , 2010) in which we considered dynamic properties of charged matter orbiting in the vicinity of massive objects. Our primary concern was to identify and investigate regions of a stable, off-equatorial motion.…”

“…In this context, we have also experimented with norms reflecting the curvature of the spacetime, however, it appeared that for a given application the choice of the norm is not crucial (Kopáček et al 2010a). Although Lyapunov exponents within the relativistic framework are generally not invariant under coordinate transformations (Karas & Vokrouhlický 1992;Dettmann et al 1995), signs of the exponents are preserved (Motter 2003;Motter & Saa 2009).…”

“…In this place, we take advantage of our former study of axisymmetric versions of given systems (Kovář et al 2010;Kopáček et al 2010a) and use the particular, previouslyinvestigated, confinements of particles in the system with aligned magnetic fields as the starting point of our current analysis. We will gradually incline the originally aligned field and observe its impact upon the dynamics of particles.…”

“…This remarkable property is guaranteed by the full integrability of the system due to the existence of the fourth constant of motion, and it holds even in the case of an electrically charged, rotating black hole. On the other hand, as soon as the black hole is embedded in an external magnetic field, chaotic dynamics may appear (Kopáček et al 2010a). While the electric charge of astronomical black holes is negligible, the role of the magnetic field is important (e.g., Camenzind 2007).…”