arXiv subjects

Ondřej Kopáček

Publications and source records attributed to Ondřej Kopáček.

16 recordsLinked to original sources

arXiv2024

Combining Machine Learning with Recurrence Analysis for resonance detection

The width of a resonance in a nearly integrable system, i.e. in a non-integrable system where chaotic motion is still not prominent, can tell us how a perturbation parameter is driving the system away from integrability. Although the tool that we are presenting here can be used is quite generic and can be used in a variety of systems, our particular interest lies in binary compact object systems known as extreme mass ratio inspirals (EMRIs). In an EMRI a lighter compact object, like a black hole or a neutron star, inspirals into a supermassive black hole due to gravitational radiation reaction. During this inspiral the lighter object crosses resonances, which are still not very well modeled. Measuring the width of resonances in EMRI models allows us to estimate the importance of each perturbation parameter able to drive the system away from resonances and decide whether its impact should be included in EMRI waveform modeling or not. To tackle this issue in our study we show first that recurrence quantifiers of orbits carry imprints of resonant behavior, regardless of the system's dimensionality. As a next step, we apply a long short-term memory machine learning architecture to automate the resonance detection procedure. Our analysis is developed on a simple standard map and gradually we extend it to more complicated systems until finally we employ it in a generic deformed Kerr spacetime known in the literature as the Johannsen-Psaltis spacetime.

gr-qc↗

arXiv2024

On Innermost Stable Spherical Orbits near a rotating black hole: A numerical study of the particle motion near the plunging region

According to General Relativity, astrophysical black holes are described by a small number of parameters. Apart from the mass of the black hole (M), among the most interesting characteristics is the spin (a), which determines the degree of rotation, i.e., the angular momentum of the black hole. The latter is observationally constrained by the spectral and timing properties of the radiation signal emerging from an accretion disk of matter orbiting near the event horizon. In the case of planar (standard, equatorial) accretion disk, it is the location of the Innermost Stable Circular Orbit (ISCO) that determines the observable radiation characteristics, and this way allows us to measure the spin. In this paper, we discuss a more general case of the Innermost Stable Spherical Orbits (ISSO) extending above and below the equatorial plane. To this end, we study the non-equatorial geodesic motion of particles following inclined, spherical, relativistically precessing trajectories with the aim of exploring the boundary between the regions of stable (energetically bound) and escaping (energetically unbound) motion. The concept of the ISSO radius should play a role in determining the inner rim of a tilted or geometrically thick accretion flow. We demonstrate that the region of inclined bound orbits has a complicated structure due to enhanced precession near the inner rim. We also explore the fate of particles launched below the radius of the Marginally Bound Spherical Orbit (MBSO): these may either plunge into the event horizon or escape to radial infinity.

astro-ph.HE↗

arXiv2020

Near-horizon structure of escape zones of electrically charged particles around weakly magnetized rotating black hole. II. Acceleration and escape in the oblique magnetosphere

Strong gravity and magnetic fields are key ingredients that power processes of accretion and ejection near compact objects. While the particular mechanisms that operate here are still discussed, it seems that the presence of an ordered magnetic field is crucial for the acceleration and collimation of relativistic jets of electrically charged particles on superhorizon length scales. In this context, we further study the effect of a large-scale magnetic field on the dynamics of charged particles near a rotating black hole. We consider a scenario in which the initially neutral particles on regular geodesic orbits in the equatorial plane are destabilized by a charging process (e.g., by photoionization). Some charged particles are accelerated out of the equatorial plane, and they follow jetlike trajectories with relativistic velocities. In our previous paper, we investigated this scenario for the case of perfect alignment of the magnetic field with the axis of rotation; i.e., the system was considered axisymmetric. Here we relax this assumption and investigate nonaxisymmetric systems in which the magnetic field is arbitrarily inclined with respect to the black hole spin. We study the system numerically in order to locate the zones of escaping trajectories and compute the maximum (terminal) escape velocity. It appears that breaking the axial symmetry (even by small inclination angles) substantially increases the fraction of escaping orbits and allows the acceleration to ultrarelativistic velocities that were excluded in the axisymmetric setup. The presence of transient chaotic dynamics in the launching region of the relativistic outflow is confirmed with chaotic indicators.

astro-ph.HE↗

arXiv2019

Growth of resonances and chaos for a spinning test particle in the Schwarzschild background

Inspirals of stellar mass compact objects into supermassive black holes are known as extreme mass ratio inspirals. In the simplest approximation, the motion of the compact object is modeled as a geodesic in the space-time of the massive black hole with the orbit decaying due to radiated energy and angular momentum, thus yielding a highly regular inspiral. However, once the spin of the secondary compact body is taken into account, integrability is broken and prolonged resonances along with chaotic motion appear. We numerically integrate the motion of a spinning test body in the field of a non-spinning black hole and analyse it using various methods. We show for the first time that resonances and chaos can be found even for astrophysical values of spin. On the other hand, we devise a method to analyse the growth of the resonances, and we conclude that the resonances we observe are only caused by terms quadratic in spin and will generally stay very small in the small-mass-ratio limit. Last but not least, we compute gravitational waveforms by solving numerically the Teukolsky equations in the time-domain and establish that they carry information on the motion's dynamics. In particular, we show that the time series of the gravitational wave strain can be used to discern regular from chaotic motion of the source.

gr-qc↗

arXiv2019

Emergence of magnetic null points in electro-vacuum magnetospheres of compact objects: The case of a plunging neutron star

Relativistic effects of compact objects onto electromagnetic fields in their vicinity are investigated using the test-field approximation. In particular, we study the possible emergence of magnetic null points which are astrophysically relevant for the processes of magnetic reconnection. While the magnetic reconnection occurs in the presence of plasma and may lead to violent mass ejection, we show here that strong gravitation of the supermassive black hole may actively support the process by suitably entangling the field lines even in the electro-vacuum description. In this contribution we further discuss the case of a dipole-type magnetic field of the neutron star on the plunging trajectory to the supermassive black hole. While we have previously shown that given model in principle admits the formation of magnetic null points, here we explore whether and where the null points appear for the astrophysically relevant values of the parameters.

astro-ph.HE↗

arXiv2018

Null Points in the Magnetosphere of a Plunging Neutron Star

We explore the structure of a dipole-type vacuum field of a slowly rotating magnetic star near the horizon of a supermassive black hole, where the structure of field lines becomes highly distorted by effects of strong gravity. Such a situation may occur near a neutron star in the final stages of a plunging trajectory into a galactic center. We solve Maxwell's equations in the Rindler approximation for the rotating conducting source of dipolar magnetic field arbitrarily inclined with respect to the axis of rotation. For the fixed inclination angle we calculate the field including the radiative terms while in the general case we discuss the electromagnetic field considering the near-field terms only. In the latter case we investigate the emergence of magnetic null points within the vacuum magnetosphere. Null points become highly relevant in the presence of astrophysical plasma where they are connected with processes of magnetic reconnection and mass ejection.

astro-ph.HE↗

arXiv2018

Near-horizon structure of escape zones of electrically charged particles around weakly magnetized rotating black hole

An interplay of magnetic fields and gravitation drives accretion and outflows near black holes. However, a specific mechanism is still a matter of debate; it is very likely that different processes dominate under various conditions. In particular, for the acceleration of particles and their collimation in jets, an ordered component of the magnetic field seems to be essential. Here we discuss the role of large-scale magnetic fields in transporting the charged particles and dust grains from the bound orbits in the equatorial plane of a rotating (Kerr) black hole and the resulting acceleration along trajectories escaping the system in a direction parallel to the symmetry axis (perpendicular to the accretion disk). We consider a specific scenario of destabilization of circular geodesics of initially neutral matter by charging (e.g., due to photoionization). Some particles may be set on escaping trajectories and attain relativistic velocity. The case of charged particles differs from charged dust grains by their charge-to-mass ratio, but the acceleration mechanism operates in a similar manner. It appears that the chaotic dynamics controls the outflow and supports the formation of near-horizon escape zones. We employ the technique of recurrence plots to characterize the onset of chaos in the outflowing medium. We investigate the system numerically and construct the basin-boundary plots, which show the location and the extent of the escape zones. The effects of black hole spin and magnetic field strength on the formation and location of escape zones are discussed, and the maximal escape velocity is computed.

astro-ph.HE↗

arXiv2017

Recurrence Analysis as a tool to study chaotic dynamics of extreme mass ratio inspiral in signal with noise

Recurrence analysis is a well settled method allowing to discern chaos from order, and determinism from noise. We apply this tool to study time series representing geodesic and inspiraling motion of a test particle in a deformed Kerr spacetime, when deterministic chaos and different levels of stochastic noise are present. In particular, we suggest a recurrence-based criterion to reveal whether the time series comes from a deterministic source and find a noise-level threshold of its applicability.

gr-qc↗

arXiv2016

Effective potential of particles in the oblique black hole magnetosphere

Dynamics of charged matter in the oblique black hole magnetosphere is investigated. In particular, we adopt a model consisting of a rotating black hole embedded in the external large-scale magnetic field that is inclined arbitrarily with respect to the rotation axis. Breaking the axial symmetry appears to have profound consequences regarding the dynamics of particles and it also poses some methodological difficulties. In this contribution we discuss the applicability of the method of effective potential for the non-axisymmetric model and show that it may only be applied in the appropriate reference frame.

gr-qc↗

arXiv2016

Application of a symplectic integrator in a non-integrable relativistic system

We present a detailed comparison of several integration schemes applied to the dynamic system consisting of a charged particle on the Kerr background endowed with the axisymmetric electromagnetic test field. In particular, we compare the performance of the symplectic integrator with several non-symplectic routines and discuss under which circumstances we should choose the symplectic one and when we should switch to some other scheme. We are basically concerned with two crucial, yet opposing aspects - accuracy of the integration and CPU time consumption. The latter is generally less critical in our application while the highest possible accuracy is strongly demanded.

gr-qc↗

arXiv2014

Regular and chaotic motion in general relativity: The case of an inclined black hole magnetosphere

Dynamics of charged particles in the vicinity of a rotating black hole embedded in the external large-scale magnetic field is numerically investigated. In particular, we consider a non-axisymmetric model in which the asymptotically uniform magnetic field is inclined with respect to the axis of rotation. We study the effect of inclination onto the prevailing dynamic regime of particle motion, i.e. we ask whether the inclined field allows regular trajectories or if instead, the deterministic chaos dominates the motion. In this contribution we further discuss the role of initial condition, particularly, the initial azimuthal angle. To characterize the measure of chaoticness we compute maximal Lyapunov exponents and employ the method of Recurrence Quantification Analysis.

astro-ph.HE↗

arXiv2014

Regular and Chaotic Motion in General Relativity: The Case of a Massive Magnetic Dipole

Circular motion of particles, dust grains and fluids in the vicinity of compact objects has been investigated as a model for accretion of gaseous and dusty environment. Here we further discuss, within the framework of general relativity, figures of equilibrium of matter under the influence of combined gravitational and large-scale magnetic fields, assuming that the accreted material acquires a small electric charge due to interplay of plasma processes and photoionization. In particular, we employ an exact solution describing the massive magnetic dipole and we identify the regions of stable motion. We also investigate situations when the particle dynamics exhibits the onset of chaos. In order to characterize the measure of chaoticness we employ techniques of Poincaré surfaces of section and of recurrence plots.

astro-ph.HE↗

arXiv2013

Regular and chaotic orbits near a massive magnetic dipole

Within the framework of Bonnor's exact solution describing a massive magnetic dipole, we study the motion of neutral and electrically charged test particles. In dependence on the Bonnor spacetime parameters, we determine regions enabling the existence of stable circular orbits confined to the equatorial plane and of those levitating above the equatorial plane. Constructing Poincaré surfaces of section and recurrence plots, we also investigate the dynamics of particles moving along general off-equatorial trajectories bound in effective potential wells forming around the stable circular orbits. We demonstrate that the motion in the Bonnor spacetime is not integrable. This extends previous investigations of generalized Störmer's problem into the realm of exact solutions of Einstein-Maxwell equations, where the gravitational and electromagnetic effects play a comparable role on the particle motion.

gr-qc↗

arXiv2011

Transition from regular to chaotic motion in black hole magnetospheres

Cosmic black holes can act as agents of particle acceleration. We study properties of a system consisting of a rotating black hole immersed in a large-scale organized magnetic field. Electrically charged particles in the immediate neighborhood of the horizon are influenced by strong gravity acting together with magnetic and induced electric components. We relax several constraints which were often imposed in previous works: the magnetic field does not have to share a common symmetry axis with the spin of the black hole but they can be inclined with respect to each other, thus violating the axial symmetry. Also, the black hole does not have to remain at rest but it can instead perform fast translational motion together with rotation. We demonstrate that the generalization brings new effects. Starting from uniform electro-vacuum fields in the curved spacetime, we find separatrices and identify magnetic neutral points forming in certain circumstances. We suggest that these structures can represent signatures of magnetic reconnection triggered by frame-dragging effects in the ergosphere. We further investigate the motion of charged particles in these black hole magnetospheres. We concentrate on the transition from the regular motion to chaos, and in this context we explore the characteristics of chaos in relativity. For the first time, we apply recurrence plots as a suitable technique to quantify the degree of chaoticness near a black hole.

astro-ph.HE↗

arXiv2010

Recurrence plots and chaotic motion around Kerr black hole

We study the motion of charged test particles around a Kerr black hole immersed in the asymptotically uniform magnetic field, concluding that off-equatorial stable orbits are allowed in this system. Being interested in dynamical properties of these astrophysically relevant orbits we employ rather novel approach based on the analysis of recurrences of the system to the vicinity of its previous states. We use recurrence plots (RPs) as a tool to visualize recurrences of the trajectory in the phase space. Construction of RPs is simple and straightforward regardless of the dimension of the phase space, which is a major advantage of this approach when compared to the "traditional" methods of the numerical analysis of dynamical systems (for instance the visual survey of Poincaré surfaces of section, evaluation of the Lyapunov spectra etc.). We show that RPs and their quantitative measures (obtained from recurrence quantification analysis -- RQA) are powerful tools to detect dynamical regime of motion (regular vs. chaotic) and precisely locate the transitions between these regimes.

astro-ph.HE↗

arXiv2010

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

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.

astro-ph.HE↗