Acceleration of charged particles due to chaotic scattering in the combined black hole gravitational field and asymptotically uniform magnetic field

To test the role of large-scale magnetic fields in accretion processes, we study dynamics of charged test particles in vicinity of a black hole immersed into an asymptotically uniform magnetic field. Using the Hamiltonian formalism of charged particle dynamics, we examine chaotic scattering in the effective potential related to the black hole gravitational field combined with the uniform magnetic field. Energy interchange between the translational and oscillatory modes od the charged particle dynamics provides mechanism for charged particle acceleration along the magnetic field lines. This energy transmutation is an attribute of the chaotic charged particle dynamics in the combined gravitational and magnetic fields only, the black hole rotation is not necessary for such charged particle acceleration. The chaotic scatter can cause transition to the motion along the magnetic field lines with small radius of the Larmor motion or vanishing Larmor radius, when the speed of the particle translational motion is largest and can be ultra-relativistic. We discuss consequences of the model of ionization of test particles forming a neutral accretion disc, or heavy ions following off-equatorial circular orbits, and we explore the fate of heavy charged test particles after ionization where no kick of heavy ions is assumed and only switch-on effect of the magnetic field is relevant. We demonstrate that acceleration and escape of the ionized particles can be efficient along the Kerr black hole symmetry axis parallel to the magnetic field lines. We show that strong acceleration of ionized particles to ultra-relativistic velocities is preferred in the direction close to the magnetic field lines. Therefore, the process of ionization of Keplerian discs around Kerr black holes can serve as a model of relativistic jets.Comment: 21 pages, 13 figure

Determination of chaotic behaviour in time series generated by charged particle motion around magnetized Schwarzschild black holes

We study behaviour of ionized region of a Keplerian disk orbiting a Schwarzschild black hole immersed in an asymptotically uniform magnetic field. In dependence on the magnetic parameter ${\cal B}$, and inclination angle $\theta$ of the disk plane with respect to the magnetic field direction, the charged particles of the ionized disk can enter three regimes: a) regular oscillatory motion, b) destruction due to capture by the magnetized black hole, c) chaotic regime of the motion. In order to study transition between the regular and chaotic type of the charged particle motion, we generate time series of the solution of equations of motion under various conditions, and study them by non-linear (box counting, correlation dimension, Lyapunov exponent, recurrence analysis, machine learning) methods of chaos determination. We demonstrate that the machine learning method appears to be the most efficient in determining the chaotic region of the $\theta-r$ space. We show that the chaotic character of the ionized particle motion increases with the inclination angle. For the inclination angles $\theta \sim 0$ whole the ionized internal part of the Keplerian disk is captured by the black hole.Comment: 21 pages, 9 figure

Possible signature of magnetic fields related to quasi-periodic oscillation observed in microquasars

The study of quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole binaries can provide a powerful tool for testing of the phenomena occurring in strong gravity regime. The high frequency (HF) QPOs usually come in pairs of double peaks which have a frequency ratio close to $3:2$. In addition to HF QPOs, some sources display simultaneous existence of the low frequency (LF) QPOs in Fourier power spectra. We demonstrate that the explanation of these phenomena can be well related to the epicyclic oscillations of charged particles in accretion disks orbiting Kerr black holes immersed in external large-scale magnetic fields. Magnetized versions of the standard geodesic models of QPOs can explain the observationally fixed data from the three microquasars. We perform a successful fitting of the HF QPOs observed in three microquasars, GRS 1915+105, XTE 1550-564 and GRO 1655-40, containing black holes, for magnetised versions of both epicyclic rezonance and relativistic precession models and discuss the corresponding constraints of parameters of the model, which are the mass and spin of black hole and the parameter related to the external magnetic field. Assuming the main source of synchrotron radiation producing X-rays are the relativistic electrons, we estimate the magnetic field in the vicinity of the black hole in the three sources to be of order $10^{-5}$ Gs which can serve as possible signature of the Galactic magnetic field magnitude. For heavier particles (protons, ions) larger magnetic fields are necessary for fitting the data.Comment: https://link.springer.com/article/10.1140/epjc/s10052-017-5431-