Quasi-harmonic oscillatory motion of charged particles around a Schwarzschild black hole immersed in a uniform magnetic field

Abstract

In order to test the role of large-scale magnetic fields in quasiperiodic oscillation phenomena observed in microquasars, we study oscillatory motion of charged particles in vicinity of a Schwarzschild black hole immersed into an external asymptotically uniform magnetic field. We determine the fundamental frequencies of small harmonic oscillations of charged test particles around stable circular orbits in the equatorial plane of a magnetized black hole, and discuss the radial profiles of frequencies of the radial and latitudinal harmonic oscillations in dependence on the mass of the black hole and the strength of the magnetic field. We demonstrate that assuming relevance of resonant phenomena of the radial and latitudinal oscillations of charged particles at their frequency ratio 3 : 2, the oscillatory frequencies of charged particles can be well related to the frequencies of the twin high-frequency quasi-periodic oscillations observed in the microquasars GRS 1915+105, XTE 1550-564 and GRO 1655

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

“…The properties of the effective potential V eff (r, θ; a, L, B) (25) related to the motion in the combined field of Kerr black holes and the asymptotically uniform magnetic field were already explored in [35], and in the simpler case of Schwarzschild black holes in [29]. Since the general form of the effective potential V eff (r, θ; a, L, B) is quite complex, we discuss here only the properties relevant for the purposes of the present paper.…”

“…For covering both minus and plus magnetic field configurations we will be using negative B < 0 and positive B > 0 values of the parameter B. For details see [29]. The stationary points of the effective potential V eff (r, θ; a, L, B), governing circular orbits of the charged test particles, are determined by the conditions…”

“…There is a large variety of studies of the charged test particle motion in such 1 Black hole immersed in an external electromagnetic field. Large-scale electromagnetic field can have dipole character for a magnetar, but at large distance from the source its character can be simplified to almost uniform magnetic field in finite element of space as shown in [7] combined fields [10,[23][24][25][26][27][28][29]. The energy from a collision of the charged particles in the vicinity of the horizon of a black hole or a naked singularity immersed into an external magnetic field can cause particle acceleration [30][31][32][33].…”

“…However, the motion of the charged test particles in the close vicinity of a black hole horizon could be strongly influenced even by relatively weak test magnetic fields [29]. For a charged test particle with charge q and mass m moving in the vicinity of a black hole with mass M surrounded by an uniform magnetic field of the strength B, one can introduce a dimensionless quantity b that can be identified as relative Lorenz force [24] b = |q|BG M/mc 4 .…”

“…It has been demonstrated that collisions of particles in the vicinity of black holes could be enhanced by the external magnetic fields [39][40][41][42][43], but these processes can be observationally efficient especially in the field of Kerr naked singularities [44]. The relation of the quasi-circular equatorial motion of charged test particles around black holes immersed in the magnetic field to the high-frequency quasiperiod oscillations observed in some microquasars has been demonstrated in [29]. Synchrotron radiation of the charged particles following quasi-circular orbits in the combined gravitational and electromagnetic fields has been studied in [10,45].…”