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.
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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 (RPs) and we compare them with Poincaré surfaces of section. We describe the RPs in terms of the recurrence quantification analysis, 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 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.
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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.
Read More
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 (RPs) and we
compare them with Poincaré surfaces of section. We describe the
RPs in terms of the recurrence quantification analysis, 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 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.
Read More
Off-equatorial circular orbits with constant latitudes (halo orbits) of electrically charged particles exist near compact objects. In the previous paper, we discussed this kind of motion and demonstrated the existence of minima of the two-dimensional effective potential which correspond to the stable halo orbits. Here, we relax previous assumptions of the pseudo-Newtonian approach for the gravitational field of the central body and study properties of the halo orbits in detail. Within the general relativistic approach, we carry out our calculations in two cases. Firstly, we examine the case of a rotating magnetic compact star. Assuming that the magnetic field axis and the rotation axis are aligned with each other, we study the orientation of motion along the stable halo orbits. In the poloidal plane, we also discuss shapes of the related effective potential halo lobes where the general off-equatorial motion can be bound. Then we focus on the halo orbits near a Kerr black hole immersed in an asymptotically uniform magnetic field of external origin. We demonstrate that, in both the cases considered, the lobes exhibit two different regimes, namely one where completely disjoint lobes occur symmetrically above and below the equatorial plane, and another where the lobes are joined across the plane. A possible application of the model concerns the structure of putative circumpulsar discs consisting of dust particles. We suggest that the particles can acquire a small (but non-zero) net electric charge, and this drives them to form the halo lobes.
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Off-equatorial circular orbits with constant latitudes (halo orbits) of
electrically charged particles exist near compact objects. In the
previous paper, we discussed this kind of motion and demonstrated the
existence of minima of the two-dimensional effective potential which
correspond to the stable halo orbits. Here, we relax previous
assumptions of the pseudo-Newtonian approach for the gravitational field
of the central body and study properties of the halo orbits in detail.
Within the general relativistic approach, we carry out our calculations
in two cases. Firstly, we examine the case of a rotating magnetic
compact star. Assuming that the magnetic field axis and the rotation
axis are aligned with each other, we study the orientation of motion
along the stable halo orbits. In the poloidal plane, we also discuss
shapes of the related effective potential halo lobes where the general
off-equatorial motion can be bound. Then we focus on the halo orbits
near a Kerr black hole immersed in an asymptotically uniform magnetic
field of external origin. We demonstrate that, in both the cases
considered, the lobes exhibit two different regimes, namely one where
completely disjoint lobes occur symmetrically above and below the
equatorial plane, and another where the lobes are joined across the
plane. A possible application of the model concerns the structure of
putative circumpulsar discs consisting of dust particles. We suggest
that the particles can acquire a small (but non-zero) net electric
charge, and this drives them to form the halo lobes.
Read More
Set of neutron star observational results is used to test some selected equations of state of dense nuclear matter. The first observational result comes from the mass-baryon number relation for pulsar B of the double pulsar system J0737-3039. The second one is based on the mass-radius relation coming from observation of the thermal radiation of the neutron star RX J1856.35-3754. The third one follows the population analysis of isolated neutron star thermal radiation sources. The last one is the test of maximum mass. The equation of state of asymmetric nuclear matter is given by the parametrized form of the relativistic Brueckner-Hartree-Fock mean field, and we test selected parametrization that represent fits of full relativistic mean field calculation. We show that only one of them is capable to pass the observational tests. This equation of state represents the first equation of state that is able to explain all the mentioned observational tests, especially the very accurate test given by the double pulsar even if no mass loss is assumed.
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Set of neutron star observational results is used to test some selected
equations of state of dense nuclear matter. The first observational
result comes from the mass-baryon number relation for pulsar B of the
double pulsar system J0737-3039. The second one is based on the
mass-radius relation coming from observation of the thermal radiation of
the neutron star RX J1856.35-3754. The third one follows the population
analysis of isolated neutron star thermal radiation sources. The last
one is the test of maximum mass. The equation of state of asymmetric
nuclear matter is given by the parametrized form of the relativistic
Brueckner-Hartree-Fock mean field, and we test selected parametrization
that represent fits of full relativistic mean field calculation. We show
that only one of them is capable to pass the observational tests. This
equation of state represents the first equation of state that is able to
explain all the mentioned observational tests, especially the very
accurate test given by the double pulsar even if no mass loss is
assumed.
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Boutloukos et al. discovered twin-peak quasi-periodic oscillations (QPOs) in 11 observations of the peculiar Z-source Circinus X-1. Among several other conjunctions the authors briefly discussed the related estimate of the compact object mass following from the geodesic relativistic precession model for kHz QPOs. Neglecting the neutron star rotation they reported the inferred mass M 0 = 2.2 ± 0.3 M sun. We present a more detailed analysis of the estimate which involves the frame-dragging effects associated with rotating spacetimes. For a free mass we find acceptable fits of the model to data for (any) small dimensionless compact object angular momentum j = cJ/GM 2. Moreover, quality of the fit tends to increase very gently with rising j. Good fits are reached when M ~ M 0[1 + 0.55(j + j 2)]. It is therefore impossible to estimate the mass without independent knowledge of the angular momentum and vice versa. Considering j up to 0.3 the range of the feasible values of mass extends up to 3 M sun. We suggest that similar increase of estimated mass due to rotational effects can be relevant for several other sources.
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Boutloukos et al. discovered twin-peak quasi-periodic oscillations
(QPOs) in 11 observations of the peculiar Z-source Circinus X-1. Among
several other conjunctions the authors briefly discussed the related
estimate of the compact object mass following from the geodesic
relativistic precession model for kHz QPOs. Neglecting the neutron star
rotation they reported the inferred mass M 0 = 2.2 ±
0.3 M sun. We present a more detailed analysis of the
estimate which involves the frame-dragging effects associated with
rotating spacetimes. For a free mass we find acceptable fits of the
model to data for (any) small dimensionless compact object angular
momentum j = cJ/GM 2. Moreover, quality of the fit tends to
increase very gently with rising j. Good fits are reached when M ~ M
0[1 + 0.55(j + j 2)]. It is therefore impossible
to estimate the mass without independent knowledge of the angular
momentum and vice versa. Considering j up to 0.3 the range of the
feasible values of mass extends up to 3 M sun. We suggest
that similar increase of estimated mass due to rotational effects can be
relevant for several other sources.
Read More
