We study motion of an electric current-carrying string loop oscillating in the vicinity of the Schwarzschild black hole immersed in an external uniform magnetic field. The dependence of boundaries and different types of motion of the string loop on magnetic field strength is found. The dynamics of the string loop in the Cartesian xy plane depends both on value and direction of the magnetic field and current. It is shown that the magnetic field influence on the behavior of the string loop is quite significant even for weak magnetic field strength. The oscillation of the string loop becomes stronger or weaker in dependence on the direction of the Lorenz force. We illustrate the various regimes of the trajectories of the string loop that can fall down into the black hole, escape to infinity, or be trapped in the finite region near the horizon for the different representative values of the magnetic field. We have also considered the flat spacetime limit as the condition of the escape of the string loop from the neighborhood of the black hole to infinity. We found the expression for the magnetic field strength for which the oscillatory motion of the string loop totally vanishes and the string loop can have maximal acceleration in the perpendicular direction to the plane of the loop.
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The multi-resonance orbital model of high-frequency quasi-periodic oscillations (HF QPOs) enables precise determination of the black hole dimensionless spin a if observed set of oscillations demonstrates three (or more) commensurable frequencies. The black hole spin a is related to the frequency ratio only, while its mass M is related to the frequency magnitude. The model is applied to the triple frequency set of HF QPOs observed in Sgr A* source with frequency ratio 3:2:1. Acceptable versions of the multi-resonance model are determined by the restrictions on the Sgr A* supermassive black hole mass. The version of strong resonances related to the black hole "magic" spin a=0.983 is acceptable but the version demonstrating the best agreement with the mass restrictions predicts spin a=0.980.
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The problem of formulating a kinetic treatment for quasi-stationary
collisionless plasmas in axisymmetric systems subject to the possibly
independent presence of local strong velocity-shear and supersonic
rotation velocities is posed. The theory is developed in the framework
of the Vlasov-Maxwell description for multi-species non-relativistic
plasmas. Applications to astrophysical accretion discs arising around
compact objects and to plasmas in laboratory devices are considered.
Explicit solutions for the equilibrium kinetic distribution function
(KDF) are constructed based on the identification of the relevant
particle adiabatic invariants. These are shown to be expressed in terms
of generalized non-isotropic Gaussian distributions. A suitable
perturbative theory is then developed which allows for the treatment of
non-uniform strong velocity-shear/supersonic plasmas. This yields a
series representation for the equilibrium KDF in which the leading-order
term depends on both a finite set of fluid fields as well as on the
gradients of an appropriate rotational frequency. Constitutive equations
for the fluid number density, flow velocity, and pressure tensor are
explicitly calculated. As a notable outcome, the discovery of a new
mechanism for generating temperature and pressure anisotropies is
pointed out, which represents a characteristic feature of plasmas
considered here. This is shown to arise as a consequence of the
canonical momentum conservation and to contribute to the occurrence of
temperature anisotropy in combination with the adiabatic conservation of
the particle magnetic moment. The physical relevance of the result and
the implications of the kinetic solution for the self-generation of
quasi-stationary electrostatic and magnetic fields through a kinetic
dynamo are discussed.
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The problem of formulating a kinetic treatment for quasi-stationary collisionless plasmas in axisymmetric systems subject to the possibly independent presence of local strong velocity-shear and supersonic rotation velocities is posed. The theory is developed in the framework of the Vlasov-Maxwell description for multi-species non-relativistic plasmas. Applications to astrophysical accretion discs arising around compact objects and to plasmas in laboratory devices are considered. Explicit solutions for the equilibrium kinetic distribution function (KDF) are constructed based on the identification of the relevant particle adiabatic invariants. These are shown to be expressed in terms of generalized non-isotropic Gaussian distributions. A suitable perturbative theory is then developed which allows for the treatment of non-uniform strong velocity-shear/supersonic plasmas. This yields a series representation for the equilibrium KDF in which the leading-order term depends on both a finite set of fluid fields as well as on the gradients of an appropriate rotational frequency. Constitutive equations for the fluid number density, flow velocity, and pressure tensor are explicitly calculated. As a notable outcome, the discovery of a new mechanism for generating temperature and pressure anisotropies is pointed out, which represents a characteristic feature of plasmas considered here. This is shown to arise as a consequence of the canonical momentum conservation and to contribute to the occurrence of temperature anisotropy in combination with the adiabatic conservation of the particle magnetic moment. The physical relevance of the result and the implications of the kinetic solution for the self-generation of quasi-stationary electrostatic and magnetic fields through a kinetic dynamo are discussed.
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Current-carrying string loops are adopted in astrophysics to model the
dynamics of isolated flux tubes of magnetized plasma expected to arise
in the gravitational field of compact objects, such as black holes.
Recent studies suggest that they could provide a framework for the
acceleration and collimation of jets of plasma observed in these
systems. However, the problem remains of the search of physical
mechanisms which can consistently explain the occurrence of such plasma
toroidal structures characterized by nonvanishing charge currents and
are able to self-generate magnetic loops. In this paper, the problem is
addressed in the context of Vlasov-Maxwell theory for nonrelativistic
collisionless plasmas subject to both gravitational and electromagnetic
fields. A kinetic treatment of quasistationary axisymmetric
configurations of charged particles exhibiting epicyclic motion is
obtained. Explicit solutions for the species equilibrium phase-space
distribution function are provided. These are shown to have generally a
non-Maxwellian character and to be characterized by nonuniform fluid
fields and temperature anisotropy. Calculation of the relevant fluid
fields and analysis of the Ampere equation then show the existence of
nonvanishing current densities. As a consequence, the occurrence of a
kinetic dynamo is proved, which can explain the self-generation of both
azimuthal and poloidal magnetic fields by the plasma itself. This
mechanism can operate in the absence of instabilities, turbulence, or
accretion phenomena and is intrinsically kinetic in character. In
particular, several kinetic effects contribute to it, identified here
with finite Larmor radius, diamagnetic and energy-correction effects
together with temperature anisotropy, and non-Maxwellian features of the
equilibrium distribution function.
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String Theory suggests existence of primordial Kerr superspinars,
extremely compact objects with external spacetime described by the Kerr
naked singularity geometry. The primordial Kerr superspinars have to be
converted to a near-extreme black hole due to accretion, but they could
survive to the era of highly redshifted quasars. We study the shape of
the profiled spectral lines generated by radiating rings or the
innermost parts of Keplerian discs orbiting the Kerr superspinars.
Influence of the superspinar surface location on the profiled lines is
also considered. We demonstrate strong difference of the character of
the profiled lines generated by radiating rings for all values of the
superspinar spin and all values of the inclination angles of the
observer when compared to those generated in the field of Kerr black
holes. For small and mediate inclination angles there are large
quantitative differences in the extension and position of the lines. For
large inclination angles even strong qualitative difference appears as
the profiled lines have a clear doubled character. The smaller,
redshifted region of the profiled line is related to the photons
reaching the regions near the superspinar surface. Strong differences
are obtained also for profiled lines generated by the innermost parts of
Keplerian discs especially in the shape of the line. The influence of
the superspinar surface location is reflected in the intermediate parts
of the the profiled lines. The line profiles can give a clear signature
of the presence of a Kerr superspinar and in principle enable estimates
of its surface location since the signatures of the superspinar surface
location are of different character as those corresponding to the
presence of the black hole horizon.
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One of the popular ways for obtaining estimations of black hole spin is
a method related to models for high-frequency quasi-periodic
oscillations (QPOs). In the past, estimations for three microquasars GRS
1915+105, GRO J1655-40, and XTE J1550-564 were carried out based on
several QPO models assuming a geodesic accretion flow. In this work we
assume a non-geodesic accretion flow described by the model of a
pressure-supported perfect fluid torus and explore the influence of the
pressure forces on the spin predictions calculated for the geodesic
flow. Our results indicate that in some cases, e.g. for the so-called
"vertical precession resonance" model, the presence of pressure forces
may have a major influence on the predicted ranges of spin. On the other
hand, in other cases, e.g. for the so-called "Keplerian resonance"
model, the predicted "non-geodesic" spin intervals do not much vary from
those corresponding to geodesic calculations.
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Results of our recent studies suggest a possibility of existence of halo
(off-equatorial) electrically charged toroidal structures (thick discs)
and polar caps circling in axially symmetric backgrounds of central
objects (compact stars, black holes, etc.) endowed with electromagnetic
fields. Along with the existence of the halo structures we have also
found equatorial tori with cusps enabling outflows of matter from the
torus, without the presence of strong gravity, i.e., also in the
Newtonian regime. These phenomena represent qualitatively new
consequence of the interplay between gravity and electromagnetism, and
can provide an insight into processes determining vertical structure of
dusty tori surrounding accretion discs. Some of these results are
summarized also in the paper accepted for the publication in The
Astrophysical Journal Supplement, scheduled for the March 2013, Volume
205.
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Kerr naked singularities (superspinars) have to be efficiently converted
to a black hole due to accretion from Keplerian discs. In the final
stages of the conversion process the near-extreme Kerr naked
singularities (superspinars) provide a variety of extraordinary physical
phenomena. Such superspinning Kerr geometries can serve as an efficient
accelerator for extremely high-energy collisions enabling direct and
clear demonstration of the outcomes of the collision processes. We shall
discuss the efficiency and visibility of the ultra-high-energy
collisions in the deepest parts of the gravitational well of
superspinning near-extreme Kerr geometries for the whole variety of
particles freely falling from infinity. We demonstrate that the
ultra-high-energy processes can be obtained with no fine tuning of the
motion constants and the products of the collision can escape to
infinity with both directional and energetical efficiency significantly
higher than in the case of the near-extreme black holes. The strongest
efficiency of the collision process is reached for particles falling
along trajectories with maximally acceptable negative angular momentum.
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Context. Using known frequencies of the twin-peak high-frequency
quasiperiodic oscillations (HF QPOs) and known mass of the central black
hole, the black-hole dimensionless spin a can be determined by assuming
a concrete version of the resonance model. However, a wide range of
observationally limited values of the black hole mass implies low
precision of the spin estimates. Aims: We discuss the possibility
of higher precision for the black hole spin a measurements in the
framework of a multi-resonance model inspired by observations of more
than two HF QPOs in the black hole systems, which are expected to occur
at two (or more) different radii of the accretion disc. This framework
is also applied in a modified form to the neutron star systems.
Methods: We determine the spin and mass dependence of the twin-peak
frequencies with a general rational ratio n:m, assuming a non-linear
resonance of oscillations with the epicyclic and Keplerian frequencies
or their combinations. In the multi-resonant model, the twin-peak
resonances are combined properly to give the observed frequency set. For
the black hole systems we focus on the special case of duplex
frequencies, when the top, bottom, or mixed frequency is common at two
different radii where the resonances occur giving triple frequency sets.
Results: The sets of triple frequency ratios and the related spin
a are given. The resonances are considered up to n = 5 since excitation
of higher order resonances is improbable. The strong resonance model for
"magic" values of the black hole spin means that two (or more) versions
of resonance could occur at the same radius, allowing cooperative
effects between the resonances. For neutron star systems we introduce a
resonant switch model that assumes switching of oscillatory modes at
resonant points. Conclusions: In the case of doubled twin-peak HF
QPOs excited at two different radii with common top, bottom, or mixed
frequency, the black hole spin a is given by the triple frequency ratio
set. The spin is determined precisely, but not uniquely, because the
same frequency set could correspond to more than one concrete spin a.
The black hole mass is given by the magnitude of the observed
frequencies. The resonant switch model puts relevant limits on the mass
and spin of neutron stars, and we expect a strong increase in the
fitting procedure precision when different twin oscillatory modes are
applied to data in the vicinity of different resonant points. We expect
the multi-resonance model to be applicable to data from the planned LOFT
or similar X-ray satellite observatory.
Appendices are available in electronic form at http://www.aanda.org
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