The proof of existence of Vlasov-Maxwell equilibria which do not exhibit
a functional dependence in terms of the single-particle energy is
established. The theory deals with the kinetic treatment of multispecies
axisymmetric magnetized plasmas, with particular reference to plasma
systems which are slowly time varying. Aside from collisionless
laboratory plasmas, the theory concerns important aspects of
astrophysical scenarios, such as accretion-disk and coronal plasmas
arising in the gravitational field of compact objects. Qualitative
properties of the solution are investigated by making use of a
perturbative kinetic theory. These concern the realization of the
equilibrium kinetic distribution functions in terms of generalized
Gaussian distributions and the constraints imposed by the Maxwell
equations. These equilibria are shown to be generally non-neutral and
characterized by the absence of the Debye screening effect. As a further
application, the stability properties of these equilibria with respect
to axisymmetric electromagnetic perturbations are addressed. This
permits us to establish absolute stability criteria holding in such a
case.
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Current-carrying string-loop dynamics is studied in the Kerr spacetimes.
With attention concentrated to the axisymmetric motion of string loops
around the symmetry axis of both black-hole (BH) and naked singularity
(NS) spacetimes, it is shown that the resulting motion is governed by
the presence of an outer tension barrier and an inner angular momentum
barrier that are influenced by the BH or NS spin. We classify the string
dynamics according to properties of the energy boundary function
(effective potential) for the string loop motion. We have found that for
NS there exist new types of energy boundary function, namely those with
off-equatorial minima. Conversion of the energy of the string
oscillations to the energy of the linear translational motion has been
studied. Such a transmutation effect is much more efficient in the NS
spacetimes because of lack of the event horizon. For BH spacetimes
efficiency of the transmutation effect is only weakly spin dependent.
Transition from the regular to chaotic regime of the string-loop
dynamics is examined and used for explanation of the string-loop motion
focusing problem. Radial and vertical frequencies of small oscillations
of string loops near minima of the effective potential in the equatorial
plane are given. These can be related to high-frequency quasiperiodic
oscillations observed near black holes.
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The proof of existence of Vlasov-Maxwell equilibria which do not exhibit a functional dependence in terms of the single-particle energy is established. The theory deals with the kinetic treatment of multispecies axisymmetric magnetized plasmas, with particular reference to plasma systems which are slowly time varying. Aside from collisionless laboratory plasmas, the theory concerns important aspects of astrophysical scenarios, such as accretion-disk and coronal plasmas arising in the gravitational field of compact objects. Qualitative properties of the solution are investigated by making use of a perturbative kinetic theory. These concern the realization of the equilibrium kinetic distribution functions in terms of generalized Gaussian distributions and the constraints imposed by the Maxwell equations. These equilibria are shown to be generally non-neutral and characterized by the absence of the Debye screening effect. As a further application, the stability properties of these equilibria with respect to axisymmetric electromagnetic perturbations are addressed. This permits us to establish absolute stability criteria holding in such a case.
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Current-carrying string-loop dynamics is studied in the Kerr spacetimes. With attention concentrated to the axisymmetric motion of string loops around the symmetry axis of both black-hole (BH) and naked singularity (NS) spacetimes, it is shown that the resulting motion is governed by the presence of an outer tension barrier and an inner angular momentum barrier that are influenced by the BH or NS spin. We classify the string dynamics according to properties of the energy boundary function (effective potential) for the string loop motion. We have found that for NS there exist new types of energy boundary function, namely those with off-equatorial minima. Conversion of the energy of the string oscillations to the energy of the linear translational motion has been studied. Such a transmutation effect is much more efficient in the NS spacetimes because of lack of the event horizon. For BH spacetimes efficiency of the transmutation effect is only weakly spin dependent. Transition from the regular to chaotic regime of the string-loop dynamics is examined and used for explanation of the string-loop motion focusing problem. Radial and vertical frequencies of small oscillations of string loops near minima of the effective potential in the equatorial plane are given. These can be related to high-frequency quasiperiodic oscillations observed near black holes.
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The study of the statistical properties of collisionless systems formed
by neutral particles subject to gravitational field represents an
intriguing theoretical issue. In astrophysics, it directly relates to
the description of collisionless gravitating dark matter (DM) halos.
Structures of this type are expected to be characterized by
intrinsically non-Maxwellian kinetic distribution functions (KDFs) and
to exhibit temperature anisotropy, i.e. an anisotropy in the directional
particle velocity dispersions. In this paper, a theoretical analysis of
the issue is proposed, based on the kinetic theory developed in the
framework of the Vlasov-Poisson description for nonrelativistic DM
systems at equilibrium. By implementing the method of invariants,
explicit solutions for the equilibrium KDFs are constructed and
expressed through generalized Gaussian distributions. A perturbative
theory is developed which allows them to be cast in terms of
Chapman-Enskog series representations and to evaluate analytically the
corresponding fluid fields. The conditions for the occurrence of
temperature anisotropy are investigated for different physical and
geometrical configurations. It is shown that this feature can arise at
equilibrium due to specifically-kinetic effects associated with
phase-space conservation laws in the presence of a nonuniform
gravitational field.
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We present results for models of neutron stars and strange stars
constructed using the Hartle-Thorne slow-rotation method with a wide
range of equations of state, focusing on the values obtained for the
angular momentum J and the quadrupole moment Q, when the gravitational
mass M and the rotational frequency Ω are specified. Building on
previous work, which showed surprising uniformity in the behaviour of
the moment of inertia for neutron-star models constructed with widely
different equations of state, we find similar uniformity for the
quadrupole moment. These two quantities, together with the mass, are
fundamental for determining the vacuum space-time outside neutron stars.
We study particularly the dimensionless combination of parameters
QM/J2 (using units for which c = G = 1). This quantity goes
to 1 in the case of a Kerr-metric black hole and deviations away from 1
then characterize the difference between neutron-star and black hole
space-time. It is found that QM/J2 for both neutron stars and
strange stars decreases with increasing mass, for a given equation of
state, reaching a value of around 2 (or even less) for maximum-mass
models, meaning that their external space-time is then not very far from
that of the Kerr metric. If QM/J2 is plotted against R/2M
(where R is the radius), it is found that the relationship is nearly
unique for neutron-star models, independent of the equation of state,
while it is significantly different for strange stars. This gives a new
way of possibly distinguishing between them.
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We present results for models of neutron stars and strange stars constructed using the Hartle-Thorne slow-rotation method with a wide range of equations of state, focusing on the values obtained for the angular momentum J and the quadrupole moment Q, when the gravitational mass M and the rotational frequency Ω are specified. Building on previous work, which showed surprising uniformity in the behaviour of the moment of inertia for neutron-star models constructed with widely different equations of state, we find similar uniformity for the quadrupole moment. These two quantities, together with the mass, are fundamental for determining the vacuum space-time outside neutron stars. We study particularly the dimensionless combination of parameters QM/J2 (using units for which c = G = 1). This quantity goes to 1 in the case of a Kerr-metric black hole and deviations away from 1 then characterize the difference between neutron-star and black hole space-time. It is found that QM/J2 for both neutron stars and strange stars decreases with increasing mass, for a given equation of state, reaching a value of around 2 (or even less) for maximum-mass models, meaning that their external space-time is then not very far from that of the Kerr metric. If QM/J2 is plotted against R/2M (where R is the radius), it is found that the relationship is nearly unique for neutron-star models, independent of the equation of state, while it is significantly different for strange stars. This gives a new way of possibly distinguishing between them.
Read More
The study of the statistical properties of collisionless systems formed by neutral particles subject to gravitational field represents an intriguing theoretical issue. In astrophysics, it directly relates to the description of collisionless gravitating dark matter (DM) halos. Structures of this type are expected to be characterized by intrinsically non-Maxwellian kinetic distribution functions (KDFs) and to exhibit temperature anisotropy, i.e. an anisotropy in the directional particle velocity dispersions. In this paper, a theoretical analysis of the issue is proposed, based on the kinetic theory developed in the framework of the Vlasov-Poisson description for nonrelativistic DM systems at equilibrium. By implementing the method of invariants, explicit solutions for the equilibrium KDFs are constructed and expressed through generalized Gaussian distributions. A perturbative theory is developed which allows them to be cast in terms of Chapman-Enskog series representations and to evaluate analytically the corresponding fluid fields. The conditions for the occurrence of temperature anisotropy are investigated for different physical and geometrical configurations. It is shown that this feature can arise at equilibrium due to specifically-kinetic effects associated with phase-space conservation laws in the presence of a nonuniform gravitational field.
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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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