Transition from Regular to Chaotic Circulation in Magnetized Coronae near Compact Objects

    by Zdeněk Stuchlík· 01 října, 2010· in Fyzika· 0 comments
    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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    Recurrence plots and chaotic motion around Kerr black hole

    by Zdeněk Stuchlík· 01 října, 2010· in Fyzika· 0 comments
    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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    Off-equatorial orbits in strong gravitational fields near compact objects—II: halo motion around magnetic compact stars and magnetized black holes

    by Zdeněk Stuchlík· 01 července, 2010· in Fyzika· 0 comments
    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 orbits in strong gravitational fields near compact objects—II: halo motion around magnetic compact stars and magnetized black holes

    by Zdeněk Stuchlík· 01 července, 2010· in Fyzika· 0 comments
    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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    Observational Tests of Neutron Star Relativistic Mean Field Equations of State

    by Zdeněk Stuchlík· 01 června, 2010· in Fyzika· 0 comments
    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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    Observational Tests of Neutron Star Relativistic Mean Field Equations of State

    by Zdeněk Stuchlík· 01 června, 2010· in Fyzika· 0 comments
    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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    On Mass Constraints Implied by the Relativistic Precession Model of Twin-peak Quasi-periodic Oscillations in Circinus X-1

    by Zdeněk Stuchlík· 01 května, 2010· in Fyzika· 0 comments
    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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    On Mass Constraints Implied by the Relativistic Precession Model of Twin-peak Quasi-periodic Oscillations in Circinus X-1

    by Zdeněk Stuchlík· 01 května, 2010· in Fyzika· 0 comments
    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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    On magnetic-field-induced non-geodesic corrections to relativistic orbital and epicyclic frequencies

    by Zdeněk Stuchlík· 01 února, 2010· in Fyzika· 0 comments
    We discuss non-geodesic corrections to orbital and epicyclic frequencies of charged test particles orbiting a non-rotating neutron star with a dipole magnetic field. Using a fully relativistic approach we consider the influence of both the magnetic attraction and repulsion on the orbital and epicyclic motion. The magnetic repulsion introduces a rather complex and unusual behaviour of the circular orbital motion that is well defined down to the radius where the vertical epicyclic frequency loses its meaning. We demonstrate that for the intensity of the magnetic interaction appropriately restricted, the stable circular orbits extend down to the magnetic innermost stable circular orbit (MISCO) that is located well under the geodetic innermost stable circular orbit (GISCO) and even can reach the region under the photon circular orbit. The lowest stable circular orbit at rMISCOmin = 2.73M, associated with the highest possible orbital frequency nu _{K}^{max} = 3284, Hz (1.5 , {it M}_{odot}/it M) , corresponds to the critical value of the particle-specific charge and the neutron star magnetic dipole moment product (tilde{q} mu )_crit = 1.87 M^2 . For the magnetic attraction acting above the GISCO, the situation is much more simple and we demonstrate that the most significant correction arises for the radial epicyclic frequency and consequently for the location of the MISCO when the strong magnetic attraction pushes its location far behind the location of GISCO. We show that the Lorentz force also naturally violates the equality of the orbital and vertical epicyclic frequencies implied by the spherical symmetry of the background Schwarzschild geometry giving rise to the new effect of nodal precession of the orbital motion plane. Finally, we apply the magnetic attraction corrections on the relativistic precession model of the twin-peak high-frequency quasiperiodic oscillations observed in the galactic low mass x-ray binaries, showing possible high relevance of the modified radial epicyclic frequency.
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    On magnetic-field-induced non-geodesic corrections to relativistic orbital and epicyclic frequencies

    by Zdeněk Stuchlík· 01 února, 2010· in Fyzika· 0 comments
    We discuss non-geodesic corrections to orbital and epicyclic frequencies of charged test particles orbiting a non-rotating neutron star with a dipole magnetic field. Using a fully relativistic approach we consider the influence of both the magnetic attraction and repulsion on the orbital and epicyclic motion. The magnetic repulsion introduces a rather complex and unusual behaviour of the circular orbital motion that is well defined down to the radius where the vertical epicyclic frequency loses its meaning. We demonstrate that for the intensity of the magnetic interaction appropriately restricted, the stable circular orbits extend down to the magnetic innermost stable circular orbit (MISCO) that is located well under the geodetic innermost stable circular orbit (GISCO) and even can reach the region under the photon circular orbit. The lowest stable circular orbit at rMISCOmin = 2.73M, associated with the highest possible orbital frequency nu _{K}^{max} = 3284, Hz (1.5 , {it M}_{odot}/it M) , corresponds to the critical value of the particle-specific charge and the neutron star magnetic dipole moment product (tilde{q} mu )_crit = 1.87 M^2 . For the magnetic attraction acting above the GISCO, the situation is much more simple and we demonstrate that the most significant correction arises for the radial epicyclic frequency and consequently for the location of the MISCO when the strong magnetic attraction pushes its location far behind the location of GISCO. We show that the Lorentz force also naturally violates the equality of the orbital and vertical epicyclic frequencies implied by the spherical symmetry of the background Schwarzschild geometry giving rise to the new effect of nodal precession of the orbital motion plane. Finally, we apply the magnetic attraction corrections on the relativistic precession model of the twin-peak high-frequency quasiperiodic oscillations observed in the galactic low mass x-ray binaries, showing possible high relevance of the modified radial epicyclic frequency.
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