Zdenĕk Stuchlík

Humpy LNRF-velocity profiles in accretion discs orbiting almost extreme Kerr black holes : A possible relation to quasi-periodic oscillations

Context. Change of sign of the LNRF-velocity gradient has been found for accretion discs orbiting rapidly rotating Kerr black hol es with spin a> 0.9953 for Keplerian discs and a> 0.99979 for marginally stable thick discs. Such a “humpy” LNRF-velocity profiles occur just above the marginally stable circular geodesic of the black hole spacetimes. Aims. Aschenbach (2004) has identified the maximal rate of change o f the orbital velocity within the “humpy” profile with a local ly defined critical frequency of disc oscillations, but it has b een done in a coordinate-dependent form that should be corrected. Methods. We define the critical “humpy” frequency νh in general relativistic, coordinate independent form, and relate the frequency defined in the LNRF to the distant observers. At radius of its d efinition, the resulting “humpy” frequency νh is compared to the radial νr and verticalνv epicyclic frequencies and the orbital frequency of the disc s. We focus our attention to Keplerian thin discs and perfect-fluid slender tori where the approximation of oscil lations with epicyclic frequencies is acceptable. Results. In the case of Keplerian discs, we show that the epicyclic resonance radii r3:1 and r4:1 (withνv :νr = 3 : 1, 4 : 1) are located in vicinity of the “humpy” radius rh where effi cient triggering of oscillations with frequencies∼νh could be expected. Asymptotically (for 1− a< 10 −4 ) the ratio of the epicyclic and Keplerian frequencies and the humpy frequency is nearly constant, i.e., almost independent of a, being for the radial epicyclic frequencyνr :νh∼ 3 : 2. In the case of thick discs, the situation is more complex due to dependence on distribution of the specific angular momentum l determining the disc properties. Forl = const tori and 1− a< 10 −6 the frequency ratios of the humpy frequency and the orbital and epicyclic frequencies are again nearly constant and independent of both a andl being for the radial epicyclic frequencyνr :νh close to 4. In the limiting case of very slender tori (l∼lms) the epicyclic resonance radius r4:1∼ rh for all the relevant interval of 1− a< 2× 10 −4 . Conclusions. The hypothetical “humpy” oscillations could be related to the QPO resonant phenomena between the epicyclic oscillations in both the thin discs and marginally stable tori givin g interesting predictions that have to be compared with QPO observations in nearly extreme Kerr black hole candidate systems. Generally, more than two observable oscillations are predicted.

Toroidal configurations of perfect fluid in the Reissner-Nordström-(anti-)de Sitter spacetimes

Influence of cosmological constant on toroidal fluid configurations around charged spherically symmetric black holes and naked singularities is demostrated by study of perfect-fluid tori with uniform distribution of specific angular momentum orbiting in the Reissner-Nordstrom-(anti-)de Sitter spacetimes. Toroidal configurations are allowed only in the spacetimes admitting existence of stable circular geodesics. Configurations with marginally closed equipotential (equipressure) surfaces crossing itself in a cusp allow accretion (through the inner cusp) and/or excretion (through the outer cusp) of matter from the toroidal configuration. Detailed classification of the Reissner-Nordstrom-(anti-)de Sitter spacetimes according to properties of the marginally stable tori is given. It is demonstrated that in the Reissner-Nordstrom-de Sitter naked-singularity spacetimes an interesting phenomenon of doubled tori can exist enabling exchange of matter between two tori in both inward and outward directions. In naked-singularity spacetimes the accretion onto the central singularity is impossible due to existence of a potential barrier.

CHARGED TORI IN SPHERICAL GRAVITATIONAL AND DIPOLAR MAGNETIC FIELDS

A Newtonian model of non-conductive, charged, perfect fluid tori orbiting in combined spherical gravitational and dipolar magnetic fields is presented and stationary, axisymmetric toroidal structures are analyzed. Matter in such tori exhibits a purely circulatory motion and the resulting convection carries charges into permanent rotation around the symmetry axis. As a main result, we demonstrate the possible existence of off-equatorial charged tori and equatorial tori with cusps that also enable outflows of matter from the torus in the Newtonian regime. These phenomena qualitatively represent a new consequence of the interplay between gravity and electromagnetism. From an astrophysical point of view, our investigation can provide insight into processes that determine the vertical structure of dusty tori surrounding accretion disks.

Mass estimate of the XTE J1650-500 black hole from the Extended Orbital Resonance Model for high-frequency QPOs

Context. XTE J1650-500 is a Galactic black-hole binary system for which at least one high-frequency QPO at 250 Hz was reported. Moreover there are indications that the system harbours a near-extreme Kerr black-hole with a spin a∗ ≃ 0.998 and mass MBH . 7.3 M⊙. Recently it was discovered that the orbital 3-velocity of t est-particle (geodesical) discs orbiting Kerr black holes with the spin a∗ > 0.9953, being analyzed in the locally non-rotating frames, reveals a hump near the marginally stable orbit. Further it was suggested that the hump could excite the epicyclic motion of particles near the ISCO with frequencies typical for high-frequency QPOs. Characteristic frequency of the hump-induced oscillations was defined as the maximal positive rate of change of th e LNRFrelated orbital velocity with the proper radial distance. I f the characteristic “humpy frequency” and the radial epicyclic frequency are commensurable, strong resonant phenomena are expected. Aims. Application of the idea of hump-induced oscillations in accretion discs around near-extreme Kerr black holes to estimate the black-hole mass in XTE J1650-500 binary system. Methods. For the Kerr black hole with spin a∗ ≃ 0.9982 the characteristic “humpy frequency” and the radial epicyclic frequency at the orbit, where the positive rate of change of the LNRF-related orbital velocity with the proper radial distance is maxi mal, are in ratio 1:3. Identifying the radial epicyclic frequency with the ob served 250 Hz QPO, we arrive at the mass of the black hole. In this method the ratio of frequencies determines the spin (and vice versa), and concrete values of frequencies determine the black-hole mass. Results. Mass of the Kerr black hole in XTE J1650-500 binary system is estimated to be around 5.1 M⊙.

Black hole spin inferred from 3:2 epicyclic resonance model of high-frequency quasi-periodic oscillations

Estimations of black hole spin in the three Galactic microquasars GRS 1915+105, GRO J1655-40, and XTE J1550-564 have been carried out based on spectral and timing X-ray measurements and various theoretical concepts. Among others, a non-linear resonance between axisymmetric epicyclic oscillation modes of an accretion disc around a Kerr black hole has been considered as a model for the observed high-frequency quasi-periodic oscillations (HF QPOs). Estimates of spin predicted by this model have been derived based on the geodesic approximation of the accreted fluid mot ion. Here we assume accretion flow described by the model of a pressure-supported torus and carry out related correction s to the mass-spin estimates. We find that for dimensionless b lack hole spin a ≡ cJ/GM 2 . 0.9, the resonant eigenfrequencies are very close to those cal culated for the geodesic motion. Their values slightly grow with increasing torus thickness. These findin gs agree well with results of a previous study carried out in t he pseudoNewtonian approximation. The situation becomes different for a& 0.9, in which case the resonant eigenfrequencies rapidly decrease as the torus thickness increases. We conclude that the assumed non-geodesic effects shift the lower limit of the spin, implied for the three microquasars by the epicyclic model and independently measured masses, from a ∼ 0.7 to a ∼ 0.6. Their consideration furthermore confirms compatibility of the model with the rap id spin of GRS 1915+105 and provides highly testable predictions of the QPO frequencies. Individual sources with a moderate spin (a. 0.9) should exhibit a smaller spread of the measured 3:2 QPO frequencies than sources with a near-extreme spin (a∼ 1). This should be further examined using the large amount of high-resolution data expected to become available with the next generation of X-ray instruments, such as the proposed Large Observatory for X-ray Timing (LOFT).

RELATIVISTIC DYNAMICS WITH COSMOLOGICAL CONSTANT: SPINNING TEST PARTICLES AND PERFECT FLUID TORI

Results of our recent studies concerning possible effects of Λ > 0 for equilibrium positions of spinning test particles and stationary configurations of perfect-fluid tori are presented.