Strong-field general relativity and quasi-periodic oscillations in x-ray binaries

Quasi-periodic oscillations (QPOs) at frequencies near 1000 Hz were recently discovered in several x-ray binaries containing neutron stars. Two sources show no correlation between QPO frequency and source count rate (Berger et al. 1996, Zhang et al. 1996). We suggest that the QPO frequency is determined by the Keplerian orbital frequency near the marginally stable orbit predicted by general relativity in strong gravitational fields (Muchotrzeb-Czerny 1986, Paczynski 1987, Kluzniak et al. 1990). The QPO frequencies observed from 4U 1636-536 imply that the mass of the neutron star is 2.02 +/- 0.12 solar masses. Interpretation of the 4.1 keV absorption line observed from 4U 1636-536 (Waki et al. 1984) as due to Fe XXV ions then implies a neutron star radius of 9.6 +/-0.6 km.Comment: 4 pages, uses aas2pp4.sty, submitted to ApJ

Time variability of accretion flows: effects of the adiabatic index and gas temperature

We report on next phase of our study of rotating accretion flows onto black holes. We consider hydrodynamical (HD) accretion flows with a spherically symmetric density distribution at the outer boundary but with spherical symmetry broken by the introduction of a small, latitude-dependent angular momentum. We study accretion flows by means of numerical two-dimensional, axisymmetric, HD simulations for variety of the adiabatic index, $\gamma$ and the gas temperature at infinity, $c_\infty$. Our work is an extension of work done by Proga & Begelman who consider models for only $\gamma=5/3$. Our main result is that the flow properties such as the topology of the sonic surface and time behavior strongly depend on $\gamma$ but little on $c_\infty$. In particular, for $1 < \gamma < 5/3$, the mass accretion rate shows large amplitude, slow time-variability which is a result of mixing between slow and fast rotating gas. This temporal behavior differs significantly from that in models with \gamma\simless 5/3 where the accretion rate is relatively constant and from that in models with \gamma\simgreat 1 where the accretion exhibits small amplitude quasi-periodic oscillations. The key parameter responsible for the differences is the sound speed of the accretion flow which in turn determines whether the flow is dominated by gas pressure, radiation pressure or rotation. Despite these differences the time-averaged mass accretion rate in units of the corresponding Bondi rate is a weak function of $\gamma$ and $c_\infty$.Comment: 31 pages, 14 figures, accepted for publication in ApJ, for full resolution version goto http://users.camk.edu.pl/mmosc/ms.pd

On the Structure of Advective Accretion Disks At High Luminosity

Global solutions of optically thick advective accretion disks around black holes are constructed. The solutions are obtained by solving numerically a set of ordinary differential equations corresponding to a steady axisymmetric geometrically thin disk. We pay special attention to consistently satisfy the regularity conditions at singular points of the equations. For this reason we analytically expand a solution at the singular point, and use coefficients of the expansion in our iterative numerical procedure. We obtain consistent transonic solutions in a wide range of values of the viscosity parameter alpha and mass acretion rate. We compare two different form of viscosity: one takes the shear stress to be proportional to the pressure, while the other uses the angular velocity gradient-dependent stress. We find that there are two singular points in solutions corresponding to the pressure-proportional shear stress. The inner singular point locates close to the last stable orbit around black hole. This point changes its type from a saddle to node depending on values of alpha and accretion rate. The outer singular point locates at larger radius and is always of a saddle-type. We argue that, contrary to the previous investigations, a nodal-type inner singular point does not introduce multiple solutions. Only one integral curve, which corresponds to the unique global solution, passes simultaneously the inner and outer singular points independently of the type of inner singular point. Solutions with the angular velocity gradient-dependent shear stress have one singular point which is always of a saddle-type and corresponds to the unique global solution. The structure of accretion disks corresponding to both viscosities are similar.Comment: 20 pages, 6 figures, submitted to Ap

Accretion disks around Black Holes with Advection and Optical Depth Transition

We consider the effects of advection and radial gradients of pressure and radial drift velocity on the structure of accretion disks around black holes with proper description of optically thick/thin transitions. We concentrated our efforts on the models with large accretion rate. Contrary to disk models neglecting advection, we find that continuous solutions extending from the outer disk regions to the inner edge exist for all accretion rates we have considered. We show that the sonic point moves outward with increasing accretion rate, and that in the innermost disk region advection acts as a heating process that may even dominate over dissipative heating. Despite the importance of advection on it's structure, the disk remains geometrically thin. Global solutions of advective accretion disks, which describe continuously the transition between optically thick outer region and optically thin inner region are constructed and analyzed.Comment: 13 pages, 8 figures, to be published in Proceedings of the Gamov Memorial International Conference, Odessa, Ukraine, August 8-14, 2004, Cambridge Scientific Publication

Strong Field Gravity and X-Ray Observations of 4U1820-30

The behavior of quasi-periodic oscillations (QPOs) at frequencies near 1 kHz in the x-ray emission from the neutron star x-ray binary 4U1820-30 has been interpreted as evidence for the existence of the marginally stable orbit, a key prediction of strong-field general relativity. The signature of the marginally stable orbit is a saturation in QPO frequency, assumed to track inner disk radius, versus mass accretion rate. Previous studies of 4U1820-30 have used x-ray count rate as an indicator of mass accretion rate. However, x-ray count rate is known to not correlate robustly with mass accretion rate or QPO frequency in other sources. Here, we examine the QPO frequency dependence on two other indicators of mass accretion rate: energy flux and x-ray spectral shape. Using either of these indicators, we find that the QPO frequency saturates at high mass accretion rates. We interpret this as strong evidence for the existence of the marginally stable orbit.Comment: accepted to the Astrophysical Journal Letters, 7 page

Sonic-Point Model of Kilohertz Quasi-Periodic Brightness Oscillations in Low-Mass X-ray Binaries

Strong, coherent, quasi-periodic brightness oscillations (QPOs) with frequencies ranging from about 300 Hz to 1200 Hz have been discovered with the Rossi X-ray Timing Explorer in the X-ray emission from some fifteen neutron stars in low-mass binary systems. Two simultaneous kilohertz QPOs differing in frequency by 250 to 350 Hertz have been detected in twelve of the fifteen sources. Here we propose a model for these QPOs. In this model the X-ray source is a neutron star with a surface magnetic field of 10^7 to 10^10 G and a spin frequency of a few hundred Hertz, accreting gas via a Keplerian disk. The frequency of the higher-frequency QPO in a kilohertz QPO pair is the Keplerian frequency at a radius near the sonic point at the inner edge of the Keplerian flow whereas the frequency of the lower-frequency QPO is approximately the difference between the Keplerian frequency at a radius near the sonic point and the stellar spin frequency. This model explains naturally many properties of the kilohertz QPOs, including their frequencies, amplitudes, and coherence. We show that if the frequency of the higher-frequency QPO in a pair is an orbital frequency, as in the sonic-point model, the frequencies of these QPOs place interesting upper bounds on the masses and radii of the neutron stars in the kilohertz QPO sources and provide new constraints on the equation of state of matter at high densities. Further observations of these QPOs may provide compelling evidence for the existence of a marginally stable orbit, confirming a key prediction of general relativity in the strong-field regime.Comment: 67 pages, including 15 figures and 5 tables; uses aas2pp4; final version to appear in the Astrophysical Journal on 1 December 199

Hysteresis effects and diagnostics of the shock formation in low angular momentum axisymmetric accretion in the Kerr metric

The secular evolution of the purely general relativistic low angular momentum accretion flow around a spinning black hole is shown to exhibit hysteresis effects. This confirms that a stationary shock is an integral part of such an accretion disc in the Kerr metric. The equations describing the space gradient of the dynamical flow velocity of the accreting matter have been shown to be equivalent to a first order autonomous dynamical systems. Fixed point analysis ensures that such flow must be multi-transonic for certain astrophysically relevant initial boundary conditions. Contrary to the existing consensus in the literature, the critical points and the sonic points are proved not to be isomorphic in general. Homoclinic orbits for the flow flow possessing multiple critical points select the critical point with the higher entropy accretion rate, confirming that the entropy accretion rate is the degeneracy removing agent in the system. However, heteroclinic orbits are also observed for some special situation, where both the saddle type critical points of the flow configuration possesses identical entropy accretion rate. Topologies with heteroclinic orbits are thus the only allowed non removable degenerate solutions for accretion flow with multiple critical points, and are shown to be structurally unstable. Depending on suitable initial boundary conditions, a homoclinic trajectory can be combined with a standard non homoclinic orbit through an energy preserving Rankine-Hugoniot type of stationary shock. An effective Lyapunov index has been proposed to analytically confirm why certain class of transonic flow can not accommodate shock solutions even if it produces multiple critical points. (Abridged)Comment: mn2e.cls format. 24 pages. 4 figure

Slim disks around Kerr black holes revisited

We investigate stationary slim accretion disks around Kerr black holes. We construct a new numerical method based on the relaxation technique. We systematically cover the whole parameter space relevant to stellar mass X-ray binaries. We also notice some non-monotonic features in the disk structure, overlooked in previous studies.Comment: 12 pages, 11 figures. The relativistic slim accretion disk solutions have been published online at http://users.camk.edu.pl/as/slimdisk. An appendix containing the manual for the data available online has been added to the previous version of the pape

Leaving the ISCO: the inner edge of a black-hole accretion disk at various luminosities

The "radiation inner edge" of an accretion disk is defined as the inner boundary of the region from which most of the luminosity emerges. Similarly, the "reflection edge" is the smallest radius capable of producing a significant X-ray reflection of the fluorescent iron line. For black hole accretion disks with very sub-Eddington luminosities these and all other "inner edges" locate at ISCO. Thus, in this case, one may rightly consider ISCO as the unique inner edge of the black hole accretion disk. However, even for moderate luminosities, there is no such unique inner edge as differently defined edges locate at different places. Several of them are significantly closer to the black hole than ISCO. The differences grow with the increasing luminosity. For nearly Eddington luminosities, they are so huge that the notion of the inner edge losses all practical significance.Comment: 12 pages, 15 figures, submitted to A&

Novel Cauchy-horizon instability

The evolution of weak discontinuity is investigated on horizons in the $n$-dimensional static solutions in the Einstein-Maxwell-scalar-$\Lambda$ system, including the Reissner-Nordstr\"om-(anti) de Sitter black hole. The analysis is essentially local and nonlinear. We find that the Cauchy horizon is unstable, whereas both the black-hole event horizon and the cosmological event horizon are stable. This new instability, the so-called kink instability, of the Cauchy horizon is completely different from the well-known ``infinite-blueshift'' instability. The kink instability makes the analytic continuation beyond the Cauchy horizon unstable.Comment: 6 pages, 1 figure, final version to appear in Physical Review