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

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

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

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

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&

Transition from radiatively inefficient to cooling dominated phase in two temperature accretion discs around black holes

We investigate the transition of a radiatively inefficient phase of a viscous two temperature accreting flow to a cooling dominated phase and vice versa around black holes. Based on a global sub-Keplerian accretion disc model in steady state, including explicit cooling processes self-consistently, we show that general advective accretion flow passes through various phases during its infall towards a black hole. Bremsstrahlung, synchrotron and inverse Comptonization of soft photons are considered as possible cooling mechanisms. Hence the flow governs a much lower electron temperature ~10^8 - 10^{9.5}K compared to the hot protons of temperature ~10^{10.2} - 10^{11.8}K in the range of the accretion rate in Eddington units 0.01 - 100. Therefore, the solutions may potentially explain the hard X-rays and the gamma-rays emitted from AGNs and X-ray binaries. We finally compare the solutions for two different regimes of viscosity and conclude that a weakly viscous flow is expected to be cooling dominated compared to its highly viscous counterpart which is radiatively inefficient. The flow is successfully able to reproduce the observed luminosities of the under-fed AGNs and quasars (e.g. Sgr A*), ultra-luminous X-ray sources (e.g. SS433), as well as the highly luminous AGNs and ultra-luminous quasars (e.g. PKS 0743-67) at different combinations of the mass accretion rate and ratio of specific heats.Comment: 13 pages including 8 figures; couple of typos corrected; to appear in Research in Astronomy and Astrophysic

Mass Accretion Rate of Rotating Viscous Accretion Flow

The mass accretion rate of transonic spherical accretion flow onto compact objects such as black holes is known as the Bondi accretion rate(Mdot_B), which is determined only by the density and the temperature of gas at the outer boundary. But most work on disc accretion has taken the mass flux to be a given with the relation between that parameter and external conditions left uncertain. Within the framework of a slim alpha disk, we have constructed global solutions of the rotating, viscous hot accretion flow and determined its mass accretion rate as a function of density, temperature, and angular momentum of gas at the outer boundary. We find that the low angular momentum flow resembles the spherical Bondi flow and its mass accretion rate approaches the Bondi accretion rate for the same density and temperature at the outer boundary. The high angular momentum flow on the other hand is the conventional hot accretion disk with advection, but its mass accretion rate can be significantly smaller than the Bondi accretion rate with the same boundary conditions. We also find that when the temperature at the outer boundary is equal to the virial temperature, solutions exist only for 0.05 ~< mdot ~< 1 when alpha=0.01 where mdot==Mdot/Mdot_B. We also find that the dimensionless mass accretion rate is roughly independent of the radius of the outer boundary but inversely proportional to the angular momentum at the outer boundary and proportional to the viscosity parameter, mdot ~= 9.0 alpha/lambda when 0.1 ~< mdot ~< 1, where the dimensionless angular momentum measure lambda == l_out/l_B is the specific angular momentum of gas at the outer boundary l_out in units of l_B == GM/c_{s,out}, and $c_{s,out}$ the isothermal sound speed at the outer boundary.Comment: 15 pages, 3 figures, to appear in Ap

Viscous Torque and Dissipation in the Inner Region of a Thin Accretion Disk: Implications for Measuring Black Hole Spin

We consider a simple Newtonian model of a steady accretion disk around a black hole. The model is based on height-integrated hydrodynamic equations, alpha-viscosity, and a pseudo-Newtonian potential that results in an innermost stable circular orbit (ISCO) that closely approximates the one predicted by GR. We find that the hydrodynamic models exhibit increasing deviations from the standard disk model of Shakura & Sunyaev as disk thickness H/R or the value of alpha increases. The latter is an analytical model in which the viscous torque is assumed to vanish at the ISCO. We consider the implications of the results for attempts to estimate black hole spin by using the standard disk model to fit continuum spectra of black hole accretion disks. We find that the error in the spin estimate is quite modest so long as H/R < 0.1 and alpha < 0.2. At worst the error in the estimated value of the spin parameter is 0.1 for a non-spinning black hole; the error is much less for a rapidly spinning hole. We also consider the density and disk thickness contrast between the gas in the disk and that inside the ISCO. The contrast needs to be large if black hole spin is to be successfully estimated by fitting the relativistically-broadened X-ray line profile of fluorescent iron emission from reflection off an accretion disk. In our hydrodynamic models, the contrast in density and thickness is low when H/R>0.1, sugesting that the iron line technique may be most reliable in extemely thin disks. We caution that these results have been obtained with a viscous hydrodynamic model and need to be confirmed with MHD simulations of radiatively cooled thin disks.Comment: 32 pages, 10 figures; accepted by Ap