Person:

McClintock, Jeffrey

The compact primary in the X-ray binary Cygnus X-1 was the first black hole to be established via dynamical observations. We have recently determined accurate values for its mass and distance, and for the orbital inclination angle of the binary. Building on these results, which are based on our favored (asynchronous) dynamical model, we have measured the radius of the inner edge of the black hole's accretion disk by fitting its thermal continuum spectrum to a fully relativistic model of a thin accretion disk. Assuming that the spin axis of the black hole is aligned with the orbital angular momentum vector, we have determined that Cygnus X-1 contains a near-extreme Kerr black hole with a spin parameter a * > 0.95 (3σ). For a less probable (synchronous) dynamical model, we find a * > 0.92 (3σ). In our analysis, we include the uncertainties in black hole mass, orbital inclination angle, and distance, and we also include the uncertainty in the calibration of the absolute flux via the Crab. These four sources of uncertainty totally dominate the error budget. The uncertainties introduced by the thin-disk model we employ are particularly small in this case given the extreme spin of the black hole and the disk's low luminosity.

We measure the spin of XTE J1550-564 in two ways: by modelling the thermal continuum spectrum of the accretion disc, and independently by modeling the broad red wing of the reflection fluorescence Fe-K line. We find that the spin measurements conducted independently using both leading methods are in agreement with one another. For the continuum-fitting analysis, we use a data sample consisting of several dozen RXTE spectra, and for the Fe-K analysis, we use a pair of ASCA spectra from a single epoch. Our spin estimate for the black hole primary using the continuum-fitting method is -0.11 < a* < 0.71 (90 per cent confidence), with a most likely spin of a* = 0.34. In obtaining this result, we have thoroughly explored the dependence of the spin value on a wide range of model-dependent systematic errors and observational errors; our precision is limited by uncertainties in the distance and orbital inclination of the system. For the Fe-line method, our estimate of spin is a* = 0.55(+0.15,-0.22). Combining these results, we conclude that the spin of this black hole is moderate, a* = 0.49(+0.13,-0.20), which suggests that the jet of this microquasar is powered largely by its accretion disc rather than by the spin energy of the black hole.

Slim-disk models describe advective accretion flows at high luminosities, while reducing to the standard thin disk form in the low luminosity limit. We have developed a new spectral model, slimbb, within the framework of XSPEC, which describes fully relativistic slim-disk accretion and includes photon ray-tracing that starts from the disk photosphere, rather than the equatorial plane. We demonstrate the features of this model by applying it to RXTE spectra of the persistent black-hole X-ray binary LMC X-3. LMC X-3 has the virtues of exhibiting large intensity variations while maintaining itself in soft spectral states which are well described using accretion-disk models, making it an ideal candidate to test the aptness of slimbb. Our results demonstrate consistency between the low-luminosity (thin-disk) and high luminosity (slim-disk) regimes. The results also illustrate that advection alone does not solve the problem of the origin of the surprisingly soft high-luminosity spectra in LMC X-3. We show that X-ray continuum-fitting in the high accretion rate regime can powerfully test black-hole accretion disk models.

We report a direct and accurate measurement of the distance to the X-ray binary Cygnus X-1, which contains the first black hole to be discovered. The distance of 1.86+0.12 – 0.11 kpc was obtained from a trigonometric parallax measurement using the Very Long Baseline Array. The position measurements are also sensitive to the 5.6 day binary orbit and we determine the orbit to be clockwise on the sky. We also measured the proper motion of Cygnus X-1 which, when coupled to the distance and Doppler shift, gives the three-dimensional space motion of the system. When corrected for differential Galactic rotation, the non-circular (peculiar) motion of the binary is only about 21 km s–1, indicating that the binary did not experience a large "kick" at formation.

Cygnus X-1 is a binary star system that is comprised of a black hole and a massive giant companion star in a tight orbit. Building on our accurate distance measurement reported in the preceding paper, we first determine the radius of the companion star, thereby constraining the scale of the binary system. To obtain a full dynamical model of the binary, we use an extensive collection of optical photometric and spectroscopic data taken from the literature. By using all of the available observational constraints, we show that the orbit is slightly eccentric (both the radial velocity and photometric data independently confirm this result) and that the companion star rotates roughly 1.4 times its pseudosynchronous value. We find a black hole mass of M = 14.8 ± 1.0 M ☉, a companion mass of M opt = 19.2 ± 1.9 M ☉, and the angle of inclination of the orbital plane to our line of sight of i = 27.1 ± 0.8 deg.

The X-ray spectra of accretion discs of eight stellar mass black holes have been analysed to date using the thermal continuum-fitting method, and the spectral fits have been used to estimate the spin parameters of the black holes. However, the underlying model used in this method of estimating spin is the general relativistic thin-disc model of Novikov & Thorne, which is only valid for razor-thin discs. We therefore expect errors in the measured values of spin due to inadequacies in the theoretical model. We investigate this issue by computing spectra of numerically calculated models of thin accretion discs around black holes, obtained via three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations. We apply the continuum-fitting method to these computed spectra to estimate the black hole spins and check how closely the values match the actual spin used in the GRMHD simulations. We find that the error in the dimensionless spin parameter is up to about 0.2 for a non-spinning black hole, depending on the inclination. For black holes with spins of 0.7, 0.9 and 0.98, the errors are up to about 0.1, 0.03 and 0.01, respectively. These errors are comparable to or smaller than those arising from current levels of observational uncertainty. Furthermore, we estimate that the GRMHD simulated discs from which these error estimates are obtained correspond to effective disc luminosities of about 0.4–0.7 Eddington, and that the errors will be smaller for discs with luminosities of 0.3 Eddington or less, which are used in the continuum-fitting method. We thus conclude that use of the Novikov–Thorne thin-disc model does not presently limit the accuracy of the continuum-fitting method of measuring black hole spin.

It is generally thought that the light coming from the inner plunging region of black hole accretion discs contributes negligibly to the disc's overall spectrum, i.e. the plunging fluid is swallowed by the black hole before it has time to radiate. In the standard disc model used to fit X-ray observations of accretion discs, the plunging region is assumed to be perfectly dark. However, numerical simulations that include the full physics of the magnetized flow predict that a small fraction of the disc's total luminosity emanates from the plunging region. We investigate the observational consequences of this neglected inner light. We compute radiative transfer based disc spectra that correspond to 3D general relativistic magnetohydrodynamic simulated discs (which produce light inside their plunging regions). In the context of black hole spin estimation, we find that the neglected inner light only has a modest effect (this bias is less than typical observational systematic errors). For rapidly spinning black holes, we find that the combined emission from the plunging region produces a weak power-law tail at high energies. This indicates that infalling matter is the origin for some of the `coronal' emission observed in the thermal dominant and steep power-law states of X-ray binaries.

We show that the 5-GHz radio flux of transient ballistic jets in black hole binaries correlates with the dimensionless black hole spin parameter a* estimated via the continuum-fitting method. The data suggest that jet power scales either as the square of a* or the square of the angular velocity of the horizon. This is the first direct evidence that jets may be powered by black hole spin energy. The observed correlation validates the continuum-fitting method of measuring spin. In addition, for those black holes that have well-sampled radio observations of ballistic jets, the correlation may be used to obtain rough estimates of their spins.

A typical galaxy is thought to contain tens of millions of stellar-mass black holes, the collapsed remnants of once massive stars, and a single nuclear supermassive black hole. Both classes of black holes accrete gas from their environments. The accreting gas forms a flattened orbiting structure known as an accretion disk. During the past several years, it has become possible to obtain measurements of the spins of the two classes of black holes by modeling the x-ray emission from their accretion disks. Two methods are employed, both of which depend upon identifying the inner radius of the accretion disk with the innermost stable circular orbit, whose radius depends only on the mass and spin of the black hole. In the Fe Kα method, which applies to both classes of black holes, one models the profile of the relativistically broadened iron line with a special focus on the gravitationally redshifted red wing of the line. In the continuum-fitting (CF) method, which has so far only been applied to stellar-mass black holes, one models the thermal x-ray continuum spectrum of the accretion disk. We discuss both methods, with a strong emphasis on the CF method and its application to stellar-mass black holes. Spin results for eight stellar-mass black holes are summarized. These data are used to argue that the high spins of at least some of these black holes are natal, and that the presence or absence of relativistic jets in accreting black holes is not entirely determined by the spin of the black hole.

During its year-long outburst in 1975–76, the transient source A0620–00 reached an intensity of 50 Crab, an all-time record for any X-ray binary. The source has been quiescent since then. We have recently determined accurate values for the black hole (BH) mass, orbital inclination angle, and distance. Building on these results, we have measured the radius of the inner edge of the accretion disk around the BH primary by fitting its thermal continuum spectrum to our version of the relativistic Novikov–Thorne thin-disk model. We have thereby estimated the spin of the BH. Although our spin estimate depends on a single high-quality spectrum, which was obtained in 1975 by OSO-8, we are confident of our result because of the consistent values of the inner-disk radius that we have obtained for hundreds of observations of other sources: H1743-322, XTE J1550-564, and notably LMC X-3. We have determined the dimensionless spin parameter of the BH to be a∗ = 0.12 ± 0.19, with a∗ < 0.49 and a∗ > −0.59 at the 3σ level of confidence. This result takes into account all sources of observational and model-parameter uncertainties. Despite the low spin, the intensity and properties of the radio counterpart, both in outburst and quiescence, attest to the presence of a strong jet. If jets are driven by BH spin, then current models indicate that jet power should be a steeply increasing function of a∗. Consequently, the low spin of A0620–00 suggests that its jet may be disk driven.