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.

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.

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.

We consider a simple Newtonian model of a steady accretion disk around a black hole. The model is based on height-integrated hydrodynamic equations, -viscosity, and a pseudo-Newtonian potential which results in an innermost stable circular orbit ( ISCO) that closely approximates the one predicted by general relativity. We find that, as the disk thickness H/R or the value of increases, the hydrodynamic model exhibits increasing deviations from the standard thin disk model of Shakura and Sunyaev. 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 0:2. At worst, the error in the estimated value of the spin parameter is 0.1 for a nonspinning 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/Rk0:1, suggesting that the iron line technique may be most reliable in extremely thin disks. We caution that these results have been obtained with a viscous hydrodynamic model. While our results are likely to be qualitatively correct, quantitative estimates of, e.g., the magnitude of the error in the spin estimate, need to be confirmed with MHD simulations of radiatively cooled thin disks.