Lijun Gou

The Mass of the Black Hole in Cygnus X-1

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 usingalloftheavailableobservationalconstraints,weshowthattheorbitisslightlyeccentric(boththeradialvelocity 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 Mopt = 19.2 ± 1.9 M� , and the angle of inclination of the orbital plane to our line of sight of i = 27.1 ± 0. 8d eg.

Measuring the spins of accreting black holes

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.

The Extreme Spin of the Black Hole in Cygnus X-1

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.

The spin of the black hole microquasar XTE J1550−564 via the continuum-fitting and Fe-line methods

We measure the spin of XTE J1550−564 using the two leading methods: (i) modelling the thermal continuum spectrum of the accretion disc; and (ii) modelling the broad red wing of the reflection fluorescence Fe Kα line. We find that these two independent measurements of spin are in agreement. For the continuum-fitting analysis, we use a data sample consisting of several dozen Rossi X-ray Timing Explorer spectra, and for the Fe Kα 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 activity of this microquasar is powered largely by its accretion disc rather than by the spin energy of the black hole.

The Inclination of the Soft X-Ray Transient A0620–00 and the Mass of its Black Hole

We analyze photometry of the soft X-ray transient A0620−00 spanning nearly 30 years, including previously published and previously unpublished data. Previous attempts to determine the inclination of A0620 using subsets of these data have yielded a wide range of measured values of i. Differences in the measured value of i have been due to changes in the shape of the light curve and uncertainty regarding the contamination from the disk. We give a new technique for estimating the disk fraction and find that disk light is significant in all light curves, even in the infrared. We also find that all changes in the shape and normalization of the light curve originate in a variable disk component. After accounting for this disk component, we find that all the data, including light curves of significantly different shapes, point to a consistent value of i. Combining results from many separate data sets, we find i = 51. 0 ± 0. 9, implying M = 6.6 ± 0.25 M� . Using our dynamical model and zero-disk stellar VIH magnitudes, we find d = 1.06 ± 0.12 kpc. Understanding the disk origin of nonellipsoidal variability may assist with making reliable determinations of i in other systems, and the fluctuations in disk light may provide a new observational tool for understanding the three-dimensional structure of the accretion disk.

THE CONSTANT INNER-DISK RADIUS OF LMC X-3: A BASIS FOR MEASURING BLACK HOLE SPIN

The black hole binary system LMC X-3 has been observed by virtually every X-ray mission since the inception of X-ray astronomy. Among the persistent sources, LMC X-3 is uniquely both habitually soft and highly variable. Using a fully relativistic accretion disk model, we analyze hundreds of spectra collected during eight X-ray missions that span 26 years. For a selected sample of 391 RXTE spectra, we find that to within ≈2% the inner radius of the accretion disk is constant over time and unaffected by source variability. Even considering an ensemble of eight X-ray missions, we find consistent values of the radius to within ≈4%-6%. Our results provide strong evidence for the existence of a fixed inner-disk radius. The only reasonable inference is that this radius is closely associated with the general relativistic innermost stable circular orbit. Our findings establish a firm foundation for the measurement of black hole spin.

A DETERMINATION OF THE SPIN OF THE BLACK HOLE PRIMARY IN LMC X-1

The first extragalactic X-ray binary, LMC X-1, was discovered in 1969. In the 1980s, its compact primary was established as the fourth dynamical black hole candidate. Recently, we published accurate values for the mass of the black hole and the orbital inclination angle of the binary system. Building on these results, we have analyzed 53 X-ray spectra obtained by RXTE and, using a selected sample of 18 of these spectra, we have determined the dimensionless spin parameter of the black hole to be a{sub *} = 0.92{sup +0.05}{sub -0.07}. This result takes into account all sources of observational and model-parameter uncertainties. The standard deviation around the mean value of a{sub *} for these 18 X-ray spectra, which were obtained over a span of several years, is only {delta}a{sub *} = 0.02. When we consider our complete sample of 53 RXTE spectra, we find a somewhat higher value of the spin parameter and a larger standard deviation. Finally, we show that our results based on RXTE data are confirmed by our analyses of selected X-ray spectra obtained by the XMM-Newton, BeppoSAX, and Ginga missions.

Detectability of long gamma-ray burst afterglows from very high redshifts

Gamma-ray bursts (GRBs) are promising tools for tracing the formation of high-redshift stars, including the first generation. At very high redshifts the reverse shock emission lasts longer in the observer frame, and its importance for detection and analysis purposes relative to the forward shock increases. We consider two different models for the GRB environment, based on current ideas about the redshift dependence of gas properties in galaxies and primordial star formation. We calculate the observed flux as a function of the redshift and observer time for typical GRB afterglows, taking into account intergalactic photoionization and Lyα absorption opacity, as well as extinction by the Milky Way. The fluxes in the X-ray and near-IR bands are compared with the sensitivity of different detectors such as Chandra, XMM, Swift XRT, and the James Webb Space Telescope (JWST). Using standard assumptions, we find that Chandra, XMM, and Swift XRT can potentially detect GRBs in the X-ray band out to very high redshifts z 30. In the K and M bands, the JWST and ground-based telescopes are potentially able to detect GRBs even 1 day after the trigger out to z ~ 16 and 33, if present. While the X-ray band is insensitive to the external density and to reverse shocks, the near-IR bands provide a sensitive tool for diagnosing both the environment and the reverse shock component.

A NEW DYNAMICAL MODEL FOR THE BLACK HOLE BINARY LMC X-1*

We present a dynamical model of the high mass X-ray binary LMC X-1 based on high-resolution optical spectroscopy and extensive optical and near-infrared photometry. From our new optical data we find an orbital period of P = 3.90917 +/- 0.00005 days. We present a refined analysis of the All Sky Monitor data from RXTE and find an X-ray period of P = 3.9094 +/- 0.0008 days, which is consistent with the optical period. A simple model of Thomson scattering in the stellar wind can account for the modulation seen in the X-ray light curves. The V-K color of the star (1.17 +/- 0.05) implies A(V) = 2.28 +/- 0.06, which is much larger than previously assumed. For the secondary star, we measure a radius of R-2 = 17.0 +/- 0.8 R-circle dot and a projected rotational velocity of V-rot sin i = 129.9 +/- 2.2 km s(-1). Using these measured properties to constrain the dynamical model, we find an inclination of i = 36 degrees.38 +/- 1 degrees.92, a secondary star mass of M-2 = 31.79 +/- 3.48 M-circle dot, and a black hole mass of 10.91 +/- 1.41 M-circle dot. The present location of the secondary star in a temperature-luminosity diagram is consistent with that of a star with an initial mass of 35 M-circle dot that is 5 Myr past the zero-age main sequence. The star nearly fills its Roche lobe (approximate to 90% or more), and owing to the rapid change in radius with time in its present evolutionary state, it will encounter its Roche lobe and begin rapid and possibly unstable mass transfer on a timescale of a few hundred thousand years.

MEASURING BLACK HOLE SPIN VIA THE X-RAY CONTINUUM FITTING METHOD: BEYOND THE THERMAL DOMINANT STATE

All prior work on measuring the spins of stellar-mass black holes (BHs) via the X-ray continuum-fitting (CF) method has relied on the use of weakly Comptonized spectra obtained in the thermal dominant (TD) state. Using a self-consistent Comptonization model, we show that one can analyze spectra that exhibit strong power-law components and obtain values of the inner disk radius, and hence spin, that are consistent with those obtained in the TD state. Specifically, we analyze many RXTE spectra of two BH transients, H1743?322 and XTE J1550?564, and we demonstrate that the radius of the inner edge of the accretion disk remains constant to within a few percent as the strength of the Comptonized component increases by an order of magnitude, i.e., as the fraction of the thermal seed photons that are scattered approaches 25%. We conclude that the CF method can be applied to a much wider body of data than previously thought possible, and to sources that have never been observed to enter the TD state (e.g., Cyg X-1).