Cygnus X-1 was a very puzzling object when it was discovered in 1964, because (as the name suggests) it was an extremely powerful X-ray source. Since X-rays are (fortunately) blocked by the Earth’s atmosphere, the exceptional nature of the object was only recognized when it became possible to do astronomy from above the atmosphere, in this case during a sub-orbital rocket flight. Even today, Cygnus X-1 is one of the strongest persistent X-ray sources known.

At the time of the discovery, black holes were considered to be perhaps nothing more than hypothetical objects. Their existence was allowed for as an admissible solution of the equations of general relativity, but they were considered by many astrophysicists to present such troublesome paradoxes that their actual existence was questionable. For instance, would a “naked singularity” perhaps exist inside a black hole’s event horizon? And would all the information associated with matter falling into a black hole be lost, in contradiction with principles of quantum mechanics?

In the past 50 years, overwhelming evidence has been found for the existence of both stellar-mass black holes (such as the one in Cygnus X-1) and supermassive black holes at the centers of all but the smallest galaxies. Most of the troublesome theoretical paradoxes have also been resolved. There is now abundant observational evidence that Cygnus X-1 is a binary system consisting of a black hole and a blue supergiant star (HDE 226868).

Artist’s conception – credit: Chandra X-Ray Observatory, NASA

According to basic theory of black holes, the mass of the black hole and its rate of spin (or its angular momentum), along with the electrical charge, are the only independent properties a black hole can possess. The physical size of an uncharged, non-spinning black hole (the Schwarzchild radius) is a simple functions of its mass, namely R = 2GM/c^{2}, where M is the mass, G is Newton’s gravitational constant, and c is the speed of light. (The function is more complicated with nonzero charge or angular momentum.)

Practically speaking, a black hole of any appreciable size should have negligible net charge, since otherwise it would attract enough nearby charged particles to neutralize the total charge. So astrophysicists are concerned only to measure the mass and rate of rotation (or the angular momentum) of a black hole. Before the latest research, the key facts about the black hole in Cygnus X-1 – its mass and rate of spin – were quite uncertain.

It’s relatively easy to figure out the mass of a supermassive black hole at the center of a galaxy, because it can be inferred from the orbital velocities of visible matter close to the black hole. For instance, the mass of the Milky Way’s black hole (Sgr A*) is known with an uncertainty of about 10%. However, in Cygnus X-1, the companion star’s mass was known only very roughly from its spectral class and luminosity, so the mass of the black hole couldn’t be estimated with much precision.

Before the appearance of the latest research, there were significant uncertainties in the basic quantities that characterize Cygnus X-1. Even the distance of the system was estimated to be between 5800 and 7800 light-years, a 15% uncertainty around the mean. The latest research puts the distance at 6060 light-years, with a bit more than 5% uncertainty. The mass and size of the black hole were quite uncertain.

The latest research puts the mass of the black hole at 14.8±1.0 M_{⊙} and the companion star at 19.2±1.9 M_{⊙}. From the black hole mass, the diameter of the event horizon can be inferred to be about 90 km. Another important parameter of the system is the degree that its orbital plane makes with our line of sight, which was found to be 27.1±0.8 degrees. The spin rate is especially surprising. Given the size of the black hole, a point at the event horizon could be moving at 95% or more of the speed of light. That corresponds to a rotation frequency of more than 790 Hz.

Both the mass and spin are quite large in comparison to values estimated for other stellar mass black holes. The spin rate, in particular, is near the theoretical maximum (when a point on the event horizon moves at the speed of light).

In addition to extensive observational data collected from a number of ground and space-based telescopes, a great deal of theoretical modeling was required, in order to find values for black hole mass and spin that would give the best statistical fit to the observed data. The amount of work required explains why good estimates of mass and spin have taken so long to obtain.

The first step required for the present research was an improvement in the estimate of the distance to Cygnus X-1. Although an uncertainty of ±15% around the mean may not sound like a lot, the inverse square law of apparent luminosity as a function of distance entails a factor of 1.8 between the low and high estimates of the luminosity of HDE 226868, and that is substantial. There is a non-linear relationship between the luminosity and the mass of the star, so a good estimate of the former is required for a good estimate of the latter. In the past astronomical distances were measured by observing parallax shifts of the sky position of target objects, based on the changing position of the Earth in its orbit. Now it can be done using long-baseline interferometry with facilities like the Very Long Baseline Array (VLBA) of radio telescopes. This system consists of 10 radio telescopes with a maximum separation of 8617 km.

A good estimate of the mass of the star is essential for determining the size and shape of the star. The star is distorted into an ellipsoidal shape because of the proximity of the black hole, whose mass (as it turns out) is almost 80% of the mass of the star. (The separation between the components is estimated at only 20% of the Earth-Sun distance.) Because the star is not spherical, its brightness varies (about 0.06 magnitudes) as the components of Cygnus X-1 revolve around their center of gravity. The orbital period was already known fairly precisely, 5.6 days. Knowing the star’s shape is important to estimating the inclination of the orbit (from our vantage point), for which estimates varied widely. The orbital inclination affects estimates for the orbital velocities, which finally yield mass estimates for the two components.

All of these numerical values interact, so it is necessary to model the size and shape of the orbit and the masses of the components of Cygnus X-1, in order to find values that best fit the observational data.

Estimating the rotation rate of the black hole depends on estimates of its mass, and also on detailed observations of another part of the system: the accretion disk of hot matter around the black hole. Since the black hole cannot be imaged directly, its rotation rate has to be deduced from the rotation rate of the accretion disk, using a dynamical model of the disk and how the two rotation rates may be related.

The rate of disk rotation can be inferred from broadening of its spectral emission lines (because of Doppler shifts). But to make matters even more complicated, the accretion disk is not always directly observable, and it may be obscured by clouds of gas and dust. In particular, the highest energy radiation (X-rays) does not come from the disk itself but from inverse Compton scattering of photons in the hot gas above the disk. Some of this high energy radiation is also reflected back from the disk itself. All in all, it’s a pretty complicated system to analyze.

As an added bonus, the research estimated the relative velocity of Cygnus X-1 within the Milky Way. This information helps understand when and how the black hole originally formed.

**NASA’s Chandra Adds to Black Hole Birth Announcement**

The radio observations also measured the motion of Cygnus X-1 through space, and this was combined with its measured velocity to give the three-dimensional velocity and position of the black hole.

This work showed that Cygnus X-1 is moving very slowly with respect to the Milky Way, implying it did not receive a large “kick” at birth. This supports an earlier conjecture that Cygnus X-1 was not born in a supernova, but instead may have resulted from the dark collapse of a progenitor star without an explosion. The progenitor of Cygnus X-1 was likely an extremely massive star, which initially had a mass greater than about 100 times the sun before losing it in a vigorous stellar wind.

Reid, M., McClintock, J., Narayan, R., Gou, L., Remillard, R., & Orosz, J. (2011). THE TRIGONOMETRIC PARALLAX OF CYGNUS X-1 The Astrophysical Journal, 742 (2) DOI: 10.1088/0004-637X/742/2/83 | |

Orosz, J., McClintock, J., Aufdenberg, J., Remillard, R., Reid, M., Narayan, R., & Gou, L. (2011). THE MASS OF THE BLACK HOLE IN CYGNUS X-1 The Astrophysical Journal, 742 (2) DOI: 10.1088/0004-637X/742/2/84 | |

Gou, L., McClintock, J., Reid, M., Orosz, J., Steiner, J., Narayan, R., Xiang, J., Remillard, R., Arnaud, K., & Davis, S. (2011). THE EXTREME SPIN OF THE BLACK HOLE IN CYGNUS X-1 The Astrophysical Journal, 742 (2) DOI: 10.1088/0004-637X/742/2/85 |

**Further reading:**

VLBA Distance Measurement Is Key to Producing First “Complete Description” of a Black Hole

Cygnus X-1: NASA’s Chandra Adds to Black Hole Birth Announcement

Astronomers determine full description of a black hole

Measuring a Tiny, Yet Mighty, Black Hole

The Trigonometric Parallax of Cygnus X-1 (arXiv.org)

The Mass of the Black Hole in Cygnus X-1 (arXiv.org)

The Extreme Spin of the Black Hole in Cygnus X-1 (arXiv.org)

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