Editing Cygnus X-1 (section)

==Binary system==
The [[black hole]] and [[blue supergiant]] star form a [[binary star|binary system]] in which they orbit around their [[center of mass]] every 5.599829 days.<ref name=aaa343_861/> From the perspective of Earth, the compact object never goes behind the other star; in other words, the system does not [[eclipse]]. However, the [[orbital inclination|inclination of the orbital plane]] to the [[Line-of-sight propagation|line of sight]] from Earth remains uncertain, with predictions ranging from 27° to 65°. A 2007 study estimated the inclination as {{val|48.0|6.8|s=°}}, which would mean that the [[semi-major axis]] is about {{val|0.2|u=[[Astronomical Unit|AU]]}}, or 20% of the distance from Earth to the Sun. The [[orbital eccentricity]] is thought to be only {{val|0.018|0.002}}, meaning a nearly circular orbit.<ref name=orosz2011/><ref name=apj200/> The system is expected to merge into a single [[black hole]] in five billion years, possibly generating [[gravitational wave]]s during the proccess.<ref name=Ramachandran2025/>

[[File:V1357CygLightCurve.png|thumb|right|A [[Photometric_system#Photometric_letters|blue-band]] [[light curve]] for Cygnus X-1, adapted from Kemp ''et al.'' (1987)<ref name="Kemp"/>]]
The HDE&nbsp;226868/Cygnus&nbsp;X-1 system shares a common motion through space with an association of massive stars named Cygnus&nbsp;OB3, which is roughly 7,000&nbsp;[[light-year]]s distant. This implies that HDE&nbsp;226868, Cygnus&nbsp;X-1 and this [[stellar association|OB association]] may have formed at the same time and location. If so, then the age of the system is about {{val|5|1.5|u=million years}}. The motion of HDE&nbsp;226868 with respect to Cygnus&nbsp;OB3 is {{val|9|3|ul=km/s}}, a typical value for random motion within a stellar association. HDE&nbsp;226868 is about {{val|60|u=parsecs}} from the center of the association and could have reached that separation in about {{val|7|2|u=million years}}—which roughly agrees with estimated age of the association.<ref name=science300_5622_1119/> The distance to Cyg X-1 is calculated by trigonometric parallax as {{Convert|1860|+/-|120|pc|ly|abbr=off|lk=on}},<ref name=apj742_2/> and by radio astrometry as {{Convert|2220|+/-|170|pc|ly}}.<ref name="SCI-20210218" />

With a [[galactic latitude]] of 4° and [[galactic longitude]] 71°,<ref name=SIMBAD/> this system lies inward along the same [[Orion Arm|Orion Spur]], in which the Sun is located within the [[Milky Way]],<ref name=apj167_L15/> near where the spur approaches the [[Carina–Sagittarius Arm|Sagittarius Arm]]. Cygnus&nbsp;X-1 has been described as belonging to the Sagittarius Arm,<ref name=goebel/> though the structure of the Milky Way is not well established.

===Compact object===
From various techniques, the mass of the compact object appears to be greater than the maximum mass for a [[neutron star]]. Stellar evolutionary models suggest a mass of {{val|20|5|u=solar masses}},<ref name=MNRAS358_3_851/> while other techniques resulted in 10 solar masses. Measuring periodicities in the X-ray emission near the object yielded a more precise value of {{val|14.8|1|u=solar masses}}. In all cases, the object is most likely a black hole<ref name=orosz2011/><ref name=esa070516/>—a region of space with a [[gravity|gravitational field]] that is strong enough to prevent the escape of [[electromagnetic radiation]] from the interior. The boundary of this region is called the [[event horizon]] and has an effective radius called the [[Schwarzschild radius]], which is about {{val|44|u=km}} for Cygnus&nbsp;X-1. Anything (including [[matter]] and [[photon]]s) that passes through this boundary is unable to escape.<ref name=mit20060109/>  Measurements published in 2021 yielded an estimated mass of {{val|21.2|2.2|u=solar masses}}.<ref name="SCI-20210218" /><ref name="NYT-20210218" /> A 2025 study estimate a mass of 17.5 [[solar mass]]es, which may be just an upper limit, with another method yielding {{solar mass|13.8}}.<ref name=Ramachandran2025/>

Evidence of just such an event horizon may have been detected in 1992 using [[ultraviolet]] (UV) observations with the [[High Speed Photometer]] on the [[Hubble Space Telescope]]. As self-luminous clumps of matter spiral into a black hole, their radiation is emitted in a series of pulses that are subject to [[gravitational redshift]] as the material approaches the horizon. That is, the [[wavelength]]s of the radiation steadily increase, as predicted by [[general relativity]]. Matter hitting a solid, compact object would emit a final burst of energy, whereas material passing through an event horizon would not. Two such "dying pulse trains" were observed, which is consistent with the existence of a black hole.<ref name=pasp113/>

[[File:Chandra image of Cygnus X-1.jpg|thumb|right|[[Chandra X-ray Observatory]] image of Cygnus&nbsp;X-1]]

The spin of the compact object is not yet well determined. Past analysis of data from the space-based [[Chandra X-ray Observatory]] suggested that Cygnus&nbsp;X-1 was not rotating to any significant degree.<ref name=mgmgr10/><ref name=roy_watzke2003/> However, evidence announced in 2011 suggests that it is rotating extremely rapidly, approximately 790 times per second.<ref name="rapid rotation"/>

====Formation====
The largest star in the Cygnus&nbsp;OB3 association has a mass 40 times that of the Sun. As more massive stars evolve more rapidly, this implies that the progenitor star for Cygnus&nbsp;X-1 had more than 40 solar masses. Given the current estimated mass of the black hole, the progenitor star must have lost over 30 solar masses of material. Part of this mass may have been lost to HDE&nbsp;226868, while the remainder was most likely expelled by a strong stellar wind. The [[helium]] enrichment of HDE&nbsp;226868's outer atmosphere may be evidence for this mass transfer.<ref name=mnras341_2_385/> Possibly the progenitor may have evolved into a [[Wolf–Rayet star]], which ejects a substantial proportion of its atmosphere using just such a powerful stellar wind.<ref name=science300_5622_1119/>

If the progenitor star had exploded as a [[supernova]], then observations of similar objects show that the remnant would most likely have been ejected from the system at a relatively high velocity. As the object remained in orbit, this indicates that the progenitor may have collapsed directly into a black hole without exploding (or at most produced only a relatively modest explosion).<ref name=science300_5622_1119/>

====Accretion disk====
[[File:Cygx1 spectrum.jpg|right|thumb|A [[Chandra X-ray Observatory|Chandra]] X-ray spectrum of Cygnus&nbsp;X-1 showing a characteristic peak near {{val|6.4|ul=keV}} due to [[ion]]ized [[iron]] in the accretion disk, but the peak is gravitationally red-shifted, broadened by the [[Doppler effect]], and skewed toward lower energies<ref name=chandra20060830/>]]

The compact object is thought to be orbited by a thin, flat disk of accreting matter known as an [[accretion disk]]. This disk is intensely heated by friction between ionized gas in faster-moving inner orbits and that in slower outer ones. It is divided into a hot inner region with a relatively high level of ionization—forming a [[Plasma (physics)|plasma]]—and a cooler, less ionized outer region that extends to an estimated 500 times the Schwarzschild radius,<ref name=mnras325_3_1045/> or about 15,000&nbsp;km.

Though highly and erratically variable, Cygnus&nbsp;X-1 is typically the brightest persistent source of [[hard X-ray]]s—those with energies from about 30 up to several hundred kiloelectronvolts—in the sky.<ref name=apj611_2_1084/> The X-rays are produced as lower-energy photons in the thin inner accretion disk, then given more energy through [[Compton scattering]] with very high-temperature [[electron]]s in a geometrically thicker, but nearly transparent [[stellar corona|corona]] enveloping it, as well as by some further reflection from the surface of the thin disk.<ref name=apj484_1_375/> An alternative possibility is that the X-rays may be Compton-scattered by the base of a jet instead of a disk corona.<ref name=asr38_12_2810/>

The X-ray emission from Cygnus&nbsp;X-1 can vary in a somewhat repetitive pattern called [[quasi-periodic oscillations]] (QPO). The mass of the compact object appears to determine the distance at which the surrounding plasma begins to emit these QPOs, with the emission radius decreasing as the mass decreases. This technique has been used to estimate the mass of Cygnus&nbsp;X-1, providing a cross-check with other mass derivations.<ref name=apj678_2_1230/>

Pulsations with a stable period, similar to those resulting from the spin of a neutron star, have never been seen from Cygnus&nbsp;X-1.<ref name=science297_5583_947/><ref name=wen1998/> The [[pulsar|pulsations from neutron stars]] are caused by the neutron star's rotating magnetic field, but the [[no-hair theorem]] guarantees that the magnetic field of a black hole is exactly aligned with its rotation axis and thus is static. For example, the X-ray binary [[V&nbsp;0332+53]] was thought to be a possible black hole until pulsations were found.<ref name=apj2le288_L45/> Cygnus&nbsp;X-1 has also never displayed X-ray bursts similar to those seen from neutron stars.<ref name=ag44_6_77/> Cygnus&nbsp;X-1 unpredictably changes between two X-ray states, although the X-rays may vary continuously between those states as well. In the most common state, the X-rays are "hard", which means that more of the X-rays have high energy. In the less common state, the X-rays are "soft", with more of the X-rays having lower energy. The soft state also shows greater variability. The hard state is believed to originate in a corona surrounding the inner part of the more opaque accretion disk. The soft state occurs when the disk draws closer to the compact object (possibly as close as {{val|150|u=km}}), accompanied by cooling or ejection of the corona. When a new corona is generated, Cygnus&nbsp;X-1 transitions back to the hard state.<ref name=apj626_2_1015/>

The spectral transition of Cygnus X-1 can be explained using a two-component [[advection|advective]] flow solution, as proposed by Chakrabarti and Titarchuk.<ref name="CHTI_1"/> A hard state is generated by the inverse Comptonisation of seed photons from the Keplarian disk and likewise synchrotron photons produced by the hot electrons in the centrifugal-pressure–supported boundary layer ([[CENBOL]]).<ref name="CHM_1"/>

The X-ray flux from Cygnus&nbsp;X-1 varies periodically every 5.6&nbsp;days, especially during [[Conjunction (astronomy)|superior conjunction]] when the orbiting objects are most closely aligned with Earth and the compact source is the more distant. This indicates that the emissions are being partially blocked by circumstellar matter, which may be the stellar wind from the star HDE&nbsp;226868. There is a roughly 300-day periodicity in the emission, which could be caused by the [[precession]] of the accretion disk.<ref name=apj531_1_546/>

====Jets====
[[File:Tulip and Cygnus X1.png|right|thumb|The picture shows a curved bow shock structure resulting from the Cygnus X-1 accretion disk jet interacting with a dense interstellar cloud]]
As accreted matter falls toward the compact object, it loses [[gravitational energy|gravitational potential energy]]. Part of this released energy is dissipated by [[Astrophysical jet|jets]] of particles, aligned [[perpendicular]] to the accretion disk, that flow outward with [[Special relativity|relativistic]] velocities (that is, the particles are moving at a significant fraction of the [[speed of light]]). This pair of jets provide a means for an accretion disk to shed excess energy and [[angular momentum]]. They may be created by [[magnetic field]]s within the gas that surrounds the compact object.<ref name=science300_5627/>

The Cygnus&nbsp;X-1 jets are inefficient radiators and so release only a small proportion of their energy in the [[electromagnetic spectrum]]. That is, they appear "dark". The estimated angle of the jets to the line of sight is 30°, and they may be [[Precession|precessing]].<ref name=apj626_2_1015/> One of the jets is colliding with a relatively dense part of the [[interstellar medium]] (ISM), forming an energized ring that can be detected by its radio emission. This collision appears to be forming a [[nebula]] that has been observed in the [[Visible spectrum|optical wavelengths]]. To produce this nebula, the jet must have an estimated average power of 4–{{val|14|e=36|u=[[erg]]/s}}, or {{val|9|5|e=29|ul=W}}.<ref name=mnras376_3_1341/> This is more than 1,000 times the power emitted by the Sun.<ref name=apj418_457/> There is no corresponding ring in the opposite direction because that jet is facing a lower-density region of the [[Interstellar medium|ISM]].<ref name=nature436_7052_819/>

In 2006, Cygnus&nbsp;X-1 became the first stellar-mass black hole found to display evidence of [[gamma-ray]] emission in the very high-energy band, above {{val|100|ul=GeV}}. The signal was observed at the same time as a flare of hard X-rays, suggesting a link between the events. The X-ray flare may have been produced at the base of the jet, while the gamma rays could have been generated where the jet interacts with the stellar wind of HDE&nbsp;226868.<ref name=apjl665_1_L51/>

===HDE&nbsp;226868===
[[File:Cygnus X-1.png|right|thumb|An artist's impression of the HDE&nbsp;226868–Cygnus&nbsp;X-1 binary system]]
HDE&nbsp;226868 is a supergiant star with a [[spectral class]] of O9.7&nbsp;Iab,<ref name=SIMBAD/> which is on the borderline between class-O and class-B stars. It has an estimated surface temperature of 31,000&nbsp;[[Kelvin|K]]<ref name=eas030610/> and mass approximately 20–40 times the [[solar mass|mass of the Sun]]. Based on a stellar evolutionary model, at the estimated distance of 2,000&nbsp;parsecs, this star may have a radius equal to about 15–17<ref name=orosz2011/> times the [[solar radius]] and has approximately 300,000–400,000 times the [[solar luminosity|luminosity of the Sun]].<ref name=MNRAS358_3_851/><ref name=iorio2007/> For comparison, the compact object is estimated to be orbiting HDE&nbsp;226868 at a distance of about 40 solar radii, or twice the radius of this star.<ref name=apj620_1_398/>

The surface of HDE&nbsp;226868 is being [[Tidal force|tidally]] distorted by the [[gravity]] of the massive companion, forming a tear-drop shape that is further distorted by rotation. This causes the optical brightness of the star to vary by 0.06&nbsp;magnitudes during each 5.6-day binary orbit, with the minimum magnitude occurring when the system is aligned with the line of sight.<ref name=caballero/> The "ellipsoidal" pattern of light variation results from the [[limb darkening]] and [[gravity darkening]] of the star's surface.<ref name=cox2001/>

When the spectrum of HDE&nbsp;226868 is compared to the similar star [[Alnilam]], the former shows an overabundance of [[helium]] and an underabundance of [[carbon]] in its atmosphere.<ref name=rmaa31_1_63/> The [[ultraviolet]] and [[H-alpha|hydrogen-alpha]] spectral lines of HDE&nbsp;226868 show profiles similar to the star [[P&nbsp;Cygni]], which indicates that the star is surrounded by a gaseous envelope that is being accelerated away from the star at speeds of about 1,500&nbsp;km/s.<ref name=aaa63_1/><ref name=apj506_1_424/>

Like other stars of its spectral type, HDE&nbsp;226868 is thought to be shedding mass in a [[stellar wind]] at an estimated rate of {{val|2.5|e=-6}} solar masses per year; or one solar mass every 400,000 years.<ref name=apj203_438/> The gravitational influence of the compact object appears to be reshaping this stellar wind, producing a focused wind geometry rather than a spherically symmetrical wind.<ref name=apj620_1_398/> X-rays from the region surrounding the compact object heat and ionize this stellar wind. As the object moves through different regions of the stellar wind during its 5.6-day orbit, the UV lines,<ref name=baas38_334/> the radio emission,<ref name=mnras302_1_L1/> and the X-rays themselves all vary.<ref name=apj583_1_424/>

The [[Roche lobe]] of HDE&nbsp;226868 defines the region of space around the star where orbiting material remains gravitationally bound. Material that passes beyond this lobe may fall toward the orbiting companion. This Roche lobe is believed to be close to the surface of HDE&nbsp;226868 but not overflowing, so the material at the stellar surface is not being stripped away by its companion. However, a significant proportion of the stellar wind emitted by the star is being drawn onto the compact object's accretion disk after passing beyond this lobe.<ref name=apj304_371/>

The gas and dust between Earth and HDE&nbsp;226868 results in a reduction in the apparent magnitude of the star, as well as a reddening of the hue—red light can more effectively penetrate the dust in the interstellar medium. The estimated value of the interstellar [[Extinction (astronomy)|extinction]] (''A<sub>V</sub>'') is 3.3&nbsp;[[Apparent magnitude|magnitudes]].<ref name=apj185_2_L113/> Without the intervening matter, HDE&nbsp;226868 would be a fifth-magnitude star,<ref name=sut_ir/> and thus visible to the unaided eye.<ref name=kaler/>