This is a real visual image of the red giant Mira by the Hubble Space Telescope. Credit: Margarita Karovska (Harvard-Smithsonian Center for Astrophysics) and NASA.

“A red giant is a luminous giant star The outer atmosphere is inflated and tenuous, making the radius immense and the surface temperature low, somewhere from 5,000 K and lower. The appearance of the red giant is from yellow orange to red, including the spectral types K and M, but also class S stars and most carbon stars. The most common red giants are the so-called red giant branch stars (RGB stars). Another case of red giants are the asymptotic giant branch stars (AGB). To the AGB stars belong the carbon stars of type C-N and late C-R. The stellar limb of a red giant is not sharply-defined, as depicted in many illustrations. Instead, due to the very low mass density of the envelope, such stars lack a well-defined photosphere. The body of the star gradually transitions into a 'corona' with increasing radii.[1]

Asteroid 65 Cybele and 2 stars with their apparent magnitudes are labeled. Credit: Kevin Heider.

Def. any "astronomical object of known diameter whose distance can then be calculated from the angle it subtends"[2] is called a standard ruler.

Def. "a numerical measure of the brightness of a star, planet etc.; a decrease of 1 unit represents an increase in the light received by a factor of 2.512"[3] is called an apparent magnitude (${\displaystyle m\!\,}$ ).

Def. "the apparent magnitude [intrinsic luminosity][4] that a star etc. [celestial body][4] would have if viewed from a distance of 10 parsecs [or about 32.6 light years][5]"[6] is called an absolute magnitude (${\displaystyle M\!\,}$ ).

Def. the "magnitude of a star in terms of the total amount of radiation received at all wavelengths"[7] is called a bolometric magnitude.

Def. a "difference between the bolometric magnitude [${\displaystyle M_{bol}}$ ] and and visual magnitude [${\displaystyle M_{V}}$ ] of a star"[8] is called a bolometric correction.

${\displaystyle M_{bol}=M_{V}+BC.}$

Def. any "astronomical object of known absolute magnitude"[9] is called a standard candle.

Its luminosity distance [${\displaystyle D_{L}\!\,}$  in parsecs] can then be calculated from its apparent magnitude.

${\displaystyle M=m-5((\log _{10}{D_{L}})-1)\!\,}$

An object's absolute magnitude may be calculated from its distance modulus (${\displaystyle \mu \!\,}$ ) and apparent magnitude using

${\displaystyle M=m-{\mu }.\!\,}$
${\displaystyle m=M+{\mu }.\!\,}$

Using the Sun (${\displaystyle \odot }$ ) as a standard candle:

${\displaystyle M_{bol_{\rm {star}}}-M_{bol_{\rm {Sun}}}=-2.5\log _{10}{\frac {L_{\rm {star}}}{L_{\odot }}},}$

Or,

${\displaystyle {\frac {L_{\rm {star}}}{L_{\odot }}}=10^{((M_{bol_{\rm {Sun}}}-M_{bol_{\rm {star}}})/2.5)},}$

where

${\displaystyle L_{\odot }}$  is the Sun's (sol) luminosity (bolometric luminosity)
${\displaystyle L_{\rm {star}}}$  is the star's luminosity (bolometric luminosity)
${\displaystyle M_{bol_{\rm {Sun}}}}$  is the bolometric magnitude of the Sun
${\displaystyle M_{bol_{\rm {star}}}}$  is the bolometric magnitude of the star.
${\displaystyle m=H+2.5\log _{10}{\left({\frac {d_{OS}^{2}d_{OOb}^{2}}{p(\chi )d_{0}^{4}}}\right)}\!\,}$

where ${\displaystyle H}$  is the absolute magnitude for a solar system object, the observer is Ob, the Sun (S), and the object is O.

${\displaystyle d_{0}\!\,=1AU}$
${\displaystyle \chi \!\,=phaseangle}$

The phase angle lies between the Sun-object and object-observer lines.

${\displaystyle \cos {\chi }={\frac {d_{OOb}^{2}+d_{OS}^{2}-d_{ObS}^{2}}{2d_{OOb}d_{OS}}}.\!\,}$

where ${\displaystyle p(\chi )\!\,}$  is between 0 and 1 for the integration of reflected light.

${\displaystyle p(\chi )={\frac {2}{3}}\left(\left(1-{\frac {\chi }{\pi }}\right)\cos {\chi }+{\frac {1}{\pi }}\sin {\chi }\right).\!\,}$
${\displaystyle d_{OOb}\!\,}$

where the distance (d) is between the observer (O) and the object (O).

${\displaystyle d_{OS}\!\,}$

where S is the Sun.

${\displaystyle d_{ObS}\!\,}$

## Hypervelocity stars

The Hubble Space Telescope image shows four high-velocity, runaway stars plowing through their local interstellar medium. Credit: NASA - Hubble's Advanced Camera for Surveys.

This ultraviolet-wavelength image mosaic, taken by NASA's GALEX, shows a comet-like "tail" stretching 13 light years across space behind the star Mira. Credit: NASA.

A close-up view of a star racing through space faster than a speeding bullet can be seen in this image from NASA's Galaxy Evolution Explorer. Credit: NASA/JPL-Caltech/C. Martin (Caltech)/M. Seibert(OCIW).

The Chandra image shows Mira A (right), a highly evolved red giant star, and Mira B (left), a white dwarf. Scalebar: 0.3 arcsec. Credit: NASA/CXC/SAO/M. Karovska et al.

"To date, all of the reported hypervelocity stars (HVSs), which are believed to be ejected from the Galactic center, are blue and therefore almost certainly young.”[10]

Def. a high-velocity star moving through space with an abnormally high velocity relative to the surrounding interstellar medium is called a runaway star.

"Of particular importance has been access to high resolution R~40,000-100,000 echelle spectra providing an ability to study the dynamics of hot plasma and separate multiple stellar and interstellar absorption components."[11]

At left is a radiated object, the binary star Mira, and its associated phenomena.

"Ultra-violet studies of Mira by NASA's Galaxy Evolution Explorer (Galex) space telescope have revealed that it sheds a trail of material from the outer envelope, leaving a tail 13 light-years in length, formed over tens of thousands of years.[12][13] It is thought that a hot bow-wave of compressed plasma/gas is the cause of the tail; the bow-wave is a result of the interaction of the stellar wind from Mira A with gas in interstellar space, through which Mira is moving at an extremely high speed of 130 kilometres/second (291,000 miles per hour).[14][15] The tail consists of material stripped from the head of the bow-wave, which is also visible in ultra-violet observations. Mira's bow-shock will eventually evolve into a planetary nebula, the form of which will be considerably affected by the motion through the interstellar medium (ISM).[16]

At second right is the only available X-ray image, by the Chandra X-ray Observatory, of Mira A on the right and Mira B (left). "Mira A is losing gas rapidly from its upper atmosphere [apparently] via a stellar wind. [Mira B is asserted to be a white dwarf. In theory] Mira B exerts a gravitational tug that creates a gaseous bridge between the two stars. Gas from the wind and bridge accumulates in an accretion disk around Mira B and collisions between rapidly moving particles in the disk produce X-rays."[17]

Mira A, spectral type M7 IIIe[18], has an effective surface temperature of 2918–3192[19]. Mira A is not a known X-ray source according to SIMBAD, but here is shown to be one.

## CME stars

Arcs rise above an active region on the surface of the Sun in this series of images taken by the STEREO (Behind) spacecraft. Credit: Images courtesy of the NASA STEREO Science Center.

A magnetic cloud is a transient event observed in the solar wind. It was defined in 1981 by Burlaga et al. 1981 as a region of enhanced magnetic field strength, smooth rotation of the magnetic field vector and low proton temperature [20]. Magnetic clouds are a possible manifestation of a Coronal Mass Ejection (CME). The association between CMEs and magnetic clouds was made by Burlaga et al. in 1982 when a magnetic cloud was observed by Helios-1 two days after being observed by SMM[21]. However, because observations near Earth are usually done by a single spacecraft, many CMEs are not seen as being associated with magnetic clouds. The typical structure observed for a fast CME by a satellite such as ACE is a fast-mode shock wave followed by a dense (and hot) sheath of plasma (the downstream region of the shock) and a magnetic cloud.

Other signatures of magnetic clouds are now used in addition to the one described above: among other, bidirectional superthermal electrons, unusual charge state or abundance of iron, helium, carbon and/or oxygen. The typical time for a magnetic cloud to move past a satellite at the L1 point is 1 day corresponding to a radius of 0.15 AU with a typical speed of 450 km s−1 and magnetic field strength of 20 nT [22]

Def. a "massive burst of solar wind, other light isotope plasma, and magnetic fields rising above the solar corona or being released into space"[23] is called a coronal mass ejection (CME).

An explosive limb flare occurred above 30,000 km in the corona of the Sun.[24] "So the aftermath of the flare explosion, usually visible in disk pictures as extensive Hα brightening, but hidden from us in this case, was seen by the ionosphere as an intense flux of ionizing radiation from the coronal cloud created by the explosion."[24] "The November 20, 1960, event is very similar to that of February 10, 1956, which was observed at Sacramento Peak. A bright ball appears above the surface, grows in size and Hα brightness, and explodes upward and outward."[24] "The great breadth and intensity of the Hα emission from the suspended ball at 2013 U.T. testify to the large amount of energy stored there, as no corresponding macroscopic motion was observed until the explosion at 2023 U.T."[24] "[T]he great energy of the preflare cloud was released into the corona by the explosion of 2023 U.T., and Hα radiation disappeared by 2035 U.T."[24]

"On 16 June 1972, the Naval Research Laboratory's coronagraph aboard OSO-7 tracked a huge coronal cloud moving outward from the Sun."[25]

A coronal mass ejection (CME) is an ejected plasma consisting primarily of electrons and protons (in addition to small quantities of heavier elements such as helium, oxygen, and iron), plus the entraining coronal closed magnetic field regions. Evolution of these closed magnetic structures in response to various photospheric motions over different time scales (convection, differential rotation, meridional circulation) somehow leads to the CME.[26] Small-scale energetic signatures such as plasma heating (observed as compact soft X-ray brightening) may be indicative of impending CMEs.

The soft X-ray sigmoid (an S-shaped intensity of soft X-rays) is an observational manifestation of the connection between coronal structure and CME production.[26]

"Relating the sigmoids at X-ray (and other) wavelengths to magnetic structures and current systems in the solar atmosphere is the key to understanding their relationship to CMEs."[26]

The "Chandra X-ray Observatory detected a CME from a star other than our own for the first time, providing a novel insight into these powerful phenomena. As the name implies these events occur in the corona, which is the outer atmosphere of a star."[27]

"This "extrasolar" CME was seen emanating from a star called HR 9024, which is located about 450 light years from Earth. This represents the first time that researchers have thoroughly identified and characterized a CME from a star other than our Sun. This event was marked by an intense flash of X-rays followed by the emission of a giant bubble of plasma, i.e., hot gas containing charged particles."[27]

"The results confirm that CMEs are produced in magnetically active stars, and they also open the opportunity to systematically study such dramatic events in stars other than the Sun."[27]

"The High-Energy Transmission Grating Spectrometer, or HETGS, aboard Chandra is the only instrument that allows measurements of the motions of coronal plasmas with speeds of just a few tens of thousands of miles per hour, like those observed in HR 9024. During the flare, the Chandra observations clearly detected very hot material (between 18 to 45 million degrees Fahrenheit) that first rises and then drops with speeds between 225,000 to 900,000 miles per hour. This is in excellent agreement with the expected behavior for material linked to the stellar flare."[27]

"Coronal mass ejections (CMEs), often associated with flares1,2,3, are the most powerful magnetic phenomena occurring on the Sun. Stars show magnetic activity levels up to 104 times higher4, and CME effects on stellar physics and circumstellar environments are predicted to be significant5,6,7,8,9."[28]

"Using time-resolved high-resolution X-ray spectroscopy of a stellar flare on the active star HR 9024 observed with Chandra/HETGS, Doppler shifts in SXVI, SiXIV, and MgXII lines that indicate upward and downward motions of hot plasmas (∼ 10 − 25 MK) within the flaring loop, with velocity v ∼ 100 − 400 km s−1, in agreement with a model of flaring magnetic tube [were detected]."[28]

A "later blueshift in the O VIII line which reveals an upward motion, with v = 90 ± 30 km s−1, of cool plasma (∼ 4 MK), that we ascribe to a CME coupled to the flare [was detected]."[28]

A "CME mass of ${\displaystyle 1.2_{-0.8}^{+2.6}\times 10^{21}}$  g and a CME kinetic energy of ${\displaystyle 5.2_{-3.6}^{+27.7}\times 10^{34}}$  erg [was derived]."[28]

"Active stars have stronger magnetic fields, higher flare energies, hotter and denser coronal plasma12. Their activity level, measured by the X-ray to bolometric luminosity ratio, LX/Lbol, can be up to 104 times higher than the solar one. Currently, the properties of stellar CMEs can only be presumed extrapolating the solar flare-CME relation up to several orders of magnitude, even though active stellar coronae differ profoundly from the solar one. This extrapolation suggests that stellar CMEs should cause enormous amounts of mass and kinetic energy loss6,7,8,9 (up to ∼ 10−9 M yr−1 and ∼ 0.1Lbol, respectively), and could significantly influence exoplanets5."[28]

"HR 9024 is a G1III single giant22, with M* ∼ 2.85 M and R* ∼ 9.45 R, located at 139.5 pc. Its convective envelope and rotational period23 (24.2 d) indicate that an efficient dynamo is at work22, as expected in single G-type giants24."[28]

"HR 9024 indeed shows coronal21 (LX ∼ 1031 erg s−1, with T ∼ 1 − 100 MK) and magnetic field properties22 (a dominant poloidal field with Bmax ∼ 102 G) analogous to that of other active stars."[28]

"HR 9024 X-ray spectrum was collected during a 98 ks-long Chandra/HETGS observation [...], during which a strong flare (peak luminosity ∼ 1032 erg s−1 and X-ray fluence ∼ 1036 erg) was registered [...]."[28]

Significant "blueshifts during the rising phase of the flare in the S XVI line at significant blueshifts during the rising phase of the flare in the S XV line at 4.73 Å (−400 ± 180 km s−1) and in the Si XIV line at 6.18 Å (−270 ± 120 km s−1), with a 99.99% combined significance of the two line shifts [occurred]."[28]

Significant "redshifts in the SiXIV line at 6.18 Å (140 ± 80 km s−1) and Mg XII line at 8.42 Å (70 ± 50 and 90 ± 40 km s−1), during the maximum and decay phases of the flare, with a 99.997% combined significance of the three line shifts [occurred]."[28]

A "significant blueshift in the O VIII line at 18.97 Å (−90 ± 30 km s−1), after the flare, significant at 99.9% level [occurred]."[28]

## Neutron stars

This graphic shows motion of the neutron star RX J0822-4300 from the Puppis A supernova event. Credit: NASA.

It is a type of stellar remnant [(a compact star)] that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons.

Neutron stars are theorized as the radiation source for anomalous X-ray pulsars (AXPs), binary pulsars, high-mass X-ray binaries, intermediate-mass X-ray binaries, low-mass X-ray binaries (LMXB), pulsars, and soft gamma-ray repeaters (SGRs).

"The [image on the right] shows two observations of [the] neutron star [RX J0822-4300] obtained with the Chandra X-ray Observatory over the span of five years, between December 1999 [on the left] and April 2005 [on the right]. By combining how far it has moved across the sky with its distance from Earth [at about 7,000 light years], astronomers determined the cosmic cannonball is moving at over 3 million miles per hour, one of the fastest moving stars ever observed. At this rate, RX J0822-4300 [at (J2000) RA 08h 23m 08.16s Dec -42° 41' 41.40" in Puppis] is destined to escape from the Milky Way after millions of years, even though it has only traveled about 20 light years so far."[29]

## Electron stars

"IN the standard model for type Ia supernovae1, a massive white dwarf in a binary system accretes matter from the companion star until it reaches the Chandrasekhar mass (the stability limit for degenerate-electron stars, corresponding to ~1.4 solar masses), and a runaway thermonuclear explosion ensues."[30]

## Neutrino stars

"In the 1980s two early water-Cherenkov experiments were built. The Irvine-Michigan-Brookhaven detector in an Ohio salt mine and the Kamiokande detector in a Japanese zinc mine were tanks containing thousands of tons of purified water, monitored with phototubes. The two detectors launched the field of neutrino astronomy by detecting some 20 low-energy (about 10 MeV) neutrinos from Supernova 1987A—the first supernova since the 17th century that was visible to the naked eye."[31]

"The water-based detectors Kamiokande II and IMB detected 11 and 8 antineutrinos of thermal origin,[32] respectively, while the scintillator-based Baksan detector found 5 neutrinos (lepton number = 1) of either thermal or electron-capture origin, in a burst lasting less than 13 seconds.

"In 1987, astronomers counted 19 neutrinos from an explosion of a star in the nearby Large Magellanic Cloud, 19 out of the billion trillion trillion trillion trillion neutrinos that flew from the supernova."[33]

## Gamma-ray stars

Gamma-ray stars have surface temperatures starting at 300,000,000 K (300 MK) corresponding to a peak wavelength of 0.010 nm (10 pm) for the beginning of super soft gamma-ray sources.

## X-ray stars

This is a Chandra X-ray Observatory image of Cygnus X-1. Credit: NASA/CXC

X-ray stars have surface temperatures starting at 300,000 K corresponding to a peak wavelength of 10 nm for the beginning of super soft X-ray sources. Cygnus X-1 may be just such a star.

Its stellar companion is spectral class O9.7Iab[34] with Radial velocity = −13 km/s[34], Temperature = 31000 K[35], rotation = every 5.6 days, in catalogs: Astronomische Gesellschaft Katalog (AG or AGK2)+35 1910, Bonner Durchmusterung BD +34 3815, Henry Draper catalogue (HD (or HDE) 226868, Hipparcos catalogue (HIP) 98298, Smithsonian Astrophysical Observatory (SAO) 69181, V1357 Cyg.[34]

Cygnus X-1 (abbreviated Cyg X-1)[36] is a galactic X-ray source in the constellation Cygnus, and the first such source widely accepted to be a black hole.[37][38] It was discovered in 1964 during a rocket flight and is one of the strongest X-ray sources seen from Earth, producing a peak X-ray flux density of 2.3×10−23
Wm−2 Hertz Hz−1
(2.3×103
Jansky
).[39][40] The compact object is now estimated to have a mass about 14.8 times the mass of the Sun[41] and has been shown to be too small to be any known kind of normal star, or other likely object besides a black hole.[42] If so, the radius of its event horizon has 300 km "as upper bound to the linear dimension of the source region" of occasional X-ray bursts lasting only for about 1 ms.[43]

Cygnus X-1 belongs to a high-mass X-ray binary system, located about 6,070 light-years from the Sun, that includes a blue supergiant variable star designated HDE 226868[44] which it orbits at about 0.2 AU, or 20% of the distance from the Earth to the Sun. A stellar wind from the star provides material for an accretion disk around the X-ray source.[45] Matter in the inner disk is heated to millions of degrees, generating the observed X-rays.[46][47] A pair of jets, arranged perpendicular to the disk, are carrying part of the energy of the infalling material away into interstellar space.[48]

This system may belong to a stellar association called Cygnus OB3, which would mean that Cygnus X-1 is about five million years old and formed from a progenitor star that had more than 40 solar masses. The majority of the star's mass was shed, most likely as a stellar wind. If this star had then exploded as a supernova, the resulting force would most likely have ejected the remnant from the system. Hence the star may have instead collapsed directly into a black hole.[49]

Observation of X-ray emissions allows astronomers to study celestial phenomena involving gas with temperatures in the millions of degrees. However, because X-ray emissions are blocked by the Earth's atmosphere, observation of celestial X-ray sources is not possible without lifting instruments to altitudes where the X-rays can penetrate.[50][51] Cygnus X-1 was discovered using X-ray instruments that were carried aloft by a sounding rocket launched from White Sands Missile Range in New Mexico. As part of an ongoing effort to map these sources, a survey was conducted in 1964 using two Aerobee suborbital rockets. The rockets carried Geiger counters to measure X-ray emission in wavelength range 1–15 Å across an 8.4° section of the sky. These instruments swept across the sky as the rockets rotated, producing a map of closely spaced scans.[36]

As a result of these surveys, eight new sources of cosmic X-rays were discovered, including Cyg XR-1 (later Cyg X-1) in the constellation Cygnus. The celestial coordinates of this source were estimated as right ascension 19h53m and declination 34.6°. It was not associated with any especially prominent radio or optical source at that position.[36]

Seeing a need for longer duration studies, in 1963 Riccardo Giacconi and Herbert Gursky proposed the first orbital satellite to study X-ray sources. NASA launched their Uhuru Satellite in 1970,[52] which led to the discovery of 300 new X-ray sources.[53] Extended Uhuru observations of Cygnus X-1 showed fluctuations in the X-ray intensity that occurs several times a second.[54] This rapid variation meant that the energy generation must take place over a relatively small region of roughly 105
km
,[55] as the speed of light restricts communication between more distant regions. For a size comparison, the diameter of the Sun is about 1.4×106
km
.

In April–May 1971, Luc Braes and George K. Miley from Leiden Observatory, and independently Robert M. Hjellming and Campbell Wade at the National Radio Astronomy Observatory,[56] detected radio emission from Cygnus X-1, and their accurate radio position pinpointed the X-ray source to the star AGK2 +35 1910 = HDE 226868.[57][58] On the celestial sphere, this star lies about half a degree from the 4th-magnitude star Eta Cygni.[59] It is a supergiant star that is, by itself, incapable of emitting the observed quantities of X-rays. Hence, the star must have a companion that could heat gas to the millions of degrees needed to produce the radiation source for Cygnus X-1.

Louise Webster and Paul Murdin, at the Royal Greenwich Observatory,[60] and Charles Thomas Bolton, working independently at the University of Toronto's David Dunlap Observatory,[61] announced the discovery of a massive hidden companion to HDE 226868 in 1971. Measurements of the Doppler shift of the star's spectrum demonstrated the companion's presence and allowed its mass to be estimated from the orbital parameters.[62] Based on the high predicted mass of the object, they surmised that it may be a black hole as the largest possible neutron star cannot exceed three times the mass of the Sun.[63]

With further observations strengthening the evidence, by the end of 1973 the astronomical community generally conceded that Cygnus X-1 was most likely a black hole.[64][65] More precise measurements of Cygnus X-1 demonstrated variability down to a single millisecond. This interval is consistent with turbulence in a disk of accreted matter surrounding a black hole—the accretion disk. X-ray bursts that last for about a third of a second match the expected time frame of matter falling toward a black hole.[66]

This X-ray image of Cygnus X-1 was taken by a balloon-borne telescope, the High-Energy Replicated Optics (HERO) project. Credit: NASA image.

Cygnus X-1 has since been studied extensively using observations by orbiting and ground-based instruments.[34] The similarities between the emissions of X-ray binaries such as HDE 226868/Cygnus X-1 and active galactic nuclei suggests a common mechanism of energy generation involving a black hole, an orbiting accretion disk and associated jets.[67] For this reason, Cygnus X-1 is identified among a class of objects called microquasars; an analog of the quasars, or quasi-stellar radio sources, now known to be distant active galactic nuclei. Scientific studies of binary systems such as HDE 226868/Cygnus X-1 may lead to further insights into the mechanics of active galaxies.[68]

The compact object and blue supergiant star form a binary system in which they orbit around their center of mass every 5.599829 days.[69] From the perspective of the Earth, the compact object never goes behind the other star; in other words, the system does not eclipse. However, the inclination of the orbital plane to the line of sight from the Earth remains uncertain, with predictions ranging from 27–65°. A 2007 study estimated the inclination is 48.0±6.8°, which would mean that the semi-major axis is about 0.2 AU, or 20% of the distance from the Earth to the Sun. The orbital eccentricity is thought to be only 0.0018±0.002; a nearly circular orbit.[41][70] Earth's distance to this system is about 1,860 ± 120 parsecs (6,070 ± 390 light-years).[71]

The HDE 226868/Cygnus X-1 system shares a common motion through space with an association of massive stars named Cygnus OB3, which is located at roughly 2,000 parsecs from the Sun. This implies that HDE 226868, Cygnus X-1 and this OB association may have formed at the same time and location. If so, then the age of the system is about 5±1.5 million year. The motion of HDE 226868 with respect to Cygnus OB3 is 9±3 km/s; a typical value for random motion within a stellar association. HDE 226868 is about 60 parsecs from the center of the association, and could have reached that separation in about 7±2 million year—which roughly agrees with estimated age of the association.[49]

With a galactic latitude of 4 degrees and galactic longitude 71 degrees,[34] this system lies inward along the same Orion Spur in which the Sun is located within the Milky Way,[72] near where the spur approaches the Sagittarius Arm. Cygnus X-1 has been described as belonging to the Sagittarius Arm,[73] though the structure of the Milky Way is not well established.

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 20±5 solar masses,[74] while other techniques resulted in 10 solar masses. Measuring periodicities in the X-ray emission near the object has yielded a more precise value of 14.8±1 solar masses. In all cases, the object is most likely a black hole[41][75]—a region of space with a 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 44 km for Cygnus X-1. Anything (including matter and photons) that passes through this boundary is unable to escape.[76]

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 will be emitted in a series of pulses that are subject to gravitational redshift as the material approaches the horizon. That is, the wavelengths of the radiation will 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.[77]

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 X-1 was not rotating to any significant degree.[78][79] However, evidence announced in 2011 suggests it is rotating extremely rapidly, approximately 790 times per second.[80]

The largest star in the Cygnus 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 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 226868, while the remainder was most likely expelled by a strong stellar wind. The helium enrichment of HDE 226868's outer atmosphere may be evidence for this mass transfer.[81] 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.[49]

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).[49]

A Chandra X-ray Observatory X-ray spectrum of Cygnus X-1 showing a characteristic peak near 6.4 keV due to ionized iron in the accretion disk, but the peak is gravitationally red-shifted, broadened by the Doppler effect, and skewed toward lower energies.[82]

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—and a cooler, less ionized outer region that extends to an estimated 500 times the Schwarzschild radius,[47] or about 15,000 km.

Though highly and erratically variable, Cygnus X-1 is typically the brightest persistent source of hard X-rays—those with energies from about 30 up to several hundred keV—in the sky.[51] 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 electrons in a geometrically thicker, but nearly transparent corona enveloping it, as well as by some further reflection from the surface of the thin disk.[83] An alternative possibility is that the X-rays may be Compton scattered by the base of a jet instead of a disk corona.[84]

The X-ray emission from Cygnus 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 X-1, providing a cross-check with other mass derivations.[85]

Pulsations with a stable period, similar to those resulting from the spin of a neutron star, have never been seen from Cygnus X-1.[86][87] The pulsations from neutron stars are caused by the neutron star's magnetic field; however, the no-hair theorem guarantees that black holes do not have magnetic poles; for example, the X-ray binary V 0332+53 was thought to be a possible black hole until pulsations were found.[88] Cygnus X-1 has also never displayed X-ray bursts similar to those seen from neutron stars.[89] Cygnus 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 150 km), accompanied by cooling or ejection of the corona. When a new corona is generated, Cygnus X-1 transitions back to the hard state.[90]

The spectral transition of Cygnus X-1 can be explained using a two component advective flow solution:[91] 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).[92]

The X-ray flux from Cygnus X-1 varies periodically every 5.6 days, especially during superior conjunction when the orbiting objects are most closely aligned with the Earth and the compact source is the more distant, which indicates that the emissions are being partially blocked by circumstellar matter, which may be the stellar wind from the star HDE 226868; there is a roughly 300 day periodicity in the emission that could be caused by the precession of the accretion disk.[93]

As accreted matter falls toward the compact object, it loses gravitational potential energy, with part of this released energy dissipated by jets of particles, aligned perpendicular to the accretion disk, that flow outward with relativistic velocities; (i.e., 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 and they may be created by magnetic fields within the gas that surrounds the compact object.[94]

The Cygnus X-1 jets are inefficient radiators and so release only a small proportion of their energy in the electromagnetic spectrum; i.e., they appear "dark",with the estimated angle of the jets to the line of sight is 30° and they may be precessing.[90] 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 optical wavelengths. To produce this nebula, the jet must have an estimated average power of 4–14×1036
erg/s
, or 9±5×1029
W
.[95] This is more than 1,000 times the power emitted by the Sun.[96] There is no corresponding ring in the opposite direction because that jet is facing a lower density region of the ISM.[95]

In 2006, Cygnus X-1 became the first stellar mass black hole found to display evidence of gamma ray emission in the very high energy band, above 100 GeV, where 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 226868.[97]

HDE 226868 is a supergiant star with a spectral class of O9.7 Iab,[34] which is on the borderline between class O and class B stars. It has an estimated surface temperature of 31,000 K[35] and mass approximately 20–40 times the mass of the Sun. Based on a stellar evolutionary model, at the estimated distance of 2,000 parsecs this star may have a radius equal to about 15–17[41] times the solar radius and is approximately 300,000–400,000 times the luminosity of the Sun.[74][98] For comparison, the compact object is estimated to be orbiting HDE 226868 at a distance of about 40 solar radii, or twice the radius of this star.[99]

The surface of HDE 226868 is being 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 magnitudes during each 5.6-day binary orbit, with the minimum magnitude occurring when the system is aligned with the line of sight.[100] The "ellipsoidal" pattern of light variation results from the limb darkening and gravity darkening of the star's surface.[101]

When the spectrum of HDE 226868 is compared to the similar star Epsilon Orionis, the former shows an overabundance of helium and an underabundance of carbon in its atmosphere.[102] The ultraviolet and hydrogen alpha spectral lines of HDE 226868 show profiles similar to the star P 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 km/S.[103][104]

Like other stars of its spectral type, HDE 226868 is thought to be shedding mass in a stellar wind at an estimated rate of 2.5×10−6
solar masses per year.[99] This is the equivalent of losing a mass equal to the Sun's every 400,000 years. 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.[99] 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,[105] the radio emission,[106] and the X-rays themselves all vary.[107]

The Roche lobe of HDE 226868 defines the region of space around the star where orbiting material remains gravitationally bound, where material that passes beyond this lobe may fall toward the orbiting companion; the Roche lobe is believed to be close to the surface of HDE 226868 but not overflowing, so the material at the stellar surface is not being stripped away by its companion; but, 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.[45]

The gas and dust between the Sun and HDE 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, where the estimated value of the interstellar extinction (AV) is 3.3 magnitudes.[108] Without the intervening matter, HDE 226868 would be a fifth-magnitude star[109] and, thus, visible to the unaided eye.[110]

## Ultraviolet stars

The central star of NGC 6826 is a low-mass O6 star. Credit: Bruce Balick (University of Washington), Jason Alexander (University of Washington), Arsen Hajian (U.S. Naval Observatory), Yervant Terzian (Cornell University), Mario Perinotto (University of Florence, Italy), Patrizio Patriarchi (Arcetri Observatory, Italy) and NASA.

A distinctive feature of this nebula are the two bright patches on either side. Credit: Judy Schmidt.{{free media}}

The diffuse X-ray emission from the central star inside NGC 6826 seen with the Chandra X-ray Observatory caused by shock waves as a wind from the hot remnant of the star collides with the ejected atmosphere. Credit: J. Kastner, et al.{{fairuse}}

The diffuse optical (red, green, and blue) emission from the central star seen with the Hubble Space Telescope is caused by shock waves as a wind from the hot remnant of the star collides with the ejected atmosphere. Credit: J. Kastner, et al.{{fairuse}}

The diffuse X-ray emission from Chandra is colored purple and the optical emission from the Hubble Space Telescope is colored red, green, and blue. Credit: J. Kastner, et al.{{fairuse}}

These line profiles show best fits to the different Balmer lines of BD+28° 4211. Credit: R. Napiwotzki.

A distinctive feature of this planetary nebula (NGC 6826) are the two bright patches on either side, which are known as Fast Low-Ionization Emission Regions, or FLIERS which appear to be relatively young, moving outwards at supersonic speeds.[111]

For NGC 6826 "the electron temperatures derived from both [O II] and [S II] lines are consistently above those determined from [O III] and [N II]. One possible explanation is the hardening of the radiation field as it passes from the high-ionization zones nearer to the star where [O III] is found, out to the lower-ionization regions where [O II] and [S II] are formed."[112]

In the image on the right, "NGC 6826's eye-like appearance is marred by two sets of blood-red "fliers" that lie horizontally across the image. The surrounding faint green "white" of the eye is believed to be gas that made up almost half of the star's mass for most of its life. The hot remnant star (in the center of the green oval) drives a fast wind into older material, forming a hot interior bubble which pushes the older gas ahead of it to form a bright rim. (The star is one of the brightest stars in any planetary.) NGC 6826 is 2,200 light-years away in the constellation Cygnus. The Hubble telescope observation was taken Jan. 27, 1996 with the Wide Field and Planetary Camera 2."[113]

In the image second down on the right, "Chandra X-ray data is in purple and optical Hubble Space Telescope data [when present] is red, green and blue. The diffuse X-ray emission seen with Chandra is caused by shock waves as a wind from the hot remnant of the star at the center [of NGC 6826] collides with the ejected atmosphere."[114]

"A planetary nebula represents a phase of stellar evolution that the Sun should experience several billion years from now. When a star like the Sun uses up all of the hydrogen in its core, it expands into a red giant, with a radius that increases by tens to hundreds of times. In this phase, a star sheds most of its outer layers, eventually leaving behind a hot core that will soon contract to form a dense white dwarf star. A fast wind emanating from the hot core rams into the ejected atmosphere, pushes it outward, and creates the graceful, shell-like filamentary structures seen with optical telescopes."[114]

In the image second down on the left, the diffuse "optical Hubble Space Telescope data is red, green and blue. The diffuse [optical] emission [from the central star] seen with [the Hubble Space Telescope] is caused by shock waves as a wind from the hot remnant of the star at the center [of NGC 6826] collides with the ejected atmosphere."[114]

The center image is a composite of the two left and right lower down images, where the diffuse X-ray emission from Chandra is colored purple and the optical emission from the Hubble Space Telescope is colored red, green, and blue.

Stellar class O stars have surface temperatures high enough that most of their luminescence is in the ultraviolet. The peaks of their Planckian spectra start at about 38,000 K and increase, and 79 nm and decrease in the ultraviolet.

Each star class is subdivided into temperature ranges using numbers: hottest - 0 to coolest - 9.9. For example, O00 or O0 0 is an O hypergiant star having the hottest known photospheric temperature.

A "new subclass, O1, has been created".[115]

"Clegg and Walsh (1989) determined Teff = 120 000 K for the central star NGC 7293 from the nebular lines. This is in reasonable agreement with the temperature determined from Hδ (Teff = 110 000 K)."[116]

An O2 VIII [BD+28 4211, sdO2VIII:He5, on the right] can have an effective temperature of 82,000 K and an O9 V can have an effective temperature of 38,000 K.[115]

"For BD+28° 4211 [...] the He I 5876 Å line in a high-resolution spectrum taken at the McDonald Observatory [has a] best fit [of] Teff = 82000 K in good agreement with Hε [on the right at the bottom]."[116]

The "effective temperatures [are] derived from [spectral] lines".[115]

If "the [helium] lines are significantly wider than the average [class VII], we use luminosity class “VIII”."[115]

 Stars Teff [103 K] log g [cm·s-2] log [n(He)/n(H)] Spectral type WR 142 200.0 WO2 H1504 170.0 7 0.00 DZQ.3 NGC 7293 120.0 0.00 DA.5 PG 1159 110.0 7 0.00 DQZO.4, DOQZ1 (SIMBAD) KPD 0311+4801 100.8 DA.5 BD+28 4211 82.0 6.20 −1.00 sdO2VIII:He5 PG1249+762 68.0 5.80 1.00 sdOC2VIII:He36 PG2158+082 67.0 5.50 1.00 sdO2VIII:He40 PG1536+690 63.0 5.80 1.00 sdOC2VIII:He40 WR11 57.0 WC8 PG1646+607 48.0 6.00 0.00 sdO7VIII:He36 PG1401+289 47.0 5.50 1.30 sdOC7VII:He40 PG0039+135 45.0 5.00 1.00 sdOC7VII:He40 PG0838+133 44.0 4.80 1.00 sdOC7VII:He40 PG1325+054 41.0 5.00 1.30 sdO8VII:He40 PG1624+085 40.0 5.30 1.30 sdO9VII:He39 PG0208+016 40.0 5.00 1.00 sdO9VII:He39 PG1127+019 39.9 5.00 2.00 sdOC9VII:He40 PG1658+273 38.8 4.90 2.00 sdOC9.5VII:He39 PG2120+062 38.0 4.25 −1.06 sdO9V:He17

## Optical stars

This is a NASA Hubble Space Telescope image of the cool red giant star Mira A (right), officially called Omicron Ceti in the constellation Cetus, and its nearby hot companion (left) taken on December 11, 1995 in visible light using the European Space Agency's Faint Object Camera (FOC). Credit: NASA.

Some data suggest that Mira B is a normal main sequence star of spectral type K and roughly 0.7 solar masses, rather than a white dwarf as first envisioned.[117]

Analysis in 2010 of rapid optical brightness variations has indicated that Mira B is in fact a white dwarf.[118]

## Violet stars

This Hubble Space Telescope image shows excess violet light escaping along the equatorial plane between the bipolar lobes of the Eta Carinae Homunculus. Credit: Jon Morse (University of Colorado) & NASA Hubble Space Telescope.

"The “Purple Haze” is a diffuse blueish/purple glow within a few arcseconds of the central star in HST images of the Homunculus (Morse et al. 1998; Smith et al. 2000, 2004). This emission is seen in excess of violet starlight scattered by dust, and the strength of the excess increases into the far UV (Smith et al. 2004; hereafter Paper I)."[119]

Notation: let the symbol LH stand for the Little Homunculus.

"The LH has no outstanding correspondence with any of the clumps and filaments seen in scattered light in normal UV or visual-wavelength images of η Car, although it does match the spatial extent of the "Purple Haze"".[120] Bold added.

The Fe II emission line at 489.1 nm occurs in the Little Homunculus (Eta Carinae)[120]

Mass "loss at the η Carinae rate produces considerable changes of Teff on a human timescale. As an example, for the 120 Mʘ model, a change from about 20,000 K to 34,000 K was obtained over a time of 50 yr as a result of the secular bluewards evolution following the rapid ejection."[121]

## Blue stars

This Hubble Space Telescope image of NGC 6397 shows a number of bright blue stragglers present.[122] Credit: NASA.

Stars are often referred to by their predominant color. For example, blue stragglers are found among the galactic halo globular clusters.[123] Blue main sequence stars, that are metal poor, ([Fe/H] ≤ -1.0) are most likely not analogous to blue stragglers.[123]

## Cyan stars

This is an optical image in the visual range of Theta Ursae Majoris. It is listed in SIMBAD as an F7V spectral type star with a parallax of 74.19 mas. Credit: Aladin at SIMBAD.

Theta Ursae Majoris is a spectral type F7V star.[124] It has a surface temperature of 6300 ± 33 K.[125] Such an effective surface temperature has a Planckian black body peak wavelength of 476 nm which places this star at the high temperature end of the cyan band.

## Green stars

This is an optical image of Capella B. Credit: Aladin at SIMBAD.

Capella B, the image at right, has a surface temperature of approximately 5700 K, a radius of approximately 9 solar radii, a mass of approximately 2.6 solar masses, and a luminosity, again measured over all wavelengths, approximately 78 times that of the Sun.[126]

Capella B is spectral type G0III star and an X-ray source from the catalog [FS2003] 0255 by ROSAT. Its surface temperature has an uncertainty of 100 K. It is part of a binary star with Capella A a G8III. From SIMBAD, the orbital period is 104.0217 d with an eccentricity is 0.001 and inclination of 137.2° to the line of sight.

Although the binary star Capella is not an eclipsing binary, it is a RS Canum Venaticorum variable. These are close binary stars[127] having active chromospheres which can cause large stellar spots. These spots are believed to cause variations in their observed luminosity. Systems can exhibit variations on timescales of years due to variation in the spot surface coverage fraction, as well as periodic variations which are, in general, close to the orbital period of the binary system. Typical brightness fluctuation is around 0.2 magnitudes.

## Yellow stars

V972 Scorpii is a variable star of the delta Scuti type. Spectral type is G2IV. Credit: Aladin at SIMBAD.

A subgiant star is a star that is slightly brighter than a normal main-sequence (dwarf) star of the same spectral class, but not as bright as true giant stars. Although certain subgiants appear to be simply unusually bright metal-rich hydrogen-fusing stars (in the same way subdwarfs are unusually dim metal-poor hydrogen-fusing stars), they are generally believed to be stars that are ceasing or have already ceased fusing hydrogen in their cores.

"Many subgiants are rich in metals, and commonly host orbiting planets.

At right is a visual image in close to true color of V972 Scorpii, which is a variable star of the delta Sct type. It has spectral type G2IV and is a star in a cluster. The system includes components CCDM J16234-2622 A and CCDM J16234-2622 B. Component A is a dwarf star in a double star system with component B. Component A is apparently V972 Scuti.

## Orange stars

The bright orange star in the upper left is Suhail in Vela. Credit: .

The variability of BD +50 961 (SY Persei, an orange star) is confirmed.[128]

"ESO Photo Ambassador Babak Tafreshi snapped this remarkable image [at right] of the antennas of the Atacama Large Millimeter/submillimeter Array (ALMA), set against the splendour of the Milky Way. The richness of the sky in this picture attests to the unsurpassed conditions for astronomy on the 5000-metre-high Chajnantor plateau in Chile’s Atacama region."[129]

"This view shows the constellations of Carina (The Keel) and Vela (The Sails). The dark, wispy dust clouds of the Milky Way streak from middle top left to middle bottom right. The bright orange star in the upper left is Suhail in Vela, while the similarly orange star in the upper middle is Avior, in Carina. Of the three bright blue stars that form an “L” near these stars, the left two belong to Vela, and the right one to Carina. And exactly in the centre of the image below these stars gleams the pink glow of the Carina Nebula"[129]

## Reds

AZ Cancri. Credit: SDSS Data Release 6.

With respect to the color 'red', there are studies of the redness of objects such as the red dwarf AZ Cancri shown in the visual image at right. Cool stars of spectral class M appear red; they are (depending on their size) referred to as "red giants" or "red dwarfs".

"Ideally all intrinsic colours should be found from unreddened stars. This is possible for dwarf and giant stars later than about A0 (Johnson, 1964) ... However, it cannot be used for stars of other spectral classes since they are all relatively infrequent in space, and generally reddened."[130]

A very important wavelength in this region is the Balmer alpha line, 656.28 nm. It is emitted or absorbed by hydrogen atoms when electrons move between the second and third electron shells. Other Balmer lines, known as beta, gamma and delta, have wavelengths of 486.13, 434.05 and 410.17 nm respectively;[1] these are also in the visual range but are less important than the alpha line.

## Infrared stars

Stars "of spectral type S are characterized by unusual photospheric abundances which imply enrichment of the stellar surface by nucleosynthesis products. Spectroscopically, S stars are identified by bands of ZrO and LaO, replacing the TiO bands found in M stars. The spectra of S stars indicate strong enhancement of s-process elements in the photosphere (an accident of nomenclature - when the S spectral type was introduced, the slow neutron capture process was unknown). Abundance analyses show that in S stars, the C/O ratio is very close to unity [...], which also implies the presence of the products of nucleosynthesis at the stellar surface."[131]

The "extrinsic S stars, includes stars which have elemental abundances which appear to have been altered by mass transfer from a binary companion."[131]

The "intrinsic S stars, includes stars which have high luminosity and lie on the asymptotic giant branch (AGB). They show evidence that their compositional abnormalities are a result of nucleosynthesis and [perhaps] convective mixing to the surface. In particular, a defining characteristic which distinguishes the two types is that the intrinsic S stars contain technetium, while the extrinsic S stars do not."[131]

"Both HCN and SiO have readily observable lines at 3 mm."[131] χ Cyg is at a distance of 170 pc, but parallax measurements put it at D = 144 ± 25 pc (Stein 1991), parallax of 5.53 mas (198 ± 38) pc as of 2007 according to SIMBAD.

"All of these stars are bright at 2 µm and therefore have circumstellar dust [...] In one observing session, we obtained a 5 x 5 cross at HPBW spacings for the star χ Cyg in the CO J = 2-1 line. The data were relatively noisy because of limited integration time and weather conditions but do indicate that the envelope is extended with respect to the 25" telescope beam."[131]

χ Cyg was "detected in the SiO v = 1 J = 2-1 maser emission line [...] χ Cyg has an unusually large dust/gas ratio of 9.0 x 10-3 [The dust-to-gas ratio for S stars detected in CO J = 1-0 is] 9.0 x 10-3 [...] For one star in our sample namely χ Cyg, the SiO J = 2-1, v = 0 emission has been mapped interferometrically [...] the SiO abundance at the base of the expanding envelope must be ~ 2 x 10-5 to explain the observed intensity distribution of the SiO emission. Thus, a substantial fraction (30%-50%) of all silicon atoms are in the form of gas phase SiO at the point where molecules are injected into the stellar wind. As the gas moves away from the star, the SiO is depleted from the gas, presumably by the process of grain formation, such that at radii of several x 1015 cm, the SiO gas phase abundance has fallen by > 90%. [...] χ Cyg, which has a relatively low mass-loss rate and hence low envelope opacity to UV photons."[131]

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