A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses (M☉)) in a late phase of stellar evolution. 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 (RGB) stars whose shells are still fusing hydrogen into helium in a shell surrounding a degenerate helium core. Other red giants are: the red clump stars in the cool half of the horizontal branch, fusing helium into carbon in their cores via the triple-alpha process; and the asymptotic-giant-branch (AGB) stars burning a helium shell outside a degenerate carbon–oxygen core, and sometimes also a hydrogen shell closer to the surface of the star.
Red giants are stars that have exhausted the supply of hydrogen in their cores and switched to thermonuclear fusion of hydrogen in a shell surrounding the core. They have radii tens to hundreds of times larger than that of the Sun. However, their outer envelope is lower in temperature, giving them a reddish-orange hue. Despite the lower energy density of their envelope, red giants are many times more luminous than the Sun because of their large size. Red-giant-branch stars have luminosities about a hundred to several hundred times the Sun (L☉), spectral types of K or M, temperatures of 3,000–4,000K, and diameters about 20–100 times the Sun (R☉). Stars on the horizontal branch are hotter, while AGB stars are around ten times more luminous, but both types are less common than normal red giants.
Among the AGB stars belong the carbon stars of type C-N and late C-R, produced when carbon and other elements from helium burning are dredged up to the surface. The first dredge up occurs during hydrogen shell burning on the red-giant branch, but does not produce dominant carbon at the surface. The second, and sometimes third, dredge up occurs during helium shell burning on the AGB and convects carbon to the surface in sufficiently massive stars.
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. The coolest red giants have complex spectra, with molecular lines, masers, and sometimes emission.
Red giants are evolved from main-sequence stars with masses in the range from about 0.3M☉ to somewhere around 8M☉. When a star initially forms from a collapsing molecular cloud in the interstellar medium, it contains primarily hydrogen and helium, with trace amounts of "metals" (in stellar structure, this simply refers to any element that is not hydrogen or helium i.e. atomic number greater than 2). These elements are all uniformly mixed throughout the star. The star reaches the main sequence when the core reaches a temperature high enough to begin fusing hydrogen (a few million kelvin) and establish hydrostatic equilibrium. Over its main sequence life, the star slowly converts the hydrogen in the core into helium; its main-sequence life ends when nearly all the hydrogen in the core has been used. For the Sun, the main-sequence lifetime is approximately 10 billion years. More-massive stars burn disproportionately faster and so have a shorter lifetime than less massive stars. 
When the star exhausts the hydrogen fuel in its core, nuclear reactions in the core stop, so the core begins to contract due to its gravity. This heats a shell just outside the core, where hydrogen remains, initiating fusion of hydrogen to helium in the shell. The higher temperatures lead to increasing reaction rates, producing enough energy to increase the star's luminosity by a factor of 1,000–10,000. The outer layers of the star then expand greatly, beginning the red-giant phase of the star's life. Due to the expansion of the outer layers of the star, the energy produced in the core of the star is spread over a much larger surface area, resulting in a lower surface temperature and a shift in the star's visible light output towards the red – hence red giant, even though the color usually is orange. At this time, the star is said to be ascending the red-giant branch of the Hertzsprung–Russell (H–R) diagram. The outer layers are convective, which causes material exposed to nuclear "burning" in the star's interior (but not its core) to be brought to the star's surface for the first time in the star's history, an event called the first dredge-up.
The mechanism that ends the complete collapse of the core and the ascent up the red-giant branch depends on the mass of the star. For the Sun and red giants less than about 2 M☉ the core will become dense enough that electron degeneracy pressure will prevent it from collapsing further. Once the core is degenerate, it will continue to heat until it reaches a temperature of roughly 108 K, hot enough to begin fusing helium to carbon via the triple-alpha process. Once the degenerate core reaches this temperature, the entire core will begin helium fusion nearly simultaneously in a so-called helium flash. In more-massive stars, the collapsing core will reach 108 K before it is dense enough to be degenerate, so helium fusion will begin much more smoothly, with no helium flash. Once the star is fusing helium in its core, it contracts and is no longer considered a red giant. The core helium fusing phase of a star's life is called the horizontal branch in metal-poor stars, so named because these stars lie on a nearly horizontal line in the H–R diagram of many star clusters. Metal-rich helium-fusing stars instead lie on the so-called red clump in the H–R diagram.
In stars massive enough to ignite helium fusion, an analogous process occurs when central helium is exhausted and the star switches to fusing helium in a shell, although with the additional complication that in many cases hydrogen fusion will continue in a shell at lesser depth. This puts stars onto the asymptotic giant branch, a second red-giant phase. A star below about 8 M☉ will never start fusion in its degenerate carbon–oxygen core. Instead, at the end of the asymptotic-giant-branch phase the star will eject its outer layers, forming a planetary nebula with the core of the star exposed, ultimately becoming a white dwarf. The ejection of the planetary nebula finally ends the red giant phase of the star's evolution. The red-giant phase typically lasts only around a billion years in total for a solar mass star, almost all of it spent on the red-giant branch, with the horizontal branch and AGB phases tens of times faster.
If the star has about 0.2 to 0.5 M☉, it is massive enough to become a red giant but does not have enough mass to initiate the helium fusion. These "intermediate" stars cool somewhat and increase their luminosity but never achieve the tip of the red-giant branch and helium core flash. When the ascent of the red-giant branch is aborted they puff off their outer layers much like a post AGB star and then become a white dwarf.
Stars that do not become red giants
At very low mass, stars are fully convective and continue to fuse hydrogen into helium for trillions of years until only a small fraction of the entire star is hydrogen. Luminosity and temperature steadily increase during this time, as for more-massive main-sequence stars, but the length of time involved means that the temperature eventually increases by about 50% and the luminosity by around 10 times. Eventually the level of helium increases to the point where the star ceases to be fully convective and the remaining hydrogen locked in the core is consumed in only a few billion more years. Depending on mass, the temperature and luminosity continue to increase for a time during hydrogen shell burning, the star can become hotter than the Sun and tens of times more luminous than when it formed although still not as luminous as the Sun. After some billions more years, they start to become less luminous and cooler even while hydrogen shell burning continues. These become cool helium white dwarf stars.
Very-high-mass stars develop into supergiants that follow an evolutionary track that takes them back and forth horizontally over the HR diagram, at the right end constituting red supergiants. These usually end their life as type II supernova. The most massive stars can become Wolf–Rayet stars without becoming giants or supergiants at all.
Well known examples
Prominent bright red giants in the night sky include Aldebaran (Alpha Tauri), Arcturus (Alpha Bootis), and Gamma Crucis (Gacrux), while the even larger Antares (Alpha Scorpii) and Betelgeuse (Alpha Orionis) are red supergiants.
- Mira (ο Ceti),a red M-type AGB giant.
- Albireo (β Cygni),a K-type giant.
- 4 Cassiopeiae (4 Cas), an M-type giant.
The Sun as a red giant
When the Sun has exhausted the hydrogen fuel in its core in around 5 billion years, it will begin to expand and at its largest it will approximately reach the orbit of the Earth, before losing its atmosphere completely to a planetary nebula and leaving the core to become a white dwarf. The evolution of the Sun into and through the red-giant phase has been extensively modelled, but it is still unclear whether the Earth will be engulfed by the Sun or will, barely, survive. At its brightest, the red-giant Sun will be several thousand times more luminous than today despite being around half the temperature.
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