The smallest stars burn their fuel so slowly they can last 100 billion years. The larger stars can last tens of millions of years.
A light-year, also light year or lightyear (symbol: ly), is an astronomical unit of length equal to just under 10 trillion kilometres (or about 6 trillion miles). As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in a vacuum in one Julian year.
The light-year is mostly used to express distances to stars and other distances on a galactic scale, especially in non-specialist and popular science publications. The preferred unit in astrometry is the parsec (approximately 3.26 light-years), because it can be more easily derived from, and compared with, observational data.
Note that the light-year is a measure of distance. It is not a measure of time, for which it is sometimes mistaken.
1 light-year = metres (exactly)
The figures above are based on a Julian year (not Gregorian year) of exactly 365.25 days (each of exactly SI seconds, totalling seconds) and a defined speed of light of m/s, both included in the IAU (1976) System of Astronomical Constants, used since 1984.
Before 1984, the tropical year (not the Julian year) and a measured (not defined) speed of light were included in the IAU (1964) System of Astronomical Constants, used from 1968 to 1983. The product of Simon Newcomb's J1900.0 mean tropical year of ephemeris seconds and a speed of light of km/s produced a light-year of (rounded to the seven significant digits in the speed of light) found in several modern sources was probably derived from an old source such as C. W. Allen's 1973 Astrophysical Quantities reference work, which was updated in 2000.
Other high-precision values are not derived from a coherent IAU system. A value of found in some modern sources is the product of a mean Gregorian year of 365.2425 days ( s) and the defined speed of light ( m/s). Another value, , is the product of the J1900.0 mean tropical year and the defined speed of light.
The first successful measurement of the distance to a star other than our Sun was made by Friedrich Bessel in 1838. The star was 61 Cygni, and he used a 6.2-inch (160 mm) heliometer designed by Joseph von Fraunhofer. The largest unit for expressing distances across space at that time was the astronomical unit (AU), equal to the radius of the Earth's orbit In those terms, trigonometric calculations based on 61 Cygni's parallax of 0.314 arcseconds, showed the distance to the star to be 660,000 astronomical units (9.91013 km; 6.11013 mi). Bessel realised that a much larger unit of length was needed to make the vast interstellar distances comprehensible.
James Bradley stated in 1729 that light travelled times faster than the Earth in its orbit. In 1769, a transit of Venus revealed the distance of the Earth from the Sun, and this, together with Bradley's figure, allowed the speed of light to be calculated as , very close to the modern value.
Bessel used this speed to work out how far light would travel in a year, and announced that the distance to 61 Cygni was 10.3 light-years.][ This was the first appearance of the light-year as a unit of distance,][ and, although modern astronomers prefer the parsec, it is popularly used to gauge the expanses of interstellar and intergalactic space.
Distances measured in fractions of a light-year (or in light-months) usually involve objects within a star system. Distances measured in light-years include distances between nearby stars, such as those in the same spiral arm or globular cluster.
One kilolight-year, abbreviated "kly", is one thousand light-years (about 307 parsecs). Kilolight-years are typically used to measure distances between parts of a galaxy.
One megalight-year, abbreviated "Mly", is one million light-years (about 307 kiloparsecs). Megalight-years are typically used to measure distances between neighbouring galaxies and galaxy clusters.
One gigalight-year, abbreviation "Gly", is one billion light-years (about 307 megaparsecs)—one of the largest distance measures used. Gigalight-years are typically used to measure distances to supergalactic structures, including quasars and the Sloan Great Wall.
Other units of length can similarly be formed by multiplying units of time by the speed of light. For example, the light-second, useful in astronomy, telecommunications and relativistic physics, is exactly metres or of a light-year. Units such as the light-minute, light-hour and light-day are sometimes used in popular science publications. The light-month, roughly one-twelfth of a light-year, is also used occasionally for approximate measures. The Hayden Planetarium specifies the light month more precisely as 30 days of light travel time.
A light-foot is not a related unit, since its a measure of time. ( commonly referred to as a nano-second ).
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.
The nearest red giant is Gamma Crucis, 88 light years away, but the orange giant Arcturus is described by some as a red giant and it is 36 light years away.
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, have surface temperatures of 3,000–4,000 K, and diameters about 20–100 times the Sun (R). Stars on the horizontal branch are hotter, whereas asymptotic-giant-branch stars are around ten times more luminous, but both types are less common than normal red giants.
Among the asymptotic-giant-branch stars belong the carbon stars of type C-N and late C-R, produced when carbon and other elements from helium burning are convected 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 asymptotic-giant branch 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.
Another noteworthy feature of red giants is that, unlike Sun-like stars whose photospheres have a large number of small convection cells (solar granules), red-giant photospheres, as well as those of red supergiants, have just a few large cells, being that feature what causes the variations of brightness so common on both types of stars.
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 asymptotic-giant-branch 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-asymptotic-giant-branch star and then become a white dwarf.
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 though hydrogen shell burning continues. These become cool helium white dwarfs.
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.
Although traditionally it has been suggested the evolution of a star into a red giant will render its planetary system, if present, unhabitable, some research suggests that, during the evolution of a star along the red giant branch, it could harbor an habitable zone -for a star with the same mass of the Sun- between 2 and 9 AU that would last at the shortest distance several 109 years and at the longest 108 years, giving perhaps enough time to life for developing on a suitable world. After the red giant stage, whereas the star is in the horizontal branch/red clump fusing helium on its core, for a solar mass star there would be a habitable zone between 7 and 22 AU for an additional 109 years.
Prominent bright red giants in the night sky include Aldebaran (Alpha Tauri), Arcturus (Alpha Bootis), and Gamma Crucis (Gacrux), whereas the even larger Antares (Alpha Scorpii) and Betelgeuse (Alpha Orionis) are red supergiants.
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 but have about half the temperature.
In astronomy the main sequence
is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell. Stars on this band are known as main-sequence stars
or "dwarf" stars.
After a star has formed, it creates energy at the hot, dense core region through the nuclear fusion of hydrogen atoms into helium. During this stage of the star's lifetime, it is located along the main sequence at a position determined primarily by its mass, but also based upon its chemical composition and other factors. All main-sequence stars are in hydrostatic equilibrium, where outward thermal pressure from the hot core is balanced by the inward gravitational pressure from the overlying layers. The strong dependence of the rate of energy generation in the core on the temperature and pressure helps to sustain this balance. Energy generated at the core makes its way to the surface and is radiated away at the photosphere. The energy is carried by either radiation or convection, with the latter occurring in regions with steeper temperature gradients, higher opacity or both.
The main sequence is sometimes divided into upper and lower parts, based on the dominant process that a star uses to generate energy. Stars below about 1.5 times the mass of the Sun (or 1.5 solar masses) primarily fuse hydrogen atoms together in a series of stages to form helium, a sequence called the proton–proton chain. Above this mass, in the upper main sequence, the nuclear fusion process mainly uses atoms of carbon, nitrogen and oxygen as intermediaries in the CNO cycle that produces helium from hydrogen atoms. Main-sequence stars with more than two solar masses undergo convection in their core regions, which acts to stir up the newly created helium and maintain the proportion of fuel needed for fusion to occur. Below this mass, stars have cores that are entirely radiative with convective zones near the surface. With decreasing stellar mass, the proportion of the star forming a convective envelope steadily increases, while main-sequence stars below 0.4 solar masses undergo convection throughout their mass. When core convection does not occur, a helium-rich core develops surrounded by an outer layer of hydrogen.
In general, the more massive the star the shorter its lifespan on the main sequence. After the hydrogen fuel at the core has been consumed, the star evolves away from the main sequence on the HR diagram. The behavior of a star now depends on its mass, with stars below 0.23 solar masses becoming white dwarfs directly, while stars with up to ten solar masses pass through a red giant stage. More massive stars can explode as a supernova, or collapse directly into a black hole.
In the early part of the 20th century, information about the types and distances of stars became more readily available. The spectra of stars were shown to have distinctive features, which allowed them to be categorized. Annie Jump Cannon and Edward C. Pickering at Harvard College Observatory developed a method of categorization that became known as the Harvard Classification Scheme, published in the Harvard Annals
In Potsdam in 1906, the Danish astronomer Ejnar Hertzsprung noticed that the reddest stars—classified as K and M in the Harvard scheme—could be divided into two distinct groups. These stars are either much brighter than the Sun, or much fainter. To distinguish these groups, he called them "giant" and "dwarf" stars. The following year he began studying star clusters; large groupings of stars that are co-located at approximately the same distance. He published the first plots of color versus luminosity for these stars. These plots showed a prominent and continuous sequence of stars, which he named the Main Sequence.
At Princeton University, Henry Norris Russell was following a similar course of research. He was studying the relationship between the spectral classification of stars and their actual brightness as corrected for distance—their absolute magnitude. For this purpose he used a set of stars that had reliable parallaxes and many of which had been categorized at Harvard. When he plotted the spectral types of these stars against their absolute magnitude, he found that dwarf stars followed a distinct relationship. This allowed the real brightness of a dwarf star to be predicted with reasonable accuracy.
Of the red stars observed by Hertzsprung, the dwarf stars also followed the spectra-luminosity relationship discovered by Russell. However, the giant stars are much brighter than dwarfs and so, do not follow the same relationship. Russell proposed that the "giant stars must have low density or great surface-brightness, and the reverse is true of dwarf stars". The same curve also showed that there were very few faint white stars.
In 1933, Bengt Strömgren introduced the term Hertzsprung–Russell diagram to denote a luminosity-spectral class diagram. This name reflected the parallel development of this technique by both Hertzsprung and Russell earlier in the century.
As evolutionary models of stars were developed during the 1930s, it was shown that, for stars of a uniform chemical composition, a relationship exists between a star's mass and its luminosity and radius. That is, for a given mass and composition, there is a unique solution for determining the star's radius and luminosity. This became known as the Vogt-Russell theorem; named after Heinrich Vogt and Henry Norris Russell. By this theorem, once a star's chemical composition and its position on the main sequence is known, so too is the star's mass and radius. (However, it was subsequently discovered that the theorem breaks down somewhat for stars of non-uniform composition.)
A refined scheme for stellar classification was published in 1943 by W. W. Morgan and P. C. Keenan. The MK classification assigned each star a spectral type—based on the Harvard classification—and a luminosity class. The Harvard classification had been developed by assigning a different letter to each star based on the strength of the hydrogen spectra line, before the relationship between spectra and temperature was known. When ordered by temperature and when duplicate classes were removed, the spectral types of stars followed, in order of decreasing temperature with colors ranging from blue to red, the sequence O, B, A, F, G, K and M. (A popular mnemonic for memorizing this sequence of stellar classes is "Oh Be A Fine Girl/Guy, Kiss Me".) The luminosity class ranged from I to V, in order of decreasing luminosity. Stars of luminosity class V belonged to the main sequence.
When a protostar is formed from the collapse of a giant molecular cloud of gas and dust in the local interstellar medium, the initial composition is homogeneous throughout, consisting of about 70% hydrogen, 28% helium and trace amounts of other elements, by mass. The initial mass of the star depends on the local conditions within the cloud. (The mass distribution of newly formed stars is described empirically by the initial mass function.) During the initial collapse, this pre-main-sequence star generates energy through gravitational contraction. Upon reaching a suitable density, energy generation is begun at the core using an exothermic nuclear fusion process that converts hydrogen into helium.
Once nuclear fusion of hydrogen becomes the dominant energy production process and the excess energy gained from gravitational contraction has been lost, the star lies along a curve on the Hertzsprung–Russell diagram (or HR diagram) called the standard main sequence. Astronomers will sometimes refer to this stage as "zero age main sequence", or ZAMS. The ZAMS curve can be calculated using computer models of stellar properties at the point when stars begin hydrogen fusion. From this point, the brightness and surface temperature of stars typically increase with age.
A star remains near its initial position on the main sequence until a significant amount of hydrogen in the core has been consumed, then begins to evolve into a more luminous star. (On the HR diagram, the evolving star moves up and to the right of the main sequence.) Thus the main sequence represents the primary hydrogen-burning stage of a star's lifetime.
The majority of stars on a typical HR diagram lie along the main-sequence curve. This line is pronounced because both the spectral type and the luminosity depend only on a star's mass, at least to zeroth-order approximation, as long as it is fusing hydrogen at its core—and that is what almost all stars spend most of their "active" lives doing.
The temperature of a star determines its spectral type via its effect on the physical properties of plasma in its photosphere. A star's energy emission as a function of wavelength is influenced by both its temperature and composition. A key indicator of this energy distribution is given by the color index, B
, which measures the star's magnitude in blue (B
) and green-yellow (V
) light by means of filters. This difference in magnitude provides a measure of a star's temperature.
Main-sequence stars are called dwarf stars, but this terminology is partly historical and can be somewhat confusing. For the cooler stars, dwarfs such as red dwarfs, orange dwarfs, and yellow dwarfs are indeed much smaller and dimmer than other stars of those colors. However, for hotter blue and white stars, the size and brightness difference between so-called dwarf
stars that are on the main sequence and the so-called giant
stars that are not becomes smaller; for the hottest stars it is not directly observable. For those stars the terms dwarf
refer to differences in spectral lines which indicate if a star is on the main sequence or off it. Nevertheless, very hot main-sequence stars are still sometimes called dwarfs, even though they have roughly the same size and brightness as the "giant" stars of that temperature.
The common use of dwarf
to mean main sequence is confusing in another way, because there are dwarf stars which are not main-sequence stars. For example, white dwarfs are a different kind of star that is much smaller than main-sequence stars—being roughly the size of the Earth. These represent the final evolutionary stage of many main-sequence stars.
By treating the star as an idealized energy radiator known as a black body, the luminosity L
and radius R
can be related to the effective temperature
by the Stefan–Boltzmann law:
is the Stefan–Boltzmann constant. As the position of a star on the HR diagram shows its approximate luminosity, this relation can be used to estimate its radius.
The mass, radius and luminosity of a star are closely interlinked, and their respective values can be approximated by three relations. First is the Stefan–Boltzmann law, which relates the luminosity L
, the radius R
and the surface temperature Teff
. Second is the mass–luminosity relation, which relates the luminosity L
and the mass M
. Finally, the relationship between M
is close to linear. The ratio of M
increases by a factor of only three over 2.5 orders of magnitude of M
. This relation is roughly proportional to the star's inner temperature TI
, and its extremely slow increase reflects the fact that the rate of energy generation in the core strongly depends on this temperature, while it has to fit the mass–luminosity relation. Thus, a too high or too low temperature will result in stellar instability.
A better approximation is to take
, the energy generation rate per unit mass, as ε is proportional to TI
15, where TI
is the core temperature. This is suitable for stars at least as massive as the Sun, exhibiting the CNO cycle, and gives the better fit R
The table below shows typical values for stars along the main sequence. The values of luminosity (L
), radius (R
) and mass (M
) are relative to the Sun—a dwarf star with a spectral classification of G2 V. The actual values for a star may vary by as much as 20–30% from the values listed below.
All main-sequence stars have a core region where energy is generated by nuclear fusion. The temperature and density of this core are at the levels necessary to sustain the energy production that will support the remainder of the star. A reduction of energy production would cause the overlaying mass to compress the core, resulting in an increase in the fusion rate because of higher temperature and pressure. Likewise an increase in energy production would cause the star to expand, lowering the pressure at the core. Thus the star forms a self-regulating system in hydrostatic equilibrium that is stable over the course of its main sequence lifetime.
Main-sequence stars employ two types of hydrogen fusion processes, and the rate of energy generation from each type depends on the temperature in the core region. Astronomers divide the main sequence into upper and lower parts, based on which of the two is the dominant fusion process. In the lower main sequence, energy is primarily generated as the result of the proton-proton chain, which directly fuses hydrogen together in a series of stages to produce helium. Stars in the upper main sequence have sufficiently high core temperatures to efficiently use the CNO cycle. (See the chart.) This process uses atoms of carbon, nitrogen and oxygen as intermediaries in the process of fusing hydrogen into helium.
At a stellar core temperature of 18 million kelvins, the PP process and CNO cycle are equally efficient, and each type generates half of the star's net luminosity. As this is the core temperature of a star with about 1.5 solar masses, the upper main sequence consists of stars above this mass. Thus, roughly speaking, stars of spectral class F or cooler belong to the lower main sequence, while class A stars or hotter are upper main-sequence stars. The transition in primary energy production from one form to the other spans a range difference of less than a single solar mass. In the Sun, a one solar mass star, only 1.5% of the energy is generated by the CNO cycle. By contrast, stars with 1.8 solar masses or above generate almost their entire energy output through the CNO cycle.
The observed upper limit for a main-sequence star is 120–200 solar masses. The theoretical explanation for this limit is that stars above this mass can not radiate energy fast enough to remain stable, so any additional mass will be ejected in a series of pulsations until the star reaches a stable limit. The lower limit for sustained proton-proton nuclear fusion is about 0.08 solar masses. Below this threshold are sub-stellar objects that can not sustain hydrogen fusion, known as brown dwarfs.
Because there is a temperature difference between the core and the surface, or photosphere, energy is transported outward. The two modes for transporting this energy are radiation and convection. A radiation zone, where energy is transported by radiation, is stable against convection and there is very little mixing of the plasma. By contrast, in a convection zone the energy is transported by bulk movement of plasma, with hotter material rising and cooler material descending. Convection is a more efficient mode for carrying energy than radiation, but it will only occur under conditions that create a steep temperature gradient.
In massive stars (above 10 solar masses) the rate of energy generation by the CNO cycle is very sensitive to temperature, so the fusion is highly concentrated at the core. Consequently, there is a high temperature gradient in the core region, which results in a convection zone for more efficient energy transport. This mixing of material around the core removes the helium ash from the hydrogen-burning region, allowing more of the hydrogen in the star to be consumed during the main-sequence lifetime. The outer regions of a massive star transport energy by radiation, with little or no convection.
Intermediate mass stars such as Sirius may transport energy primarily by radiation, with a small core convection region. Medium-sized, low mass stars like the Sun have a core region that is stable against convection, with a convection zone near the surface that mixes the outer layers. This results in a steady buildup of a helium-rich core, surrounded by a hydrogen-rich outer region. By contrast, cool, very low-mass stars (below 0.4 solar masses) are convective throughout. Thus the helium produced at the core is distributed across the star, producing a relatively uniform atmosphere and a proportionately longer main sequence lifespan.
As non-fusing helium ash accumulates in the core of a main-sequence star, the reduction in the abundance of hydrogen per unit mass results in a gradual lowering of the fusion rate within that mass. Since it is the outflow of fusion-supplied energy that supports the higher layers of the star, the core is compressed, producing higher temperatures and pressures. Both factors increase the rate of fusion thus moving the equilibrium towards a smaller, denser, hotter core producing more energy whose increased outflow pushes the higher layers further out. Thus there is a steady increase in the luminosity and radius of the star over time. For example, the luminosity of the early Sun was only about 70% of its current value. As a star ages this luminosity increase changes its position on the HR diagram. This effect results in a broadening of the main sequence band because stars are observed at random stages in their lifetime. That is, the main sequence band develops a thickness on the HR diagram; it is not simply a narrow line.
Other factors that broaden the main sequence band on the HR diagram include uncertainty in the distance to stars and the presence of unresolved binary stars that can alter the observed stellar parameters. However, even perfect observation would show a fuzzy main sequence because mass is not the only parameter that affects a star's color and luminosity. Variations in chemical composition caused by the initial abundances, the star's evolutionary status, interaction with a close companion, rapid rotation, or a magnetic field can all slightly change a main-sequence star's HR diagram position, to name just a few factors. As an example, there are metal-poor stars (with a very low abundance of elements with higher atomic numbers than helium) that lie just below the main sequence and are known as subdwarfs. These stars are fusing hydrogen in their cores and so they mark the lower edge of main sequence fuzziness caused by variance in chemical composition.
A nearly vertical region of the HR diagram, known as the instability strip, is occupied by pulsating variable stars known as Cepheid variables. These stars vary in magnitude at regular intervals, giving them a pulsating appearance. The strip intersects the upper part of the main sequence in the region of class A
stars, which are between one and two solar masses. Pulsating stars in this part of the instability strip that intersects the upper part of the main sequence are called Delta Scuti variables. Main-sequence stars in this region experience only small changes in magnitude and so this variation is difficult to detect. Other classes of unstable main-sequence stars, like Beta Cephei variables, are unrelated to this instability strip.
The total amount of energy that a star can generate through nuclear fusion of hydrogen is limited by the amount of hydrogen fuel that can be consumed at the core. For a star in equilibrium, the energy generated at the core must be at least equal to the energy radiated at the surface. Since the luminosity gives the amount of energy radiated per unit time, the total life span can be estimated, to first approximation, as the total energy produced divided by the star's luminosity.
For a star with at least 0.5 solar masses, once the hydrogen supply in its core is exhausted and it expands to become a red giant, it can start to fuse helium atoms to form carbon. The energy output of the helium fusion process per unit mass is only about a tenth the energy output of the hydrogen process, and the luminosity of the star increases. This results in a much shorter length of time in this stage compared to the main sequence lifetime. (For example, the Sun is predicted to spend burning helium, compared to about 12 billion years burning hydrogen.) Thus, about 90% of the observed stars above 0.5 solar masses will be on the main sequence. On average, main-sequence stars are known to follow an empirical mass-luminosity relationship. The luminosity (L
) of the star is roughly proportional to the total mass (M
) as the following power law:
This relationship applies to main-sequence stars in the range 0.1–50 solar masses.
The amount of fuel available for nuclear fusion is proportional to the mass of the star. Thus, the lifetime of a star on the main sequence can be estimated by comparing it to solar evolutionary models. The Sun has been a main-sequence star for about 4.5 billion years and it will become a red giant in 6.5 billion years, for a total main sequence lifetime of roughly 1010 years. Hence:
are the mass and luminosity of the star, respectively,
is a solar mass,
is the solar luminosity and
is the star's estimated main sequence lifetime.
Although more massive stars have more fuel to burn and might be expected to last longer, they also must radiate a proportionately greater amount with increased mass. Thus, the most massive stars may remain on the main sequence for only a few million years, while stars with less than a tenth of a solar mass may last for over a trillion years.
The exact mass-luminosity relationship depends on how efficiently energy can be transported from the core to the surface. A higher opacity has an insulating effect that retains more energy at the core, so the star does not need to produce as much energy to remain in hydrostatic equilibrium. By contrast, a lower opacity means energy escapes more rapidly and the star must burn more fuel to remain in equilibrium. Note, however, that a sufficiently high opacity can result in energy transport via convection, which changes the conditions needed to remain in equilibrium.
In high-mass main-sequence stars, the opacity is dominated by electron scattering, which is nearly constant with increasing temperature. Thus the luminosity only increases as the cube of the star's mass. For stars below 10 times the solar mass, the opacity becomes dependent on temperature, resulting in the luminosity varying approximately as the fourth power of the star's mass. For very low mass stars, molecules in the atmosphere also contribute to the opacity. Below about 0.5 solar masses, the luminosity of the star varies as the mass to the power of 2.3, producing a flattening of the slope on a graph of mass versus luminosity. Even these refinements are only an approximation, however, and the mass-luminosity relation can vary depending on a star's composition.
Once a main-sequence star consumes the hydrogen at its core, the loss of energy generation causes gravitational collapse to resume. For stars with less than 0.23 solar masses, they are predicted to become white dwarfs once energy generation by nuclear fusion of hydrogen at the core comes to a halt. For stars above this threshold with up to 10 solar masses, the hydrogen surrounding the helium core reaches sufficient temperature and pressure to undergo fusion, forming a hydrogen-burning shell. In consequence of this change, the outer envelope of the star expands and decreases in temperature, turning it into a red giant. At this point the star is evolving off the main sequence and entering the giant branch. The path the star now follows across the HR diagram, to the upper right of the main sequence, is called an evolutionary track.
The helium core of a red giant continues to collapse until it is entirely supported by electron degeneracy pressure—a quantum mechanical effect that restricts how closely matter can be compacted. For stars of more than about 0.5 solar masses, the core can reach a temperature where it becomes hot enough to burn helium into carbon via the triple alpha process. Stars with more than 5–7.5 solar masses can also fuse elements with higher atomic numbers. For stars with ten or more solar masses, this process can lead to an increasingly dense core that finally collapses, ejecting the star's overlying layers in a Type II supernova explosion, Type Ib supernova or Type Ic supernova.
When a cluster of stars is formed at about the same time, the life span of these stars will depend on their individual masses. The most massive stars will leave the main sequence first, followed steadily in sequence by stars of ever lower masses. Thus the stars will evolve in order of their position on the main sequence, proceeding from the most massive at the left toward the right of the HR diagram. The current position where stars in this cluster are leaving the main sequence is known as the turn-off point. By knowing the main sequence lifespan of stars at this point, it becomes possible to estimate the age of the cluster.
The solar mass
) is a standard unit of mass in astronomy that is used to indicate the masses of other stars, as well as clusters, nebulae and galaxies. It is equal to the mass of the Sun, about two nonillion kilograms:
The above mass is about 332,946 times the mass of the Earth or 1,048 times the mass of Jupiter.
Because the Earth follows an elliptical orbit around the Sun, its solar mass can be computed from the equation for the orbital period of a small body orbiting a central mass. Based upon the length of the year, the distance from the Earth to the Sun (an astronomical unit or AU), and the gravitational constant (G
), the mass of the Sun is given by:
The value of the gravitational constant was derived from measurements that were made by Henry Cavendish in 1798 from his using a torsion balance. The value he obtained differed only by about 1% from the modern value. The diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769, yielding a value of 9″ (compared to the present 1976 value of 8.794148″). If we know the value of the diurnal parallax, we can determine the distance to the Sun from the geometry of the Earth.
The first person to estimate the mass of the Sun was Isaac Newton. In his work Principia
, he estimated that the ratio of the mass of the Earth to the Sun was about 1/28,700. Then later he determined that his value was based upon a faulty value for the solar parallax, which he had used to estimate the distance to the Sun (1 AU). So, he revised his result to obtain a ratio of 1/169,282 in the third edition of the Principia
. The current estimated value for the solar parallax is smaller still, giving us a mass ratio of 1/332,946.
As a unit of measurement, the solar mass came into use before the AU and the gravitational constant were precisely measured. This is because the determination of the relative mass of another planet in the Solar System or of a binary star in units of solar masses does not depend on these poorly known constants. So it was useful to express these masses in units of solar masses (see Gaussian gravitational constant).
The mass of the Sun changes slowly, compared to the lifetime of the Sun. Mass is lost due to two main processes in nearly equal amounts. First, in the Sun's core hydrogen is converted into helium by nuclear fusion, in particular the pp chain. Thereby mass is converted to energy in correspondence to the mass–energy equivalence. This energy is eventually radiated away by the Sun. The second process is the solar wind, which is the ejection of mainly protons and electrons to outer space. The actual net mass of the Sun since it reached the main sequence remains uncertain. The early Sun had much higher mass loss rates than at present, so, realistically, it may have lost anywhere from 1–7% of its total mass over the course of its main-sequence lifetime. The Sun also gains mass when foreign bodies such as asteroids and comets crash into it. Because the Sun already holds 99.86% of the Solar System's total mass, foreign body impacts are not expected to offset its loss of mass by the two aforementioned processes.
One solar mass, M☉
, can be converted to related units:
It is also frequently useful in general relativity to express mass in units of length or time.
A white dwarf, also called a degenerate dwarf, is a stellar remnant composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun, and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored thermal energy. The nearest known white dwarf is Sirius B, 8.6 light years away, the smaller component of the Sirius binary star. There are currently thought to be eight white dwarfs among the hundred star systems nearest the Sun. The unusual faintness of white dwarfs was first recognized in 1910 by Henry Norris Russell, Edward Charles Pickering, and Williamina Fleming;, p. 1 the name white dwarf was coined by Willem Luyten in 1922.
White dwarfs are thought to be the final evolutionary state of all stars whose mass is not high enough to become a neutron star—over 97% of the stars in the Milky Way., §1. After the hydrogen–fusing lifetime of a main-sequence star of low or medium mass ends, it will expand to a red giant which fuses helium to carbon and oxygen in its core by the triple-alpha process. If a red giant has insufficient mass to generate the core temperatures required to fuse carbon, around 1 billion K, an inert mass of carbon and oxygen will build up at its center. After shedding its outer layers to form a planetary nebula, it will leave behind this core, which forms the remnant white dwarf. Usually, therefore, white dwarfs are composed of carbon and oxygen. If the mass of the progenitor is above 8 solar masses but below 10.5 solar masses, the core temperature suffices to fuse carbon but not neon, in which case an oxygen-neon–magnesium white dwarf may be formed. Also, some helium white dwarfs appear to have been formed by mass loss in binary systems.
The material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy, nor is it supported by the heat generated by fusion against gravitational collapse. It is supported only by electron degeneracy pressure, causing it to be extremely dense. The physics of degeneracy yields a maximum mass for a non-rotating white dwarf, the Chandrasekhar limit—approximately 1.4 solar masses—beyond which it cannot be supported by electron degeneracy pressure. A carbon-oxygen white dwarf that approaches this mass limit, typically by mass transfer from a companion star, may explode as a Type Ia supernova via a process known as carbon detonation. (SN 1006 is thought to be a famous example.)
A white dwarf is very hot when it is formed, but since it has no source of energy, it will gradually radiate away its energy and cool down. This means that its radiation, which initially has a high color temperature, will lessen and redden with time. Over a very long time, a white dwarf will cool to temperatures at which it will no longer emit significant heat or light, and it will become a cold black dwarf. However, the length of time it takes for a white dwarf to reach this state is calculated to be longer than the current age of the Universe (approximately 13.8 billion years), and since no white dwarf can be older than the age of the Universe; it is thought that no black dwarfs exist yet. Also, even the oldest white dwarfs still radiate at temperatures of a few thousand kelvins.
The first white dwarf discovered was in the triple star system of 40 Eridani, which contains the relatively bright main sequence star 40 Eridani A, orbited at a distance by the closer binary system of the white dwarf 40 Eridani B and the main sequence red dwarf 40 Eridani C. The pair 40 Eridani B/C was discovered by William Herschel on 31 January 1783;, p. 73 it was again observed by Friedrich Georg Wilhelm Struve in 1825 and by Otto Wilhelm von Struve in 1851. In 1910, Henry Norris Russell, Edward Charles Pickering and Williamina Fleming discovered that, despite being a dim star, 40 Eridani B was of spectral type A, or white. In 1939, Russell looked back on the discovery:, p. 1
I was visiting my friend and generous benefactor, Prof. Edward C. Pickering. With characteristic kindness, he had volunteered to have the spectra observed for all the stars—including comparison stars—which had been observed in the observations for stellar parallax which Hinks and I made at Cambridge, and I discussed. This piece of apparently routine work proved very fruitful—it led to the discovery that all the stars of very faint absolute magnitude were of spectral class M. In conversation on this subject (as I recall it), I asked Pickering about certain other faint stars, not on my list, mentioning in particular 40 Eridani B. Characteristically, he sent a note to the Observatory office and before long the answer came (I think from Mrs Fleming) that the spectrum of this star was A. I knew enough about it, even in these paleozoic days, to realize at once that there was an extreme inconsistency between what we would then have called "possible" values of the surface brightness and density. I must have shown that I was not only puzzled but crestfallen, at this exception to what looked like a very pretty rule of stellar characteristics; but Pickering smiled upon me, and said: "It is just these exceptions that lead to an advance in our knowledge", and so the white dwarfs entered the realm of study!
The spectral type of 40 Eridani B was officially described in 1914 by Walter Adams.
The companion of Sirius, Sirius B, was next to be discovered. During the nineteenth century, positional measurements of some stars became precise enough to measure small changes in their location. Friedrich Bessel used position measurements to determine that the stars Sirius (α Canis Majoris) and Procyon (α Canis Minoris) were changing their positions periodically. In 1844 he predicted that both stars had unseen companions:
If we were to regard Sirius and Procyon as double stars, the change of their motions would not surprise us; we should acknowledge them as necessary, and have only to investigate their amount by observation. But light is no real property of mass. The existence of numberless visible stars can prove nothing against the existence of numberless invisible ones.
Bessel roughly estimated the period of the companion of Sirius to be about half a century; C. A. F. Peters computed an orbit for it in 1851. It was not until 31 January 1862 that Alvan Graham Clark observed a previously unseen star close to Sirius, later identified as the predicted companion. Walter Adams announced in 1915 that he had found the spectrum of Sirius B to be similar to that of Sirius.
In 1917, Adriaan Van Maanen discovered Van Maanen's Star, an isolated white dwarf. These three white dwarfs, the first discovered, are the so-called classical white dwarfs., p. 2 Eventually, many faint white stars were found which had high proper motion, indicating that they could be suspected to be low-luminosity stars close to the Earth, and hence white dwarfs. Willem Luyten appears to have been the first to use the term white dwarf when he examined this class of stars in 1922; the term was later popularized by Arthur Stanley Eddington. Despite these suspicions, the first non-classical white dwarf was not definitely identified until the 1930s. 18 white dwarfs had been discovered by 1939., p. 3 Luyten and others continued to search for white dwarfs in the 1940s. By 1950, over a hundred were known, and by 1999, over 2,000 were known. Since then the Sloan Digital Sky Survey has found over 9,000 white dwarfs, mostly new.
Although white dwarfs are known with estimated masses as low as 0.17 and as high as 1.33 solar masses, the mass distribution is strongly peaked at 0.6 solar mass, and the majority lie between 0.5 to 0.7 solar mass. The estimated radii of observed white dwarfs, however, are typically between 0.008 and 0.02 times the radius of the Sun; this is comparable to the Earth's radius of approximately 0.009 solar radius. A white dwarf, then, packs mass comparable to the Sun's into a volume that is typically a million times smaller than the Sun's; the average density of matter in a white dwarf must therefore be, very roughly, 1,000,000 times greater than the average density of the Sun, or approximately 106 3g/cm, or 1 tonne per cubic centimetre. White dwarfs are composed of one of the densest forms of matter known, surpassed only by other compact stars such as neutron stars, black holes and, hypothetically, quark stars.
White dwarfs were found to be extremely dense soon after their discovery. If a star is in a binary system, as is the case for Sirius B and 40 Eridani B, it is possible to estimate its mass from observations of the binary orbit. This was done for Sirius B by 1910, yielding a mass estimate of 0.94 solar mass. (A more modern estimate is 1.00 solar mass.) Since hotter bodies radiate more than colder ones, a star's surface brightness can be estimated from its effective surface temperature, and hence from its spectrum. If the star's distance is known, its overall luminosity can also be estimated. Comparison of the two figures yields the star's radius. Reasoning of this sort led to the realization, puzzling to astronomers at the time, that Sirius B and 40 Eridani B must be very dense. For example, when Ernst Öpik estimated the density of a number of visual binary stars in 1916, he found that 40 Eridani B had a density of over 25,000 times the Sun's, which was so high that he called it "impossible". As Arthur Stanley Eddington put it later in 1927:, p. 50
We learn about the stars by receiving and interpreting the messages which their light brings to us. The message of the Companion of Sirius when it was decoded ran: "I am composed of material 3,000 times denser than anything you have ever come across; a ton of my material would be a little nugget that you could put in a matchbox." What reply can one make to such a message? The reply which most of us made in 1914 was—"Shut up. Don't talk nonsense."
As Eddington pointed out in 1924, densities of this order implied that, according to the theory of general relativity, the light from Sirius B should be gravitationally redshifted. This was confirmed when Adams measured this redshift in 1925.
Such densities are possible because white dwarf material is not composed of atoms bound by chemical bonds, but rather consists of a plasma of unbound nuclei and electrons. There is therefore no obstacle to placing nuclei closer to each other than electron orbitals—the regions occupied by electrons bound to an atom—would normally allow. Eddington, however, wondered what would happen when this plasma cooled and the energy which kept the atoms ionized was no longer present. This paradox was resolved by R. H. Fowler in 1926 by an application of the newly devised quantum mechanics. Since electrons obey the Pauli exclusion principle, no two electrons can occupy the same state, and they must obey Fermi–Dirac statistics, also introduced in 1926 to determine the statistical distribution of particles which satisfy the Pauli exclusion principle. At zero temperature, therefore, electrons could not all occupy the lowest-energy, or ground, state; some of them had to occupy higher-energy states, forming a band of lowest-available energy states, the Fermi sea. This state of the electrons, called degenerate, meant that a white dwarf could cool to zero temperature and still possess high energy.
Compression of a white dwarf will increase the number of electrons in a given volume. Applying the Pauli exclusion principle, we can see that this will increase the kinetic energy of the electrons, causing pressure. This electron degeneracy pressure is what supports a white dwarf against gravitational collapse. It depends only on density and not on temperature. Degenerate matter is relatively compressible; this means that the density of a high-mass white dwarf is so much greater than that of a low-mass white dwarf that the radius of a white dwarf decreases as its mass increases.
The existence of a limiting mass that no white dwarf can exceed is another consequence of being supported by electron degeneracy pressure. These masses were first published in 1929 by Wilhelm Anderson and in 1930 by Edmund C. Stoner. The modern value of the limit was first published in 1931 by Subrahmanyan Chandrasekhar in his paper "The Maximum Mass of Ideal White Dwarfs". For a nonrotating white dwarf, it is equal to approximately solar masses, where is the average molecular weight per electron of the star., eq. (63) As the carbon-12 and oxygen-16 which predominantly compose a carbon-oxygen white dwarf both have atomic number equal to half their atomic weight, one should take equal to 2 for such a star, leading to the commonly quoted value of 1.4 solar masses. (Near the beginning of the 20th century, there was reason to believe that stars were composed chiefly of heavy elements,, p. 955 so, in his 1931 paper, Chandrasekhar set the average molecular weight per electron, , equal to 2.5, giving a limit of 0.91 solar mass.) Together with William Alfred Fowler, Chandrasekhar received the Nobel prize for this and other work in 1983. The limiting mass is now called the Chandrasekhar limit.
If a white dwarf were to exceed the Chandrasekhar limit, and nuclear reactions did not take place, the pressure exerted by electrons would no longer be able to balance the force of gravity, and it would collapse into a denser object such as a neutron star. However, carbon-oxygen white dwarfs accreting mass from a neighboring star undergo a runaway nuclear fusion reaction, which leads to a Type Ia supernova explosion in which the white dwarf is destroyed, just before reaching the limiting mass.
New research indicates that many white dwarfs—at least in certain types of galaxies—may not approach that limit by way of accretion. In a paper published in the journal Nature in February 2010, astronomers Marat Gilfanov and Akos Bogdan, both of the Max Planck Institute for Astrophysics in Garching, Germany, postulated that at least some of the white dwarfs that become supernovae attain the necessary mass not by accretion but by colliding with one another. Gilfanov and Bogdan said that in elliptical galaxies such collisions are the major source of supernovae. Their hypothesis is based on the fact that the x-rays produced by the white dwarfs' accretion of matter—measured using NASA's Chandra X-Ray Observatory—are no more than 1/30 to 1/50 of what would be expected to be produced by an amount of matter falling onto a population of accreting white dwarfs sufficient to produce supernovae at the observed rate. The two astronomers concluded that no more than 5 percent of the supernovae in such galaxies could be created by the process of accretion onto white dwarfs. The significance of this finding is that there could be two types of supernovae, which could mean that the Chandrasekhar limit might not always apply in determining when a white dwarf goes supernova, given that two colliding white dwarfs could have a range of masses. This in turn would confuse efforts to use exploding white dwarfs as standard candles in determining distances across the universe.
White dwarfs have low luminosity and therefore occupy a strip at the bottom of the Hertzsprung–Russell diagram, a graph of stellar luminosity versus color (or temperature). They should not be confused with low-luminosity objects at the low-mass end of the main sequence, such as the hydrogen-fusing red dwarfs, whose cores are supported in part by thermal pressure, or the even lower-temperature brown dwarfs.
It is simple to derive a rough relationship between the mass and radii of white dwarfs using an energy minimization argument. The energy of the white dwarf can be approximated by taking it to be the sum of its gravitational potential energy and kinetic energy. The gravitational potential energy of a unit mass piece of white dwarf, , will be on the order of , where is the gravitational constant, M is the mass of the white dwarf, and is its radius. The kinetic energy of the unit mass, , will primarily come from the motion of electrons, so it will be approximately , where is the average electron momentum, is the electron mass, and is the number of electrons per unit mass. Since the electrons are degenerate, we can estimate to be on the order of the uncertainty in momentum, , given by the uncertainty principle, which says that is on the order of the reduced Planck constant, ħ. will be on the order of the average distance between electrons, which will be approximately , i.e., the reciprocal of the cube root of the number density, , of electrons per unit volume. Since there are electrons in the white dwarf and its volume is on the order of , will be on the order of .
Solving for the kinetic energy per unit mass, Ek, we find that
The white dwarf will be at equilibrium when its total energy, , is minimized. At this point, the kinetic and gravitational potential energies should be comparable, so we may derive a rough mass-radius relationship by equating their magnitudes:
Solving this for the radius, , gives
Dropping , which depends only on the composition of the white dwarf, and the universal constants leaves us with a relationship between mass and radius:
i.e., the radius of a white dwarf is inversely proportional to the cube root of its mass.
Since this analysis uses the non-relativistic formula for the kinetic energy, it is non-relativistic. If we wish to analyze the situation where the electron velocity in a white dwarf is close to the speed of light, , we should replace by the extreme relativistic approximation for the kinetic energy. With this substitution, we find
If we equate this to the magnitude of , we find that drops out and the mass, , is forced to be
To interpret this result, observe that as we add mass to a white dwarf, its radius will decrease, so, by the uncertainty principle, the momentum, and hence the velocity, of its electrons will increase. As this velocity approaches , the extreme relativistic analysis becomes more exact, meaning that the mass of the white dwarf must approach . Therefore, no white dwarf can be heavier than the limiting mass , or 1.4 Solar masses.
For a more accurate computation of the mass-radius relationship and limiting mass of a white dwarf, one must compute the equation of state which describes the relationship between density and pressure in the white dwarf material. If the density and pressure are both set equal to functions of the radius from the center of the star, the system of equations consisting of the hydrostatic equation together with the equation of state can then be solved to find the structure of the white dwarf at equilibrium. In the non-relativistic case, we will still find that the radius is inversely proportional to the cube root of the mass., eq. (80) Relativistic corrections will alter the result so that the radius becomes zero at a finite value of the mass. This is the limiting value of the mass—called the Chandrasekhar limit—at which the white dwarf can no longer be supported by electron degeneracy pressure. The graph on the right shows the result of such a computation. It shows how radius varies with mass for non-relativistic (blue curve) and relativistic (green curve) models of a white dwarf. Both models treat the white dwarf as a cold Fermi gas in hydrostatic equilibrium. The average molecular weight per electron, , has been set equal to 2. Radius is measured in standard solar radii and mass in standard solar masses.
These computations all assume that the white dwarf is non-rotating. If the white dwarf is rotating, the equation of hydrostatic equilibrium must be modified to take into account the centrifugal pseudo-force arising from working in a rotating frame. For a uniformly rotating white dwarf, the limiting mass increases only slightly. However, if the star is allowed to rotate nonuniformly, and viscosity is neglected, then, as was pointed out by Fred Hoyle in 1947, there is no limit to the mass for which it is possible for a model white dwarf to be in static equilibrium. Not all of these model stars, however, will be dynamically stable.
The degenerate matter that makes up the bulk of a white dwarf has a very low opacity, because any absorption of a photon requires an electron transition to a higher empty state, which may not be available given the energy of the photon; it also has a high thermal conductivity. As a result, the interior of the white dwarf maintains a constant temperature, approximately 107 K. However, an outer shell of non-degenerate matter cools from approximately 107 K to 104 K. This matter radiates roughly as a black body to determine the visible color of the white dwarf. A white dwarf remains visible for a long time, because it radiates as a roughly 104 K body, while its interior is at 107 K.
The visible radiation emitted by white dwarfs varies over a wide color range, from the blue-white color of an O-type main sequence star to the red of a M-type red dwarf. White dwarf effective surface temperatures extend from over 150,000 K to barely under 4,000 K. In accordance with the Stefan–Boltzmann law, luminosity increases with increasing surface temperature; this surface temperature range corresponds to a luminosity from over 100 times the Sun's to under 1/10,000 that of the Sun's. Hot white dwarfs, with surface temperatures in excess of 30,000 K, have been observed to be sources of soft (i.e., lower-energy) X-rays. This enables the composition and structure of their atmospheres to be studied by soft X-ray and extreme ultraviolet observations.
As was explained by Leon Mestel in 1952, unless the white dwarf accretes matter from a companion star or other source, its radiation comes from its stored heat, which is not replenished., §2.1. White dwarfs have an extremely small surface area to radiate this heat from, so they cool gradually, remaining hot for a long time. As a white dwarf cools, its surface temperature decreases, the radiation which it emits reddens, and its luminosity decreases. Since the white dwarf has no energy sink other than radiation, it follows that its cooling slows with time. Pierre Bergeron, Maria Tereza Ruiz, and Sandy Leggett, for example, estimate that after a carbon white dwarf of 0.59 solar mass with a hydrogen atmosphere has cooled to a surface temperature of 7,140 K, taking approximately 1.5 billion years, cooling approximately 500 more kelvins to 6,590 K takes around 0.3 billion years, but the next two steps of around 500 kelvins (to 6,030 K and 5,550 K) take first 0.4 and then 1.1 billion years., Table 2. Although white dwarf material is initially plasma—a fluid composed of nuclei and electrons—it was theoretically predicted in the 1960s that at a late stage of cooling, it should crystallize, starting at the center of the star. The crystal structure is thought to be a body-centered cubic lattice. In 1995 it was pointed out that asteroseismological observations of pulsating white dwarfs yielded a potential test of the crystallization theory, and in 2004, Antonio Kanaan, Travis Metcalfe and a team of researchers with the Whole Earth Telescope estimated, on the basis of such observations, that approximately 90% of the mass of BPM 37093 had crystallized. Other work gives a crystallized mass fraction of between 32% and 82%.
Most observed white dwarfs have relatively high surface temperatures, between 8,000 K and 40,000 K. A white dwarf, though, spends more of its lifetime at cooler temperatures than at hotter temperatures, so we should expect that there are more cool white dwarfs than hot white dwarfs. Once we adjust for the selection effect that hotter, more luminous white dwarfs are easier to observe, we do find that decreasing the temperature range examined results in finding more white dwarfs. This trend stops when we reach extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below 4,000 K, and one of the coolest so far observed, WD 0346+246, has a surface temperature of approximately 3,900 K. The reason for this is that, as the Universe's age is finite, there has not been time for white dwarfs to cool down below this temperature. The white dwarf luminosity function can therefore be used to find the time when stars started to form in a region; an estimate for the age of the Galactic disk found in this way is 8 billion years.
A white dwarf will eventually, in many trillion years, cool and become a non-radiating black dwarf in approximate thermal equilibrium with its surroundings and with the cosmic background radiation. However, no black dwarfs are thought to exist yet.
Although most white dwarfs are thought to be composed of carbon and oxygen, spectroscopy typically shows that their emitted light comes from an atmosphere which is observed to be either hydrogen-dominated or helium-dominated. The dominant element is usually at least 1,000 times more abundant than all other elements. As explained by Schatzman in the 1940s, the high surface gravity is thought to cause this purity by gravitationally separating the atmosphere so that heavy elements are on the bottom and lighter ones on top., §5–6 This atmosphere, the only part of the white dwarf visible to us, is thought to be the top of an envelope which is a residue of the star's envelope in the AGB phase and may also contain material accreted from the interstellar medium. The envelope is believed to consist of a helium-rich layer with mass no more than 1/100 of the star's total mass, which, if the atmosphere is hydrogen-dominated, is overlain by a hydrogen-rich layer with mass approximately 1/10,000 of the stars total mass., §4–5.
Although thin, these outer layers determine the thermal evolution of the white dwarf. The degenerate electrons in the bulk of a white dwarf conduct heat well. Most of a white dwarf's mass is therefore almost isothermal, and it is also hot: a white dwarf with surface temperature between 8,000 K and 16,000 K will have a core temperature between approximately 5,000,000 K and 20,000,000 K. The white dwarf is kept from cooling very quickly only by its outer layers' opacity to radiation.
The first attempt to classify white dwarf spectra appears to have been by G. P. Kuiper in 1941, and various classification schemes have been proposed and used since then. The system currently in use was introduced by Edward M. Sion, Jesse L. Greenstein and their coauthors in 1983 and has been subsequently revised several times. It classifies a spectrum by a symbol which consists of an initial D, a letter describing the primary feature of the spectrum followed by an optional sequence of letters describing secondary features of the spectrum (as shown in the table to the right), and a temperature index number, computed by dividing 50,400 K by the effective temperature. For example:
The symbols ? and : may also be used if the correct classification is uncertain.
White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority (approximately 80%) of all observed white dwarfs. The next class in number is of DBs (approximately 16%). A small fraction (roughly 0.1%) have carbon-dominated atmospheres, the hot (above 15,000 K) DQ class. Those classified as DB, DC, DO, DZ, and cool DQ have helium-dominated atmospheres. Assuming that carbon and metals are not present, which spectral classification is seen depends on the effective temperature. Between approximately 100,000 K to 45,000 K, the spectrum will be classified DO, dominated by singly ionized helium. From 30,000 K to 12,000 K, the spectrum will be DB, showing neutral helium lines, and below about 12,000 K, the spectrum will be featureless and classified DC.,§ 2.4.
Magnetic fields in white dwarfs with a strength at the surface of ~1 million gauss (100 teslas) were predicted by P. M. S. Blackett in 1947 as a consequence of a physical law he had proposed which stated that an uncharged, rotating body should generate a magnetic field proportional to its angular momentum. This putative law, sometimes called the Blackett effect, was never generally accepted, and by the 1950s even Blackett felt it had been refuted., pp. 39–43 In the 1960s, it was proposed that white dwarfs might have magnetic fields because of conservation of total surface magnetic flux during the evolution of a non-degenerate star to a white dwarf. A surface magnetic field of ~100 gauss (0.01 T) in the progenitor star would thus become a surface magnetic field of ~100·1002 = 1 million gauss (100 T) once the star's radius had shrunk by a factor of 100., §8;, p. 484 The first magnetic white dwarf to be observed was GJ 742, which was detected to have a magnetic field in 1970 by its emission of circularly polarized light. It is thought to have a surface field of approximately 300 million gauss (30 kT)., §8 Since then magnetic fields have been discovered in well over 100 white dwarfs, ranging from to 109 gauss (0.2 T to 100 kT). Only a small number of white dwarfs have been examined for fields, and it has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T).
The magnetic fields in a white dwarf star may allow for the existence of a new type of chemical bond, perpendicular paramagnetic bonding, in addition to ionic and covalent bonds, resulting in what has been initially described as "magnetized matter" in research published in 2012.
Early calculations suggested that there might be white dwarfs whose luminosity varied with a period of around 10 seconds, but searches in the 1960s failed to observe this., § 7.1.1; The first variable white dwarf found was HL Tau 76; in 1965 and 1966, Arlo U. Landolt observed it to vary with a period of approximately 12.5 minutes. The reason for this period being longer than predicted is that the variability of HL Tau 76, like that of the other pulsating variable white dwarfs known, arises from non-radial gravity wave pulsations., § 7. Known types of pulsating white dwarf include the DAV, or ZZ Ceti, stars, including HL Tau 76, with hydrogen-dominated atmospheres and the spectral type DA;, pp. 891, 895 DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB;, p. 3525 and GW Vir stars (sometimes subdivided into DOV and PNNV stars), with atmospheres dominated by helium, carbon, and oxygen.,§1.1, 1.2;,§1. GW Vir stars are not, strictly speaking, white dwarfs, but are stars which are in a position on the Hertzsprung-Russell diagram between the asymptotic giant branch and the white dwarf region. They may be called pre-white dwarfs., § 1.1; These variables all exhibit small (1%–30%) variations in light output, arising from a superposition of vibrational modes with periods of hundreds to thousands of seconds. Observation of these variations gives asteroseismological evidence about the interiors of white dwarfs.
White dwarfs are thought to represent the end point of stellar evolution for main-sequence stars with masses from about 0.07 to 10 solar masses. The composition of the white dwarf produced will differ depending on the initial mass of the star.
If the mass of a main-sequence star is lower than approximately half a solar mass, it will never become hot enough to fuse helium at its core. It is thought that, over a lifespan exceeding the age (~13.8 billion years) of the Universe, such a star will eventually burn all its hydrogen and end its evolution as a helium white dwarf composed chiefly of helium-4 nuclei. Owing to the time this process takes, it is not thought to be the origin of observed helium white dwarfs. Rather, they are thought to be the product of mass loss in binary systems or mass loss due to a large planetary companion.
If the mass of a main-sequence star is between approximately 0.5 and 8 solar masses, its core will become sufficiently hot to fuse helium into carbon and oxygen via the triple-alpha process, but it will never become sufficiently hot to fuse carbon into neon. Near the end of the period in which it undergoes fusion reactions, such a star will have a carbon-oxygen core which does not undergo fusion reactions, surrounded by an inner helium-burning shell and an outer hydrogen-burning shell. On the Hertzsprung-Russell diagram, it will be found on the asymptotic giant branch. It will then expel most of its outer material, creating a planetary nebula, until only the carbon-oxygen core is left. This process is responsible for the carbon-oxygen white dwarfs which form the vast majority of observed white dwarfs.
If a star is massive enough, its core will eventually become sufficiently hot to fuse carbon to neon, and then to fuse neon to iron. Such a star will not become a white dwarf, because the mass of its central, non-fusing core, supported by electron degeneracy pressure, will eventually exceed the largest possible mass supportable by degeneracy pressure. At this point the core of the star will collapse and it will explode in a core-collapse supernova which will leave behind a remnant neutron star, black hole, or possibly a more exotic form of compact star. Some main-sequence stars, of perhaps 8 to 10 solar masses, although sufficiently massive to fuse carbon to neon and magnesium, may be insufficiently massive to fuse neon. Such a star may leave a remnant white dwarf composed chiefly of oxygen, neon, and magnesium, provided that its core does not collapse, and provided that fusion does not proceed so violently as to blow apart the star in a supernova. Although some isolated white dwarfs have been identified which may be of this type, most evidence for the existence of such stars comes from the novae called ONeMg or neon novae. The spectra of these novae exhibit abundances of neon, magnesium, and other intermediate-mass elements which appear to be only explicable by the accretion of material onto an oxygen-neon-magnesium white dwarf.
A white dwarf is stable once formed and will continue to cool almost indefinitely; eventually, it will become a black white dwarf, also called a black dwarf. Assuming that the Universe continues to expand, it is thought that in 1019 to 1020 years, the galaxies will evaporate as their stars escape into intergalactic space., §IIIA. White dwarfs should generally survive this, although an occasional collision between white dwarfs may produce a new fusing star or a super-Chandrasekhar mass white dwarf which will explode in a Type Ia supernova., §IIIC, IV. The subsequent lifetime of white dwarfs is thought to be on the order of the lifetime of the proton, known to be at least 1032 years. Some simple grand unified theories predict a proton lifetime of no more than 1049 years. If these theories are not valid, the proton may decay by more complicated nuclear processes, or by quantum gravitational processes involving a virtual black hole; in these cases, the lifetime is estimated to be no more than 10200 years. If protons do decay, the mass of a white dwarf will decrease very slowly with time as its nuclei decay, until it loses enough mass to become a nondegenerate lump of matter, and finally disappears completely., §IV.
A white dwarf's stellar and planetary system is inherited from its progenitor star and may interact with the white dwarf in various ways. Infrared spectroscopic observations made by NASA's Spitzer Space Telescope of the central star of the Helix Nebula suggest the presence of a dust cloud, which may be caused by cometary collisions. It is possible that infalling material from this may cause X-ray emission from the central star. Similarly, observations made in 2004 indicated the presence of a dust cloud around the young white dwarf star G29-38 (estimated to have formed from its AGB progenitor about 500 million years ago), which may have been created by tidal disruption of a comet passing close to the white dwarf.
It has been proposed that white dwarfs with surface temperatures of less than 10,000 Kelvin could harbor a habitable zone at a distance between ~0.005 to 0.02 AU that would last 3 billion years. The goal is to search for transits of hypothetical Earth-like planets that could have migrated inward and/or formed there. As a white dwarf has a size similar to that of a planet, these kinds of transits would produce strong eclipses.
If a white dwarf is in a binary star system and is accreting matter from its companion, a variety of phenomena may occur, including novae and Type Ia supernovae. It may also be a super-soft x-ray source if it is able to take material from its companion fast enough to sustain fusion on its surface. A close binary system of two white dwarfs can radiate energy in the form of gravitational waves, causing their mutual orbit to steadily shrink until the stars merge.
The mass of an isolated, nonrotating white dwarf cannot exceed the Chandrasekhar limit of ~1.4 solar masses. (This limit may increase if the white dwarf is rotating rapidly and nonuniformly.) White dwarfs in binary systems, however, can accrete material from a companion star, increasing both their mass and their density. As their mass approaches the Chandrasekhar limit, this could theoretically lead to either the explosive ignition of fusion in the white dwarf or its collapse into a neutron star.
Accretion provides the currently favored mechanism, the single-degenerate model, for Type Ia supernovae. In this model, a carbon–oxygen white dwarf accretes material from a companion star,, p. 14. increasing its mass and compressing its core. It is believed that compressional heating of the core leads to ignition of carbon fusion as the mass approaches the Chandrasekhar limit. Because the white dwarf is supported against gravity by quantum degeneracy pressure instead of by thermal pressure, adding heat to the star's interior increases its temperature but not its pressure, so the white dwarf does not expand and cool in response. Rather, the increased temperature accelerates the rate of the fusion reaction, in a runaway process that feeds on itself. The thermonuclear flame consumes much of the white dwarf in a few seconds, causing a Type Ia supernova explosion that obliterates the star. In another possible mechanism for Type Ia supernovae, the double-degenerate model, two carbon-oxygen white dwarfs in a binary system merge, creating an object with mass greater than the Chandrasekhar limit in which carbon fusion is then ignited., p. 14.
Observations have failed to note signs of accretion leading up to Type Ia supernovae, and this is now thought to be because the star is first loaded up to above the Chandrasekhar limit while also being spun up to a very fast rate by the same process. Once the accretion stops the star gradually slows down until the spin is no longer fast enough to prevent the explosion.
Before accretion of material pushes a white dwarf close to the Chandrasekhar limit, accreted hydrogen-rich material on the surface may ignite in a less destructive type of thermonuclear explosion powered by hydrogen fusion. Since the white dwarf's core remains intact, these surface explosions can be repeated as long as accretion continues. This weaker kind of repetitive cataclysmic phenomenon is called a (classical) nova. Astronomers have also observed dwarf novae, which have smaller, more frequent luminosity peaks than classical novae. These are thought to be caused by the release of gravitational potential energy when part of the accretion disc collapses onto the star, rather than by fusion. In general, binary systems with a white dwarf accreting matter from a stellar companion are called cataclysmic variables. As well as novae and dwarf novae, several other classes of these variables are known. Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources.
Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only a few million years for the most massive to trillions of years for the least massive, which is considerably longer than the age of the universe. All stars are born from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, becoming what is known as a main-sequence star.
Nuclear fusion powers a star for most of its life. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star. Later, as the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core. This process causes the star to gradually grow in size, passing through the subgiant stage until it reaches the red giant phase. Stars with at least half the mass of the Sun can also begin to generate energy through the fusion of helium at their core, whereas more massive stars can fuse heavier elements along a series of concentric shells. Once a star like the Sun has exhausted its nuclear fuel, its core collapses into a dense white dwarf and the outer layers are expelled as a planetary nebula. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into an extremely dense neutron star or black hole. Although the universe is not old enough for any of the smallest red dwarfs to have reached the end of their lives, stellar models suggest they will slowly become brighter and hotter before running out of hydrogen fuel and becoming low-mass white dwarfs.
Stellar evolution is not studied by observing the life of a single star, as most stellar changes occur too slowly to be detected, even over many centuries. Instead, astrophysicists come to understand how stars evolve by observing numerous stars at various points in their lifetime, and by simulating stellar structure using computer models.
Stellar evolution begins with the gravitational collapse of a giant molecular cloud. Typical giant molecular clouds are roughly 100 light-years (9.51014 km) across and contain up to 6,000,000 solar masses (1.21037 kg). As it collapses, a giant molecular cloud breaks into smaller and smaller pieces. In each of these fragments, the collapsing gas releases gravitational potential energy as heat. As its temperature and pressure increase, a fragment condenses into a rotating sphere of superhot gas known as a protostar.
The further development heavily depends on the mass of the evolving protostar; in the following, the protostar mass is compared to the mass of the Sun: 1.0 M☉ (2.01030 kg) means 1 solar mass.
Protostars with masses less than roughly 0.08 M☉ (1.61029 kg) never reach temperatures high enough for nuclear fusion of hydrogen to begin. These are known as brown dwarfs. The International Astronomical Union defines brown dwarfs as stars massive enough to fuse deuterium at some point in their lives (13 Jupiter masses, 2.5 × 1028 kg, or 0.0125 solar masses). Objects smaller than 13 Jupiter masses are classified as sub-brown dwarfs (but if they orbit around another stellar object they are classified as planets). Both types, deuterium-burning and not, shine dimly and die away slowly, cooling gradually over hundreds of millions of years.
For a more massive protostar, the core temperature will eventually reach 10 million kelvin, initiating the proton-proton chain reaction and allowing hydrogen to fuse, first to deuterium and then to helium. In stars of slightly over 1 M☉ (2.01030 kg), the carbon–nitrogen–oxygen fusion reaction (CNO cycle) contributes a large portion of the energy generation. The onset of nuclear fusion leads relatively quickly to a hydrostatic equilibrium in which energy released by the core exerts a "radiation pressure" balancing the weight of the star's matter, preventing further gravitational collapse. The star thus evolves rapidly to a stable state, beginning the main-sequence phase of its evolution.
A new star will sit at a specific point on the main sequence of the Hertzsprung–Russell diagram, with the main-sequence spectral type depending upon the mass of the star. Small, relatively cold, low-mass red dwarfs fuse hydrogen slowly and will remain on the main sequence for hundreds of billions of years or longer, whereas massive, hot supergiants will leave the main sequence after just a few million years. A mid-sized star like the Sun will remain on the main sequence for about 10 billion years. The Sun is thought to be in the middle of its lifespan; thus, it is currently on the main sequence.
Eventually the core exhausts its supply of hydrogen and the star begins to evolve off of the main sequence. Without the outward pressure generated by the fusion of hydrogen to counteract the force of gravity the core contracts until either electron degeneracy becomes sufficient to oppose gravity or the core becomes hot enough (around 100 MK) for helium fusion to begin. Which of these happens first depends upon the star's mass.
What happens after a low-mass star ceases to produce energy through fusion has not been directly observed; the universe is thought to be around 13.8 billion years old, which is less time (by several orders of magnitude, in some cases) than it takes for fusion to cease in such stars.
Recent astrophysical models suggest that red dwarfs of 0.1 solar mass may stay on the main sequence for some six to twelve trillion years, gradually increasing in both temperature and luminosity, and take several hundred billion more to slowly collapse into a white dwarf. Such stars are fully convective and will not develop a degenerate helium core with hydrogen burning shells, or at least not until almost the whole star is helium, so they don't ever expand into a red giant.
Slightly more massive stars do expand into red giants, but their helium cores are not massive enough to ever reach the temperatures required for helium fusion so they never reach the tip of the red giant branch. When hydrogen shell burning finishes, these stars move directly off the red giant branch like a post AGB star, but at lower luminosity, to become a white dwarf. A star of about 0.5 solar mass will be able to reach temperatures high enough to fuse helium, and these "mid-sized" stars go on to further stages of evolution beyond the red giant branch.
Stars of roughly 0.5–10 solar masses become red giants, which are large non-main-sequence stars of stellar classification K or M. Red giants lie along the right edge of the Hertzsprung–Russell diagram due to their red color and large luminosity. Examples include Aldebaran in the constellation Taurus and Arcturus in the constellation of Boötes. Red giants all have inert cores with hydrogen-burning shells: concentric layers atop the core that are still fusing hydrogen into helium.
Mid-sized stars are red giants during two different phases of their post-main-sequence evolution: red-giant-branch stars, whose inert cores are made of helium, and asymptotic-giant-branch stars, whose inert cores are made of carbon. Asymptotic-giant-branch stars have helium-burning shells inside the hydrogen-burning shells, whereas red-giant-branch stars have hydrogen-burning shells only. In either case, the accelerated fusion in the hydrogen-containing layer immediately over the core causes the star to expand. This lifts the outer layers away from the core, reducing the gravitational pull on them, and they expand faster than the energy production increases. This causes the outer layers of the star to cool, which causes the star to become redder than it was on the main sequence.
The red-giant-branch phase of a star's life follows the main sequence. Initially, the cores of red-giant-branch stars collapse, as the internal pressure of the core is insufficient to balance gravity. This gravitational collapse releases energy, heating concentric shells immediately outside the inert helium core so that hydrogen fusion continues in these shells. The core of an red-giant-branch star of up to a few solar masses stops collapsing when it is dense enough to be supported by electron degeneracy pressure. Once this occurs, the core reaches hydrostatic equilibrium: the electron degeneracy pressure is sufficient to balance gravitational pressure. The core's gravity compresses the hydrogen in the layer immediately above it, causing it to fuse faster than hydrogen would fuse in a main-sequence star of the same mass. This in turn causes the star to become more luminous (from 1,000–10,000 times brighter) and expand; the degree of expansion outstrips the increase in luminosity, causing the effective temperature to decrease.
The expanding outer layers of the star are convective, with the material being mixed by turbulence from near the fusing regions up to the surface of the star. For all but the lowest-mass stars, the fused material has remained deep in the stellar interior prior to this point, so the convecting envelope makes fusion products visible at the star's surface for the first time. At this stage of evolution, the results are subtle, with the largest effects, alterations to the isotopes of hydrogen and helium, being unobservable. The effects of the CNO cycle appear at the surface, with lower 12C/13C ratios and altered proportions of carbon and nitrogen. These are detectable with spectroscopy and have been measured for many evolved stars.
As the hydrogen around the core is consumed, the core absorbs the resulting helium, causing it to contract further, which in turn causes the remaining hydrogen to fuse even faster. This eventually leads to ignition of helium fusion (which includes the triple-alpha process) in the core. In stars of more than approximately solar mass, it can take a billion years or more for the core to reach helium ignition temperatures.
When the temperature and pressure in the core become sufficient to ignite helium fusion, a helium flash will occur if the core is largely supported by electron degeneracy pressure (stars under 1.4 solar mass). In more massive stars, the ignition of helium fusion occurs relatively quietly. Even if a helium flash does occur, the time of very rapid energy release (on the order of 108 Suns) is brief, so that the visible outer layers of the star are relatively undisturbed. The energy released by helium fusion causes the core to expand, so that hydrogen fusion in the overlying layers slows and total energy generation decreases. The star contracts, although not all the way to the main sequence, and it migrates to the horizontal branch on the Hertzsprung–Russell diagram, gradually shrinking in radius and increasing its surface temperature. Core helium flash stars evolve to the red end of the horizontal branch but do not migrate to higher temperatures before they gain a degenerate carbon-oxygen core and start helium shell burning. These stars are often observed as a red clump of stars in the colour-magnitude diagram of a cluster, hotter and less luminous than the red giants. Higher-mass stars with larger helium cores move along the horizontal branch to higher temperatures, some becoming unstable pulsating stars in the yellow instability strip (RR Lyrae variables), whereas some become even hotter and can form a blue tail or blue hook to the horizontal branch. The exact morphology of the horizontal branch depends on parameters such as metallicity, age, and helium content, but the exact details are still being modelled.
After a star has consumed the helium at the core, fusion continues in a shell around a hot core of carbon and oxygen. The star follows the asymptotic giant branch on the Hertzsprung–Russell diagram, paralleling the original red giant evolution, but with even faster energy generation (which lasts for a shorter time). Although helium is being burnt in a shell, the majority of the energy is produced by hydrogen burning in a shell closer to the surface of the star. Helium from these hydrogen burning shells drops towards the center of the star and periodically the energy output from the helium shell increases dramatically. This is known as a thermal pulse and they occur towards the end of the asymptotic-giant-branch phase, sometimes even into the post-asymptotic-giant-branch phase. Depending on mass and composition, there may be several to hundreds of thermal pulses.
There is a phase on the ascent of the asymptotic-giant-branch where a deep convective zone forms and can bring carbon from the core to the surface, This is known as the second dredge up, and in some stars there may even be a third dredge up. In this way a carbon star is formed, very cool and strongly reddened stars showing strong carbon lines in their spectra. A process known as hot bottom burning may convert carbon into oxygen and nitrogen before it can be dredged to the surface, and the interaction between these processes determines the observed luminosities and spectra of carbon stars in particular clusters.
Another well known class of asymptotic-giant-branch stars are the Mira variables, which pulsate with well-defined periods of tens to hundreds of days and large amplitudes up to about 10 magnitudes (in the visual, total luminosity changes by a much smaller amount). In more massive stars the stars become more luminous and the pulsation period is longer, leading to enhanced mass loss, and the stars become heavily obscured at visual wavelengths. These stars can be observed as OH/IR stars, pulsating in the infra-red and showing OH maser activity. These stars are clearly oxygen rich, in contrast to the carbon stars, but both must be produced by dredge ups.
These mid-range stars ultimately reach the tip of the asymptotic-giant-branch and run out of fuel for shell burning. They are not sufficiently massive to start full-scale carbon fusion, so they contract again, going through a period of post-asymptotic-giant-branch superwind to produce a planetary nebula with an extremely hot central star. The central star then cools to a white dwarf. The expelled gas is relatively rich in heavy elements created within the star and may be particularly oxygen or carbon enriched, depending on the type of the star. The gas builds up in an expanding shell called a circumstellar envelope and cools as it moves away from the star, allowing dust particles and molecules to form. With the high infrared energy input from the central star, ideal conditions are formed in these circumstellar envelopes for maser excitation.
It is possible for thermal pulses to be produced once post-asymptotic-giant-branch evolution has begun, producing a variety of unusual and poorly understood stars known as born-again asymptotic-giant-branch stars. These may result in extreme horizontal-branch stars (subdwarf B stars), hydrogen deficient post-asymptotic-giant-branch stars, variable planetary nebula central stars, and R Coronae Borealis variables.
In massive stars, the core is already large enough at the onset of hydrogen burning shell that helium ignition will occur before electron degeneracy pressure has a chance to become prevalent. Thus, when these stars expand and cool, they do not brighten as much as lower-mass stars; however, they were much brighter than lower-mass stars to begin with, and are thus still brighter than the red giants formed from less massive stars. These stars are unlikely to survive as red supergiants; instead they will destroy themselves as type II supernovas.
Extremely massive stars (more than approximately 40 solar masses), which are very luminous and thus have very rapid stellar winds, lose mass so rapidly due to radiation pressure that they tend to strip off their own envelopes before they can expand to become red supergiants, and thus retain extremely high surface temperatures (and blue-white color) from their main-sequence time onwards. The largest stars of the current generation are about 100-150 solar masses because the outer layers would be expelled by the extreme radiation. Although lower-mass stars normally do not burn off their outer layers so rapidly, they can likewise avoid becoming red giants or red supergiants if they are in binary systems close enough so that the companion star strips off the envelope as it expands, or if they rotate rapidly enough so that convection extends all the way from the core to the surface, resulting in the absence of a separate core and envelope due to thorough mixing.
The core grows hotter and denser as it gains material from fusion of hydrogen at the base of the envelope. In all massive stars, electron degeneracy pressure is insufficient to halt collapse by itself, so as each major element is consumed in the center, progressively heavier elements ignite, temporarily halting collapse. If the core of the star is not too massive (less than approximately 1.4 solar mass, taking into account mass loss that has occurred by this time), it may then form a white dwarf (possibly surrounded by a planetary nebula) as described above for less massive stars, with the difference that the white dwarf is composed chiefly of oxygen, neon, and magnesium.
Above a certain mass (estimated at approximately 2.5 solar masses and whose star's progenitor was around 10 solar masses), the core will reach the temperature (approximately 1.1 gigakelvins) at which neon partially breaks down to form oxygen and helium, the latter of which immediately fuses with some of the remaining neon to form magnesium; then oxygen fuses to form sulfur, silicon, and smaller amounts of other elements. Finally, the temperature gets high enough that any nucleus can be partially broken down, most commonly releasing an alpha particle (helium nucleus) which immediately fuses with another nucleus, so that several nuclei are effectively rearranged into a smaller number of heavier nuclei, with net release of energy because the addition of fragments to nuclei exceeds the energy required to break them off the parent nuclei.
A star with a core mass too great to form a white dwarf but insufficient to achieve sustained conversion of neon to oxygen and magnesium, will undergo core collapse (due to electron capture) before achieving fusion of the heavier elements. Both heating and cooling caused by electron capture onto minor constituent elements (such as aluminum and sodium) prior to collapse may have a significant impact on total energy generation within the star shortly before collapse. This may produce a noticeable effect on the abundance of elements and isotopes ejected in the subsequent supernova.
Once the nucleosynthesis process arrives at iron-56, the continuation of this process consumes energy (the addition of fragments to nuclei releases less energy than required to break them off the parent nuclei). If the mass of the core exceeds the Chandrasekhar limit, electron degeneracy pressure will be unable to support its weight against the force of gravity, and the core will undergo sudden, catastrophic collapse to form a neutron star or (in the case of cores that exceed the Tolman-Oppenheimer-Volkoff limit), a black hole. Through a process that is not completely understood, some of the gravitational potential energy released by this core collapse is converted into a Type Ib, Type Ic, or Type II supernova. It is known that the core collapse produces a massive surge of neutrinos, as observed with supernova SN 1987A. The extremely energetic neutrinos fragment some nuclei; some of their energy is consumed in releasing nucleons, including neutrons, and some of their energy is transformed into heat and kinetic energy, thus augmenting the shock wave started by rebound of some of the infalling material from the collapse of the core. Electron capture in very dense parts of the infalling matter may produce additional neutrons. Because some of the rebounding matter is bombarded by the neutrons, some of its nuclei capture them, creating a spectrum of heavier-than-iron material including the radioactive elements up to (and likely beyond) uranium. Although non-exploding red giants can produce significant quantities of elements heavier than iron using neutrons released in side reactions of earlier nuclear reactions, the abundance of elements heavier than iron (and in particular, of certain isotopes of elements that have multiple stable or long-lived isotopes) produced in such reactions is quite different from that produced in a supernova. Neither abundance alone matches that found in the Solar System, so both supernovae and ejection of elements from red giants are required to explain the observed abundance of heavy elements and isotopes thereof.
The energy transferred from collapse of the core to rebounding material not only generates heavy elements, but (by a mechanism which is not fully understood) provides for their acceleration well beyond escape velocity, thus causing a Type Ib, Type Ic, or Type II supernova. Note that current understanding of this energy transfer is still not satisfactory; although current computer models of Type Ib, Type Ic, and Type II supernovae account for part of the energy transfer, they are not able to account for enough energy transfer to produce the observed ejection of material. Some evidence gained from analysis of the mass and orbital parameters of binary neutron stars (which require two such supernovae) hints that the collapse of an oxygen-neon-magnesium core may produce a supernova that differs observably (in ways other than size) from a supernova produced by the collapse of an iron core.
The most massive stars may be completely destroyed by a supernova with an energy greatly exceeding its gravitational binding energy. This rare event, caused by pair-instability, leaves behind no black hole remnant.
After a star has burned out its fuel supply, its remnants can take one of three forms, depending on the mass during its lifetime.
For a star of 1 solar mass, the resulting white dwarf is of about 0.6 solar mass, compressed into approximately the volume of the Earth. White dwarfs are stable because the inward pull of gravity is balanced by the degeneracy pressure of the star's electrons, a consequence of the Pauli exclusion principle. Electron degeneracy pressure provides a rather soft limit against further compression; therefore, for a given chemical composition, white dwarfs of higher mass have a smaller volume. With no fuel left to burn, the star radiates its remaining heat into space for billions of years.
A white dwarf is very hot when it first forms, more than 100,000 K at the surface and even hotter in its interior. It is so hot that a lot of its energy is lost in the form of neutrinos for the first 10 million years of its existence, but will have lost most of its energy after a billion years.
The chemical composition of the white dwarf depends upon its mass. A star of a few solar masses will ignite carbon fusion to form magnesium, neon, and smaller amounts of other elements, resulting in a white dwarf composed chiefly of oxygen, neon, and magnesium, provided that it can lose enough mass to get below the Chandrasekhar limit (see below), and provided that the ignition of carbon is not so violent as to blow the star apart in a supernova. A star of mass on the order of magnitude of the Sun will be unable to ignite carbon fusion, and will produce a white dwarf composed chiefly of carbon and oxygen, and of mass too low to collapse unless matter is added to it later (see below). A star of less than about half the mass of the Sun will be unable to ignite helium fusion (as noted earlier), and will produce a white dwarf composed chiefly of helium.
In the end, all that remains is a cold dark mass sometimes called a black dwarf. However, the universe is not old enough for any black dwarfs to exist yet.
If the white dwarf's mass increases above the Chandrasekhar limit, which is 1.4 solar mass for a white dwarf composed chiefly of carbon, oxygen, neon, and/or magnesium, then electron degeneracy pressure fails due to electron capture and the star collapses. Depending upon the chemical composition and pre-collapse temperature in the center, this will lead either to collapse into a neutron star or runaway ignition of carbon and oxygen. Heavier elements favor continued core collapse, because they require a higher temperature to ignite, because electron capture onto these elements and their fusion products is easier; higher core temperatures favor runaway nuclear reaction, which halts core collapse and leads to a Type Ia supernova. These supernovae may be many times brighter than the Type II supernova marking the death of a massive star, even though the latter has the greater total energy release. This inability to collapse means that no white dwarf more massive than approximately 1.4 solar mass can exist (with a possible minor exception for very rapidly spinning white dwarfs, whose centrifugal force due to rotation partially counteracts the weight of their matter). Mass transfer in a binary system may cause an initially stable white dwarf to surpass the Chandrasekhar limit.
If a white dwarf forms a close binary system with another star, hydrogen from the larger companion may accrete around and onto a white dwarf until it gets hot enough to fuse in a runaway reaction at its surface, although the white dwarf remains below the Chandrasekhar limit. Such an explosion is termed a nova.
When a stellar core collapses, the pressure causes electron capture, thus converting the great majority of the protons into neutrons. The electromagnetic forces keeping separate nuclei apart are gone (proportionally, if nuclei were the size of dust mites, atoms would be as large as football stadiums), and most of the core of the star becomes a dense ball of contiguous neutrons (in some ways like a giant atomic nucleus), with a thin overlying layer of degenerate matter (chiefly iron unless matter of different composition is added later). The neutrons resist further compression by the Pauli Exclusion Principle, in a way analogous to electron degeneracy pressure, but stronger.
These stars, known as neutron stars, are extremely small—on the order of radius 10 km, no bigger than the size of a large city—and are phenomenally dense. Their period of rotation shortens dramatically as the stars shrink (due to conservation of angular momentum); observed rotational periods of neutron stars range from about 1.5 milliseconds (over 600 revolutions per second) to several seconds. When these rapidly rotating stars' magnetic poles are aligned with the Earth, we detect a pulse of radiation each revolution. Such neutron stars are called pulsars, and were the first neutron stars to be discovered. Though electromagnetic radiation detected from pulsars is most often in the form of radio waves, pulsars have also been detected at visible, X-ray, and gamma ray wavelengths.
If the mass of the stellar remnant is high enough, the neutron degeneracy pressure will be insufficient to prevent collapse below the Schwarzschild radius. The stellar remnant thus becomes a black hole. The mass at which this occurs is not known with certainty, but is currently estimated at between 2 and 3 solar masses.
Black holes are predicted by the theory of general relativity. According to classical general relativity, no matter or information can flow from the interior of a black hole to an outside observer, although quantum effects may allow deviations from this strict rule. The existence of black holes in the universe is well supported, both theoretically and by astronomical observation.
Because the core-collapse supernova mechanism itself is imperfectly understood, it is still not known whether it is possible for a star to collapse directly to a black hole without producing a visible supernova, or whether some supernovae initially form unstable neutron stars which then collapse into black holes; the exact relation between the initial mass of the star and the final remnant is also not completely certain. Resolution of these uncertainties requires the analysis of more supernovae and supernova remnants.
A stellar evolutionary model is a mathematical model that can be used to compute the evolutionary phases of a star from its formation until it becomes a remnant. The mass and chemical composition of the star are used as the inputs, and the luminosity and surface temperature are the only constraints. The model formulae are based upon the physical understanding of the star, usually under the assumption of hydrostatic equilibrium. Extensive computer calculations are then run to determine the changing state of the star over time, yielding a table of data that can be used to determine the evolutionary track of the star across the Hertzsprung–Russell diagram, along with other evolving properties. Accurate models can be used to estimate the current age of a star by comparing its physical properties with those of stars along a matching evolutionary track.
The triple-alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei (alpha particles) are transformed into carbon.
Older stars start to accumulate helium produced by the proton–proton chain reaction and the carbon–nitrogen–oxygen cycle in their cores. The products of further nuclear fusion reactions of helium with hydrogen or another helium nucleus produce lithium-5 and beryllium-8 respectively, both of which are highly unstable and decay almost instantly back into smaller nuclei. When the star starts to run out of hydrogen to fuse, the core of the star begins to collapse until the central temperature rises to 108 K (8.6 keV). At this point helium nuclei are fusing together at a rate high enough to exceed the rate at which their product, beryllium-8, decays back into two helium nuclei. This means that there are always a few beryllium-8 nuclei in the core, which can fuse with yet another helium nucleus to form carbon-12, which is stable:
The net energy release of the process is .
Because the triple-alpha process is unlikely, it requires a long period of time to produce much carbon. One consequence of this is that no significant amount of carbon was produced in the Big Bang because within minutes after the Big Bang, the temperature fell below that necessary for nuclear fusion.
Ordinarily, the probability of the triple alpha process would be extremely small. However, the beryllium-8 ground state has almost exactly the energy of two alpha particles. In the second step, 8Be + 4He has almost exactly the energy of an of 12C. These resonances greatly increase the probability that an incoming alpha particle will combine with beryllium-8 to form carbon. The existence of this resonance was predicted by Fred Hoyle before its actual observation, based on the physical necessity for it to exist, in order for carbon to be formed in stars. In turn, prediction and then discovery of this energy resonance and process gave very significant support to Hoyle's hypothesis of stellar nucleosynthesis, which posited that all chemical elements had originally been formed from hydrogen, the true primordial substance.
As a side effect of the process, some carbon nuclei can fuse with additional helium to produce a stable isotope of oxygen and release energy:
See alpha process for more details about this reaction and further steps in the chain of stellar nucleosynthesis.
This creates a situation in which stellar nucleosynthesis produces large amounts of carbon and oxygen but only a small fraction of these elements is converted into neon and heavier elements. Both oxygen and carbon make up the 'ash' of helium-4 burning. The anthropic principle has been controversially cited to explain the fact that nuclear resonances are sensitively arranged to create large amounts of carbon and oxygen in the Universe.
Fusion processes produce elements only up to nickel (which decays later to iron); heavier elements (those beyond Ni) are created mainly by neutron capture. The slow capture of neutrons, the s-process, produces about half of these heavy elements. The other half are produced by rapid neutron capture, the r-process, which probably occurs in a core-collapse supernova.
The triple-alpha steps are strongly dependent on the temperature and density of the stellar material. The power released by the reaction is approximately proportional to the temperature to the 40th power, and the density squared. Contrast this to the PP chain which produces energy at a rate proportional to the fourth power of temperature and directly with density.
This strong temperature dependence has consequences for the late stage of stellar evolution, the red giant stage.
For lower mass stars, the helium accumulating in the core is prevented from further collapse only by electron degeneracy pressure. The pressure in the core is thus nearly independent of temperature. A consequence of this is that once a smaller star begins burning using the triple-alpha process, the core does not expand and cool in response; the temperature can only increase, which results in the reaction rate increasing further still and becoming a runaway reaction. This process, known as the helium flash, lasts a matter of seconds but burns 60–80% of the helium in the core. In the core flash prodigious quantities of energy are produced, allowing the star to reach approximately 1011 solar luminosities which is comparable to a whole galaxy, although no effects will be immediately visible at the star's surface.
For higher mass stars, the helium burning occurs in a shell surrounding a degenerate carbon core. Since the helium shell is not degenerate, the increased thermal pressure due to energy released by helium burning causes the star to expand. The expansion cools the helium layer and shuts off the reaction, and the star contracts again. This cyclical process causes the star to become strongly variable, and results in it blowing off material from its outer layers.
The triple alpha process is highly dependent on carbon-12 and beryllium-8 having resonances with the same energy as helium-4, and before 1952 no such energy level was known. Astrophysicist Fred Hoyle used the fact that carbon-12 is abundant in the universe as evidence for the existence of the carbon-12 resonance, in what is an example of the application of the Anthropic Principle: we are here, and we are made of carbon, so carbon must have originated somehow and the only physically conceivable way is through triple alpha processes that requires the existence of a resonance in a given very specific location in the spectra of carbon-12 nuclei. Hoyle suggested the idea to nuclear physicist William (Willy) A. Fowler, who conceded that it was possible that this energy level had been missed in previous work. By 1952, Fowler had already discovered the beryllium-8 resonance, and Edwin Salpeter calculated the reaction rate taking this resonance into account. This helped to explain the rate of the process, but the rate calculated by Salpeter was still somewhat too low. A few years later, after an undertaking by his research group at the Kellogg Radiation Laboratory at the California Institute of Technology, Fowler discovered a carbon-12 resonance near 7.65 MeV, which has eliminated the final discrepancy between the nuclear theory and the theory of stellar evolution.
The final reaction product lies in a 0+ state. Since the Hoyle State was predicted to be either a 0+ or a 2+ state, electron-positron pairs or gamma rays were expected to be seen. However, when experiments were carried out, the gamma emission reaction channel was not observed, and this meant the state must be a 0+ state. This state completely suppresses single gamma emission, since single gamma emission must carry away at least 1 unit of angular momentum. Production of an electron–positron pair from an excited 0+ state is possible because their combined spins (0) can couple to a reaction that has a change in angular momentum of 0.
Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only a few million years for the most massive to trillions of years for the least massive, which is considerably longer than the age of the universe. The table shows the lifetimes of stars as a function of their masses. All stars are born from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, becoming what is known as a main-sequence star.
Nuclear fusion powers a star for most of its life. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star. Later, as the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core. This process causes the star to gradually grow in size, passing through the subgiant stage until it reaches the red giant phase. Stars with at least half the mass of the Sun can also begin to generate energy through the fusion of helium at their core, whereas more massive stars can fuse heavier elements along a series of concentric shells. Once a star like the Sun has exhausted its nuclear fuel, its core collapses into a dense white dwarf and the outer layers are expelled as a planetary nebula. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into an extremely dense neutron star or black hole. Although the universe is not old enough for any of the smallest red dwarfs to have reached the end of their lives, stellar models suggest they will slowly become brighter and hotter before running out of hydrogen fuel and becoming low-mass white dwarfs.
Astronomy is a natural science that is the study of celestial objects (such as moons, planets, stars, nebulae, and galaxies), the physics, chemistry, mathematics, and evolution of such objects, and phenomena that originate outside the atmosphere of Earth, including supernovae explosions, gamma ray bursts, and cosmic background radiation. A related but distinct subject, cosmology, is concerned with studying the universe as a whole.
Astronomy is one of the oldest sciences. Prehistoric cultures left behind astronomical artifacts such as the Egyptian monuments and Nubian monuments, and early civilizations such as the Babylonians, Greeks, Chinese, Indians, Iranians and Maya performed methodical observations of the night sky. However, the invention of the telescope was required before astronomy was able to develop into a modern science. Historically, astronomy has included disciplines as diverse as astrometry, celestial navigation, observational astronomy, and the making of calendars, but professional astronomy is nowadays often considered to be synonymous with astrophysics. Star
In journalism, a human interest story is a feature story that discusses a person or people in an emotional way. It presents people and their problems, concerns, or achievements in a way that brings about interest, sympathy or motivation in the reader or viewer.
Human interest stories may be "the story behind the story" about an event, organization, or otherwise faceless historical happening, such as about the life of an individual soldier during wartime, an interview with a survivor of a natural disaster, a random act of kindness or profile of someone known for a career achievement. Environment