Star

2007 Schools Wikipedia Selection. Related subjects: Space (Astronomy)

A star is a massive, luminous ball of plasma. Stars group together to form galaxies, and they dominate the visible universe. The nearest star is the Sun, which is the source of most of the energy on Earth, including daylight. Other stars are visible in the night sky, when they are not outshone by the Sun. A star shines because nuclear fusion in its core releases energy which traverses the star's interior and then radiates into outer space. Without stars, life on Earth and most atomic elements would not exist.

Astronomers can determine the mass, age, chemical composition and many other properties of a star by observing its spectrum, luminosity and motion through space. The total mass of a star is the principal determinant in its evolution and eventual fate. Other characteristics of a star that are determined by its evolutionary history include the diameter, rotation, movement and temperature. A plot of the temperature of many stars against their luminosities, known as a Hertzsprung-Russell diagram (H-R diagram), allows the current age and evolutionary state of a particular star to be determined.

A star begins as a collapsing cloud of material that is composed primarily of hydrogen along with some helium and heavier trace elements. Once the stellar core is sufficiently dense, some of the hydrogen is steadily converted into helium through the process of nuclear fusion. The remainder of the star's interior carries energy away from the core through a combination of radiation and convective processes. These processes keep the star from collapsing upon itself and the energy generates a stellar wind at the surface and radiation into outer space.

Once the hydrogen fuel at the core is exhausted, a star of at least 0.4 times the mass of the Sun expands to become a red giant, fusing heavier elements at the core, or in shells around the core. It then evolves into a degenerate form, recycling a portion of the matter into the interstellar environment where it will form a new generation of stars with a higher proportion of heavy elements.

Binary and multi-star systems consist of two or more stars that are gravitationally bound, and generally move around each other in stable orbits. When two such stars have a relatively close orbit, their gravitational interaction can have a significant impact on their evolution.

Observation history

Stars have been important to every culture. They have been used in religious practices and for celestial navigation and orientation. The Gregorian calendar, used nearly everywhere in the world, is a solar calendar based on the angle of the Earth's rotational axis relative to the nearest star, the Sun.

Early astronomers such as Tycho Brahe identified new stars in the night sky (later termed novae) suggesting that the heavens were not immutable. In 1584 Giordano Bruno suggested that the stars were actually other suns, and may have other planets, possibly even Earth-like, in orbit around them, an idea that had been suggested earlier by such ancient Greek philosophers as Democritus and Epicurus. By the following century the idea of the stars as distant suns was reaching a consensus among astronomers. To explain why these stars exerted no net gravitational pull on the solar system, Isaac Newton suggested that the stars were equally distributed in every direction, an idea prompted by the theologian Richard Bentley.

The Italian astronomer Geminiano Montanari recorded observing variations in luminosity of the star Algol in 1667. Edmond Halley published the first measurements of the proper motion of a pair of nearby "fixed" stars, demonstrating that they had changed positions from the time of the ancient Greek astronomers Ptolemy and Hipparchus. The first direct measurement of the distance to a star ( 61 Cygni at 11.4 light years) was made in 1838 by Friedrich Bessel using the parallax technique. Parallax measurements demonstrated the vast separation of the stars in the heavens.

William Herschel was the first astronomer to attempt to determine the distribution of stars in the sky. During the 1780s, he performed a series of gauges in 600 directions, and counted the stars observed along each line of sight. From this he deduced that the number of stars steadily increased toward one side of the sky, in the direction of the Milky Way core. His son John Herschel repeated this study in the southern hemisphere and found a corresponding increase in the same direction. In addition to his other accomplishments, William Herschel is also noted for his discovery that some stars do not merely lie along the same line of sight, but are also physical companions that form binary star systems.

The science of stellar spectroscopy was pioneered by Joseph von Fraunhofer and Angelo Secchi. By comparing the spectra of stars such as Sirius to the Sun, they found differences in the strength and number of their absorption lines—the dark lines in a stellar spectra due to the absorption of specific frequencies by the atmosphere. In 1865 Secchi began classifying stars into spectral types. However, the modern version of the stellar classification scheme was developed by Annie J. Cannon during the 1900s.

Observation of double stars gained increasing importance during the 19th century. In 1834, Friedrich Bessel observed changes in the proper motion of the star Sirius, and inferred a hidden companion. Edward Pickering discovered the first spectroscopic binary in 1899 when he observed the periodic splitting of the spectral lines of the star Mizar in a 104 day period. Detailed observations of many binary star systems were collected by astronomers such as William Struve and S. W. Burnham, allowing the masses of stars to be determined from computation of the orbital elements. The first solution to the problem of deriving an orbit of binary stars from telescope observations was made by Felix Savary in 1827.

The twentieth century saw increasingly rapid advances in the scientific study of stars. The photograph became a valuable astronomical tool. Karl Schwarzschild discovered that the colour of a star, and hence its temperature, could be determined by comparing the visual magnitude against the photographic magnitude. The development of the photoelectric photometer allowed very precise measurements of magnitude at multiple wavelength intervals. In 1921 Albert A. Michelson made the first measurements of a stellar diameter using an interferometer on the Hooker telescope.

Important conceptual work on the physical basis of stars occurred during the first decades of the twentieth century. In 1913, the Hertzsprung-Russell diagram was developed, propelling the astrophysical study of stars. Successful models were developed to explain the interiors of stars and stellar evolution. The spectra of stars were also successfully explained through advances in quantum physics. This allowed the chemical composition of the stellar atmosphere to be determined.

Star designations

The concept of the constellation was known to exist during the Babylonian period. Ancient sky watchers imagined that prominent arrangements of stars formed patterns, and they associated these with particular aspects of nature or their myths. Twelve of these formations lay along the band of the ecliptic and these became the basis of astrology. Many of the more prominent individual stars were also given names, particularly with Arabic or Latin designations.

As well as certain constellations and the Sun itself, stars as a whole have their own myths. They were thought to be the souls of the dead or gods. An example is the star Algol, which was thought to represent the eye of the Gorgon Medusa.

To the Ancient Greeks, some "stars," later identified as planets, represented various important deities, from which the names of the planets Mercury, Venus, Mars, Jupiter and Saturn were taken. (Uranus and Neptune were also Greek and Roman gods, but neither planet was known in Antiquity because of their low brightness. Their names were assigned by later astronomers.)

Circa 1600, the names of the constellations were used to name the stars in the corresponding regions of the sky. The German astronomer Johann Bayer created a series of star maps and applied Greek letters as designations to the stars in each constellation. Later the English astronomer John Flamsteed came up with a system using numbers, which would later be known as the Flamsteed designation. Numerous additional systems have since been created as star catalogues have appeared.

The only body which has been recognized by the scientific community as having the authority to name stars or other celestial bodies is the International Astronomical Union (IAU). A number of private companies (for instance, the " International Star Registry") purport to sell names to stars; however, these names are neither recognized by the scientific community nor used by them, and many in the astronomy community view these organizations as frauds preying on people ignorant of star naming procedure.

Units of measurement

Most stellar parameters are expressed in SI units by convention, but CGS units are also used (e.g., expressing luminosity in ergs per second). Mass, luminosity, and radii are usually given in solar units, based on the characteristics of the Sun:

solar mass:	kg
solar luminosity:	watts
solar radius:	m

Large lengths, such as the radius of a giant star or the semi-major axis of a binary star system, are often expressed in terms of the astronomical unit (AU) — approximately the mean distance between the Earth and the Sun (150 million km or 93 million miles).

Formation and evolution

Stars are formed within molecular clouds; large regions of high density in the interstellar medium (though still less dense than the inside of an earthly vacuum chamber). These clouds consist mostly of hydrogen, with about 23–28% helium and a few percent heavier elements. One example of such a star-forming nebula is the Orion Nebula. As massive stars are formed from these clouds, they powerfully illuminate and ionize the clouds from which they formed, creating an H II region.

Protostar formation

The formation of a star begins with a gravitational instability inside a molecular cloud, often triggered by shockwaves from supernovae (massive stellar explosions) or the collision of two galaxies (as in a starburst galaxy). Once a region reaches a sufficient density of matter to satisfy the criteria for Jeans Instability it begins to collapse under its own gravitational force.

As the cloud collapses, individual conglomerations of dense dust and gas form that are known as Bok globules. These can contain up to 50 solar masses of material. As a globule collapses and the density increases, the gravitational energy is converted into heat and the temperature rises. When the protostellar cloud has approximately reached the stable condition of hydrostatic equilibrium, a protostar forms at the core. These pre-main sequence stars are often surrounded by a protoplanetary disk. The period of gravitational contraction lasts for about 10–15 million years.

Early stars of less than 2 solar masses are called T Tauri stars, while those with greater mass are Herbig Ae/Be stars. These newly-born stars emit jets of gas along their axis of rotation, producing small patches of nebulosity known as Herbig-Haro objects.

Main sequence

Stars spend about 90% of their lifetime fusing hydrogen to produce helium in high-temperature and high-pressure reactions near the core. Such stars are said to be on the main sequence and are called dwarf stars. Starting at zero-age main sequence, the proportion of helium in a star's core will steadily increase. As a consequence, in order to maintain the required rate of nuclear fusion at the core, the star will slowly increase in temperature and luminosity. The Sun, for example, is estimated to have increased in luminosity by about 40% since it reached the main sequence 4.6 billion years ago.

Every star generates a stellar wind of particles that causes a continual outflow of gas into space. For most stars, the amount of mass lost is negligible. The Sun loses 10⁻¹⁴ solar masses every year, or about 0.01% of its total mass over its entire lifespan. However very massive stars can lose 10⁻⁷ to 10⁻⁵ solar masses each year, significantly affecting their evolution. Stars that begin with more than 50 solar masses can lose over half their total mass while they remain on the main sequence.

The duration that a star spends on the main sequence depends primarily on the amount of fuel it has to burn and the rate at which it burns that fuel. In other words, its initial mass and its luminosity. For the Sun, this is estimated to be about 10¹⁰ years. Large stars burn their fuel very rapidly and are short-lived. Small stars (called red dwarfs) burn their fuel very slowly and last tens to hundreds of billions of years. At the end of their lives, they simply become dimmer and dimmer, fading into black dwarfs. However, since the lifespan of such stars is greater than the current age of the universe (13.7 billion years), no black dwarfs are expected to exist yet.

Besides mass, the portion of elements heavier than helium can play a significant role in the evolution of stars. In astronomy all elements heavier than helium are considered a "metal", and the chemical concentration of these elements is called the metallicity. The metallicity can influence the duration that a star will burn its fuel, control the formation of magnetic fields and modify the strength of the stellar wind. Older, population II stars have substantially less metallicity than the younger, population I stars due to the composition of the molecular clouds from which they formed. (Over time these clouds become increasingly enriched in heavier elements as older stars die and shed portions of their atmospheres.)

Post-main sequence

As stars of at least 0.4 solar masses exhaust their supply of hydrogen at their core, their outer layers expand and cool to form a red giant. In about 5 billion years, when the Sun is a red giant, it will be so large that it will consume Mercury and possibly Venus. Models predict that the Sun will expand out to about 99% of the distance to the Earth's present orbit (1 astronomical unit, or AU). By that time, however, the orbit of the Earth will expand to about 1.7 AUs due to mass loss by the Sun and thus the Earth will escape envelopment. However, the Earth will be stripped of its oceans and atmosphere as the Sun's luminosity increases several thousand-fold.

In a red giant, hydrogen fusion proceeds in a shell-layer surrounding the core. Eventually the core is compressed enough to start helium fusion, and the star now gradually shrinks in radius and increases its surface temperature.

After the star has consumed the helium at the core, fusion continues in a shell around a hot core of carbon and oxygen. The star now follows an evolutionary path that parallels the original red giant phase, but at a higher surface temperature.

Massive stars

During their helium-burning phase, very high mass stars with more than nine solar masses expand to form red supergiants. Once this fuel is exhausted at the core, they can continue to fuse elements heavier than helium. The core contracts until the temperature and pressure are sufficient to fuse carbon. This process continues, with the successive stages being fueled by oxygen, neon, silicon, and sulfur. Near the end of the star's life, fusion can occur along a series of onion-layer shells within the star. Each shell fuses a different element, with the outermost shell fusing hydrogen; the next shell fusing helium, and so forth.

The final stage is reached when the star begins producing iron. Since iron nuclei are more tightly bound than any heavier nuclei, if they are fused they do not release energy — the process would, on the contrary, consume energy. Likewise, since they are more tightly bound than all lighter nuclei, energy cannot be released by fission. In relatively old, very massive stars, a large core of inert iron will accumulate in the centre of the star. The heavier elements in these stars can work their way up to the surface, forming evolved objects known as Wolf-Rayet stars that have a dense stellar wind which sheds the outer atmosphere.

Collapse

An evolved, average-size star will now shed its outer layers as a planetary nebula. If what remains after the outer atmosphere has been shed is less than 1.4 solar masses, it shrinks to a relatively tiny object (about the size of Earth) that is not massive enough for further compression to take place, known as a white dwarf. The electron-degenerate matter inside a white dwarf is no longer a plasma, even though stars are generally referred to as being spheres of plasma. White dwarfs will eventually fade into black dwarfs over a very long stretch of time.

In larger stars, fusion continues until the iron core has grown so large (more than 1.4 solar masses) that it can no longer support its own mass. This core will suddenly collapse as its electrons are driven into its protons, forming neutrons and neutrinos in a burst of inverse beta decay, or electron capture. The shockwave formed by this sudden collapse causes the rest of the star to explode in a supernova. Supernovae are so bright that they may briefly outshine the star's entire home galaxy. When they occur within the Milky Way, supernovae have historically been observed by naked-eye observers as "new stars" where none existed before.

Most of the matter in the star is blown away by the supernovae explosion (forming nebulae such as the Crab Nebula) and what remains will be a neutron star (which sometimes manifests itself as a pulsar or X-ray burster) or, in the case of the largest stars (large enough to leave a stellar remnant greater than roughly 4 solar masses), a black hole. In a neutron star the matter is in a state known as neutron-degenerate matter, with a more exotic form of degenerate matter, QCD matter, possibly present in the core. Within a black hole the matter is in a state that is not currently understood.

The blown-off outer layers of dying stars include heavy elements which may be recycled during new star formation. These heavy elements allow the formation of rocky planets. The outflow from supernovae and the stellar wind of large stars play an important part in shaping the interstellar medium.

Distribution

It has been a long-held assumption that the majority of stars occur in gravitationally-bound, multiple-star systems, forming binary stars. This is particularly true for very massive O and B class stars, where 80% of the systems are believed to be multiple. However the portion of single star systems increases for smaller stars, so that only 25% of red dwarfs are known to have stellar companions. As 85% of all stars are red dwarfs, most stars in the Milky Way are likely single from birth.

Larger groups called star clusters also exist. These range from loose stellar associations with only a few stars, up to enormous globular clusters with hundreds of thousands of stars.

Stars are not spread uniformly across the universe, but are normally grouped into galaxies along with interstellar gas and dust. A typical galaxy contains hundreds of billions of stars, and there are more than 100 billion (10¹¹) galaxies in the observable universe. While it is often believed that stars only exist within galaxies, intergalactic stars have been discovered.

Astronomers estimate that there are at least 70 sextillion (7×10²²) stars in the known universe. That is 230 billion times as many as the 300 billion in our own Milky Way.

The nearest star to the Earth, apart from the Sun, is Proxima Centauri, which is 39.9 trillion (10¹²) kilometres, or 4.2 light-years away. Light from Proxima Centauri takes 4.2 years to reach Earth. Travelling at the orbital speed of the Space Shuttle (5 miles per second — almost 30,000 kilometres per hour), it would take about 150,000 years to get there. Distances like this are typical inside galactic discs, including the vicinity of the solar system. Stars can be much closer to each other in the centres of galaxies and in globular clusters, or much farther apart in galactic halos.

Because of their low density, collisions of stars in the galaxy are thought to be rare. However in dense regions such as the core of globular clusters or the galactic centre, collisions can be more common. Such collisions can produce what are known as blue stragglers. These abnormal stars have a higher surface temperature than the other main sequence stars in the cluster with the same luminosity.

Characteristics

Almost everything about a star is determined by its initial mass, including essential characteristics such as luminosity and size, as well as the star's evolution, lifespan, and eventual fate.

Age

Many stars are between 1 billion and 10 billion years old. Some stars may even be close to 13.7 billion years old — the observed age of the universe. (See Big Bang theory and stellar evolution.) The more massive the star, the shorter its lifespan, primarily because massive stars have greater pressure on their cores, causing them to burn hydrogen more rapidly. The most massive stars last an average of about one million years, while stars of minimum mass (red dwarfs) burn their fuel very slowly and last tens to hundreds of billions of years.

Chemical composition

When stars form they are composed of about 70% hydrogen and 28% helium, as measured by mass, with a small fraction of heavier elements. Typically the portion of heavy elements is measured in terms of the iron content of the stellar atmosphere, as iron is a common element and its absorption lines are relatively easy to measure. Because the molecular clouds where stars form are steadily enriched by heavier elements from supernovae explosions, a measurement of the chemical composition of a star can be used to infer its age. The portion of heavier elements may also be an indicator of the likelihood that the star has a planetary system.

The star with the lowest iron content ever measured is the dwarf HE1327-2326, with only 1/200,000th the iron content of the Sun.

Diameter

Due to their great distance from the Earth, all stars except the Sun appear to the human eye as shining points in the night sky that twinkle because of the effect of the Earth's atmosphere. The disks of stars are much too small in angular size to be observed with current ground-based optical telescopes, and so Interferometer telescopes are required in order to produce images of these objects. The Sun is also a star, but it is close enough to the Earth to appear as a disk instead, and to provide daylight. Other than the Sun, the star with the largest apparent size is R Doradus, with an angular diameter of only 0.057 arcseconds.

Stars range in size from neutron stars no bigger than a city to supergiants like Betelgeuse in the Orion constellation, which has a diameter about 1,000 times larger than the Sun — about 1.6 billion kilometres. However, Betelgeuse has a much lower density than the Sun.

Kinematics

The motion of a star relative to the Sun can provide useful information about the origin and age of a star, as well as the structure and evolution of the surrounding galaxy.

The proper motion of a star is the traverse velocity across the sky. This is determined by precise astrometric measurements in units of milli- arc seconds (mas) per year. By determining the parallax of a star, the proper motion can then be converted into units of velocity. Stars with high rates of proper motion are likely to be relatively close to the Sun, making them good candidates for parallax measurements.

The radial velocity is the movement of the star toward or away from the Sun. This is determined by measurements in the doppler shift of spectral lines, and is given in units of km/ s.

Once both rates of movement are known, the space velocity of the star relative to the Sun or the galaxy can be computed. Among nearby stars, it has been found that population I stars have generally lower velocities than older, population II stars. The latter have elliptical orbits that are inclined to the plane of the galaxy. Comparison of the kinematics of nearby stars has also led to the identification of stellar associations. These are most likely groups of stars that share a common point of origin in giant molecular clouds.

Mass

One of the most massive stars known is Eta Carinae, with 100 – 150 times as much mass as the Sun; its lifespan is very short — only several million years at most. A recent study of the Arches cluster suggests that 150 solar masses is the upper limit for stars in the current era of the universe. The reason for this limit is not precisely known, but it is partially due to the Eddington luminosity which defines the maximum amount of luminosity that can pass through the atmosphere of a star without ejecting the gases into space.

The first stars to form after the Big Bang may have been larger, up to 300 solar masses or more, due to the complete absence of elements heavier than lithium in their composition. This generation of supermassive, population III stars is long extinct, however, and currently only theoretical.

With a mass only 93 times that of Jupiter, AB Doradus C, a companion to AB Doradus A, is the smallest known star undergoing nuclear fusion in its core. For stars with similar metallicity to the Sun, the theoretical minimum mass the star can have, and still undergo fusion at the core, is estimated to be about 75 times the mass of Jupiter. When the metallicity is very low, however, a recent study of the faintest stars found that the minimum star size seems to be about 8.3% of the solar mass, or about 87 times the mass of Jupiter. Smaller bodies are called brown dwarfs, which occupy a poorly-defined grey area between stars and gas giants.

The combination of the radius and the mass of a star determines the surface gravity. Giant stars have a much lower surface gravity than main sequence stars, while the opposite is the case for degenerate, compact stars such as white dwarfs. The surface gravity can influence the appearance of a star's spectrum, with higher gravity causing a broadening of the absorption lines.

Rotation

The rotation rate of stars can be approximated through spectroscopic measurement, or more exactly determined by tracking the rotation rate of starspots. Young stars can have a rapid rate of rotation greater than 100 km/s at the equator. The B-class star Achernar, for example, has an equatorial rotation velocity of about 225 km/s or greater, giving it an equatorial diameter that is more than 50% larger than the distance between the poles. This rate of rotation is just below the critical velocity of 300 km/s where the star would break apart. By contrast, the Sun only rotates once every 25 – 35 days, with an equatorial velocity of 1.994 km/s. The star's magnetic field and the stellar wind serve to slow down a main sequence star's rate of rotation by a significant amount as it evolves on the main sequence.

Degenerate stars have contracted into a compact mass, resulting in a rapid rate of rotation. However they have relatively low rates of rotation compared to what would be expected by conservation of angular momentum—the tendency of a rotating body to compensate for a contraction in size by increasing its rate of spin. A large portion of the star's angular momentum is dissipated as a result of mass loss through the stellar wind. In spite of this, the rate of rotation for a pulsar can be very rapid. The pulsar at the heart of the Crab nebula, for example, rotates 30 times per second. The rotation rate of the pulsar will gradually slow due to the emission of radiation.

Temperature

The surface temperature of a main sequence star is determined by the rate of energy production at the core and the radius of the star. Massive stars can have surface temperatures of 50,000  K. Smaller stars such as the Sun have surface temperatures of a few thousand degrees. Red giants have relatively low surface temperatures of about 3,600 K, but they also have a high luminosity due to their large exterior surface area.

The stellar temperature will determine the rate of energization or ionization of different elements, resulting in characteristic absorption lines in the spectrum. The surface temperature of a star, along with its visual absolute magnitude and absorption features, is used to classify a star (see classification below).

Radiation

The energy produced by stars, as a by-product of nuclear fusion, radiates into space as both electromagnetic radiation and particle radiation. The particle radiation emitted by a star is manifested as the stellar wind (which exists as a steady stream of electrically charged particles, such as free protons, alpha particles, and beta particles, emanating from the star’s outer layers) and as a steady stream of neutrinos emanating from the star’s core.

The production of energy at the core is the reason why stars shine so brightly: every time two or more atomic nuclei of one element fuse together to form an atomic nucleus of a new heavier element, gamma ray photons are released from the nuclear fusion reaction. This energy is converted to other forms of electromagnetic energy, including visible light, by the time it reaches the star’s outer layers.

The colour of a star, as determined by the peak frequency of the visible light, depends on the temperature of the star’s outer layers, including its photosphere. Besides visible light, stars also emit forms of electromagnetic radiation that are invisible to the human eye. In fact, stellar electromagnetic radiation spans the entire electromagnetic spectrum, from the longest wavelengths of radio waves and infrared to the shortest wavelengths of ultraviolet, X-rays, and gamma rays. All components of stellar electromagnetic radiation, both visible and invisible, are typically significant.

Using the stellar spectrum, astronomers can also determine the surface temperature, surface gravity, metallicity and rotational velocity of a star. If the distance of the star is known, such as by measuring the parallax, then the luminosity of the star can be derived. The mass, radius, surface gravity, and rotation period can then be estimated based on stellar models. (Mass can be measured directly for stars in binary systems. The technique of gravitational microlensing will also yield the mass of a star.) With these parameters, astronomers can also estimate the age of the star.

Luminosity

In astronomy, luminosity is the amount of light, and other forms of radiant energy, a star radiates per unit of time. The luminosity of a star is determined by the radius and the surface temperature.

Surface patches with a lower temperature and luminosity than average are known as starspots. Small, dwarf stars such as the Sun generally have essentially featureless disks with only small starspots. Larger, giant stars have much bigger, much more obvious starspots, and they also exhibit strong stellar limb darkening. That is, the brightness decreases towards the edge of the stellar disk. Red dwarf flare stars such as UV Ceti may also possess prominent starspot features.

Magnitude

The apparent brightness of a star is measured by its apparent magnitude, which is the brightness of a star with respect to the star’s luminosity, distance from Earth, and the altering of the star’s light as it passes through Earth’s atmosphere.

Number of stars brighter than magnitude

Apparent magnitude	Number  of Stars
0	4
1	15
2	48
3	171
4	513
5	1,602
6	4,800
7	14,000

Intrinsic or absolute magnitude is what the apparent magnitude a star would be if the distance between the Earth and the star were 10 parsecs (32.6 light-years), and it is directly related to a star’s luminosity.

Both the apparent and absolute magnitude scales are logarithmic units: one whole number difference in magnitude is equal to a brightness variation of about 2.5 times (the 5th root of 100 or approximately 2.512). This means that a first magnitude (+1.00) star is about 2.5 times brighter than a second magnitude (+2.00) star, and approximately 100 times brighter than a sixth magnitude (+6.00) star. The faintest stars visible to the naked eye under good seeing conditions are about magnitude +6.

On both apparent and absolute magnitude scales, the smaller the magnitude number, the brighter the star; the larger the magnitude number, the fainter. The brightest stars, on either scale, have negative magnitude numbers. The variation in brightness between two stars is calculated by subtracting the magnitude number of the brighter star (m_b) from the magnitude number of the fainter star (m_f), then using the difference as an exponent for the base number 2.512; that is to say:

Δm = m_f − m_b

2.512^Δm = variation in brightness

Relative to both luminosity and distance from Earth, absolute magnitude (M) and apparent magnitude (m) are not exactly equivalent for an individual star; for example, the bright star Sirius has an apparent magnitude of −1.44, but it has an absolute magnitude of +1.41.

The Sun has an apparent magnitude of −26.7, but its absolute magnitude is only +4.83. Sirius, the brightest star in the night sky as seen from Earth, is approximately 23 times more luminous than the Sun, while Canopus, the second brightest star in the night sky with an absolute magnitude of −5.53, is approximately 14,000 times more luminous than the Sun. Despite Canopus being vastly more luminous than Sirius, however, Sirius appears brighter than Canopus. This is because Sirius is merely 8.6 light-years from the Earth, while Canopus is much further away at a distance of 310 light-years.

As of 2006, the star with the highest known absolute magnitude is LBV 1806-20, with a magnitude of −14.2. This star is 38,000,000 times more luminuous as the Sun. The least luminous stars that are currently known are located in the NGC 6397 cluster. The faintest red dwarfs in the cluster were magnitude 26, while a 28th magnitude white dwarf was also discovered. These faint stars are so dim that their light is as bright as a birthday candle on the Moon when viewed from the Earth.

Classification

Surface Temperature Ranges for
Different Stellar Classes

Class	Temperature	Sample star
O	33,000 K or more	Zeta Ophiuchi
B	10,500–30,000 K	Rigel
A	7,500–10,000 K	Altair
F	6,000–7,200 K	Procyon A
G	5,500–6,000 K	Sun
K	4,000–5,250 K	Epsilon Indi
M	2,600–3,850 K	Proxima Centauri

There are different classifications of stars according to their spectra ranging from type O, which are very hot, to M, which are so cool that molecules may form in their atmospheres. The main classifications in order of decreasing surface temperature are O, B, A, F, G, K, and M. A variety of rare spectral types have special classifications. The most common of these are types L and T, which classify the coldest low-mass stars and brown dwarfs.

Each letter has 10 sub-classifications numbered (hottest to coldest) from 0 to 9. This system matches closely with temperature, but breaks down at the extreme hottest end; class O0 and O1 stars may not exist.

In addition, stars may be classified by their "luminosity effects", which correspond to their spatial size and is determined by the surface gravity. These range from 0 ( hypergiants) through III ( giants) to V (main sequence dwarfs) and VII (white dwarfs). Most stars fall into the main sequence, which consists of ordinary hydrogen-burning stars. These fall along a narrow band when graphed according to their absolute magnitude and spectral type. Our Sun is a main sequence G2V (yellow dwarf), being of intermediate temperature and ordinary size.

Additional nomenclature, in the form of lower-case letters, can follow the spectral type to indicate peculiar features of the spectrum. For example, an "e" can indicate the presence of emission lines; "m" represents unusually strong levels of metals, and "var" can mean variations in the spectral type.

White dwarf stars have their own class that begins with the letter D. This is further sub-divided into the classes DA, DB, DC, DO, DZ, and DQ, depending on the types of prominent lines found in the spectrum. This is followed by a numerical value that indicates the temperature index.

Variable stars

Variable stars have periodic or random changes in luminosity because of intrinsic or extrinsic properties. Of the intrinsically variable stars, the primary types can be subdivided into three principal groups.

Pulsating variables are stars that vary in radius over time, expanding and contracting as a result of the stellar aging process. This category includes Cepheid and cepheid-like stars, and long-period variables such as Mira.

Eruptive variables are stars that experience sudden increases in luminosity because of flares or mass ejection events. This group includes protostars, Wolf-Rayet stars, and Flare stars, as well as giant and supergiant stars.

Cataclysmic or explosive variables undergo a dramatic change in their properties. This group includes novae and supernovae. A binary star system that includes a nearby white dwarf can produce certain types of these spectacular stellar explosions, including the nova and a Type 1a supernova. The explosion is created when the white dwarf accretes hydrogen from the companion star, building up mass until the hydrogen undergoes fusion. Some novae are also recurrent, having periodic outbursts of moderate amplitude.

Stars can also vary in luminosity because of extrinsic factors, such as eclipsing binaries, as well as rotating stars that produce extreme starspots. A notable example of an eclipsing binary is Algol, which regularly varies in magnitude from 2.3 to 3.5 over a period of 2.87 days.

Structure

The interior of a stable, main sequence star is in a state of equilibrium in which the forces in any small volume almost exactly counterbalance each other. The balancing forces consist of inward directed gravitational force and the opposing pressure from the thermal energy of the plasma gas. For these forces to balance out, the temperature at the core of a typical star has to be on the order of 10⁷ K or higher. The resulting temperature and pressure at the hydrogen-burning core of a main sequence star are sufficient for nuclear fusion to occur, and for sufficient energy to be produced to prevent further collapse of the star.

As atomic nuclei are fused in the core, they emit energy in the form of gamma rays. These photons interact with the surrounding plasma, adding to the thermal energy at the core. Stars on the main sequence convert hydrogen into helium, creating a slowly but steadily increasing proportion of helium in the core. Eventually the helium content becomes predominant and energy production ceases at the core. Instead, for stars of greater than 0.4 solar masses, fusion occurs in a slowly expanding shell around the degenerate helium core.

In addition to hydrostatic equilibrium, the interior of a stable star will also maintain an energy balance of thermal equilibrium. There is a radial temperature gradient throughout the interior that results in a flux of energy flowing toward the exterior. The outgoing flux of energy leaving any layer within the star will exactly match the incoming flux from below.

The radiation zone is the region within the stellar interior where radiative transfer is sufficiently efficient to maintain the flux of energy. In this region the plasma will not be perturbed and any mass motions will die out. If this is not the case, however, then the plasma becomes unstable and convection will occur, forming a convection zone. This can occur, for example, in regions where very high energy fluxes occur, such near the core or in areas with high opacity as in the outer envelope.

The occurrence of convection in the outer envelope of a main sequence star depends on the spectral type. Stars with several times the mass of the Sun have a convection zone deep within the interior and a radiative zone in the outer layers. Smaller stars such as the Sun are just the opposite, with the convective zone located in the outer layers. Red dwarf stars with less than 0.4 solar masses are convective throughout, which prevents the accumulation of a helium core. For most stars the convective zones will also vary over time as the star ages and the constitution of the interior is modified.

The portion of a main sequence star that is visible to an observer is called the photosphere. This is the layer at which the plasma gas of the star becomes transparent to photons of light. From here, the energy generated at the core becomes free to propagate out into space. It is within the photosphere that sun spots, or regions of lower than average temperature, appear.

Above the level of the photosphere is the stellar atmosphere. In a main sequence star such as the Sun, the lowest level of the atmosphere is the thin chromosphere region, where spicules appear and stellar flares begin. This is surrounded by a transition region, where the temperature rapidly increases within a distance of only 100 km. Beyond this is the corona, a volume of super-heated plasma that can extend outward to several million kilometres. The existence of a corona appears to be dependent on a convective zone in the outer layers of the star. Despite its high temperature, the corona emits very little light. The corona region of the Sun is normally only visible during a solar eclipse.

From the corona, a stellar wind of plasma particles expands outward from the star, propagating until it interacts with the interstellar medium.

Nuclear fusion reaction pathways

A variety of different nuclear fusion reactions take place inside the cores of stars, depending upon their mass and composition, as part of stellar nucleosynthesis. The net mass of the fused atomic nuclei is smaller than the sum of the constituents. This lost mass is converted into energy, according to the mass-energy relationship E=mc².

The hydrogen fusion process is temperature-sensitive, so a moderate increase in the core temperature will result in a significant increase in the fusion rate. As a result the core temperature of main sequence stars only varies from 4 million °K for a small M-class star to 40 million °K for a massive O-class star.

In the Sun, with a 10⁷ °K core, hydrogen fuses to form helium in the proton-proton chain reaction:

4 ¹H → 2 ²H + 2 e⁺ + 2 ν_e (4.0 M eV + 1.0 MeV)

2¹H + 2²H → 2 ³He + 2γ (5.5 MeV)

2³He → ⁴He + 2¹H (12.9 MeV)

These reactions result in the overall reaction:

4¹H → ⁴He + 2e⁺ + 2γ + 2ν_e (26.7 MeV)

where e⁺ is a positron, γ is a gamma ray photon, ν_e is a neutrino, and H and He are isotopes of hydrogen and helium, respectively. The energy released by this reaction is in millions of electron volts, which is actually only a tiny amount of energy. However enormous numbers of these reactions occur constantly, producing all the energy necessary to sustain the star's radiation output.

In more massive stars, helium is produced in a cycle of reactions catalyzed by carbon—the carbon-nitrogen-oxygen cycle.

In evolved stars with cores at 10⁸ °K and masses between 0.5 and 10 solar masses, helium can be transformed into carbon in the triple-alpha process that uses the intermediate element beryllium:

⁴He + ⁴He + 92 keV → ^8*Be

⁴He + ^8*Be + 67 keV → ^12*C

^12*C → ¹²C + γ + 7.4 MeV

For an overall reaction of:

3⁴He → ¹²C + γ + 7.2 MeV

In massive stars, heavier elements can also be burned in a contracting core through the Neon burning process and Oxygen burning process. The final stage in the stellar nucleosynthesis process is the Silicon burning process that results in the production of the stable isotope iron-56. Fusion can not proceed any further except through an endothermic process, and so further energy can only be produced through gravitational collapse.

The example below shows the amount of time required for a star of 20 solar masses to consume all of its nuclear fuel. As an O-class main sequence star, it would be 8 times the solar radius and 62,000 times the Sun's luminosity.

Fuel material	Temperature (million Kelvin)	Density (kg/cm³)	Burn duration τ
H	37	0.0045	8.1 million years
He	188	0.97	1.2 million years
C	870	170	976 years
Ne	1,570	3,100	0.6 years
O	1,980	5,550	1.25 years
S/Si	3,340	33,400	11.5 days