Alpha Centauri is the closest star system and closest planetary system to the Solar System at 4.37 light-years from the Sun. It is a triple star system, consisting of three stars: α Centauri A, α Centauri B, α Centauri C. Alpha Centauri A and B are Sun-like stars, together they form the binary star Alpha Centauri AB. To the naked eye, the two main components appear to be a single star with an apparent magnitude of −0.27, forming the brightest star in the southern constellation of Centaurus and the third-brightest in the night sky, outshone only by Sirius and Canopus. Alpha Centauri A has 1.1 times the mass and 1.519 times the luminosity of the Sun, while Alpha Centauri B is smaller and cooler, at 0.907 times the Sun's mass and 0.445 times its luminosity. The pair orbit about a common centre with an orbital period of 79.91 years. Their elliptical orbit is eccentric, so that the distance between A and B varies from 35.6 astronomical units, or about the distance between Pluto and the Sun, to that between Saturn and the Sun.
Alpha Centauri C, or Proxima Centauri, is a faint red dwarf. Though not visible to the naked eye, Proxima Centauri is the closest star to the Sun at a distance of 4.24 light-years closer than Alpha Centauri AB. The distance between Proxima Centauri and Alpha Centauri AB is about 13,000 astronomical units, equivalent to about 430 times the radius of Neptune's orbit. Proxima Centauri b is an Earth-sized exoplanet in the habitable zone of Proxima Centauri. Α Centauri is the system's designation given by Johann Bayer in 1603. It once bore the name Rigil Kentaurus, a Latinisation of the Arabic name رجل القنطورس Rijl al-Qanṭūris, meaning'Foot of the Centaur'. Alpha Centauri C was discovered in 1915 by Robert T. A. Innes, who suggested that it be named Proxima Centaurus amended to Proxima Centauri; the name is from Latin, meaning'nearest of Centaurus'. In 2016, the Working Group on Star Names of the International Astronomical Union, having decided to attribute proper names to individual stars rather than entire multiple systems, approved the names Rigil Kentaurus for Alpha Centauri A and Proxima Centauri for Alpha Centauri C.
In 10 August 2018, IAU approved the name Toliman for Alpha Centauri B. Alpha Centauri is a triple star system, with its two main stars, Alpha Centauri A and Alpha Centauri B, being a binary component; the AB designation, or older A×B, denotes the mass centre of a main binary system relative to companion star in a multiple star system. AB-C refers to the component of Proxima Centauri in relation to the central binary, being the distance between the centre of mass and the outlying companion; because the distance between Proxima and either of Alpha Centauri A or B is similar, the AB binary system is sometimes treated as a single gravitational object. The A and B components of Alpha Centauri have an orbital period of 79.91 years. Their orbit is moderately eccentric, e = 0.5179. Viewed from Earth, the apparent orbit of A and B means that their separation and position angle are in continuous change throughout their projected orbit. Observed stellar positions in 2019 are separated by 4.92 arcsec through the PA of 337.1°, increasing to 5.49 arcsec through 345.3° in 2020.
The closest recent approach was in February 2016, at 4.0 arcsec through the PA of 300°. The observed maximum separation of these stars is about 22 arcsec, while the minimum distance is 1.7 arcsec. The widest separation occurred during February 1976, the next will be in January 2056; the most recent, true orbit, closest approach or periastron was in August 1955, the next will be in May 2035. The furthest orbital separation or apastron last occurred in May 1995, the next will be in 2075; the apparent distance between Alpha Centauri A and B is decreasing, at least until 2019. Alpha Centauri C is about 13,000 astronomical units away from Alpha Centauri AB; this is equivalent to 0.21 ly or 1.9 trillion km—about 5% the distance between Alpha Centauri AB and the Sun. For a long time, estimates of Proxima's small orbital speed around AB were insufficiently accurate to determine whether Proxima Centauri is bound to the Alpha Centauri system or an unrelated star that happens to be passing by at a low speed.
Radial velocity measurements made in 2017 were precise enough to show that Proxima Centauri and Alpha Centauri AB are gravitationally bound. The orbital period of Proxima Centauri is 547000+6600−4000 years, with an eccentricity of 0.50 ± 0.08, more eccentric than Mercury's. Proxima Centauri comes within 4300+1100−900 AU of AB at periastron, the apastron occurs at 13000+300−100 AU. Asteroseismic studies, chromospheric activity, stellar rotation are all consistent with the Alpha Centauri system being similar in age to, or older than, the Sun. Asteroseismic analyses that incorporate tight observational constraints on the stellar parameters for the Alpha Centauri stars have yielded age estimates of 4.85±0.5 Gyr, 5.0±0.5 Gyr, 5.2 ± 1.9 Gyr, 6.4 Gyr, 6.52±0.3 Gyr. Age estimates for the stars based on chromospheric activity yield 4.4 ± 2.1 Gyr, whereas gyrochronology yields 5.0±0.3 Gyr. Stellar evolution theory implies both stars are older than the Sun at 5 to 6 billion years, as derived by their mass and spectral characteristics.
From the orbital elements, th
Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. The information obtained by astrometric measurements provides information on the kinematics and physical origin of the Solar System and our galaxy, the Milky Way; the history of astrometry is linked to the history of star catalogues, which gave astronomers reference points for objects in the sky so they could track their movements. This can be dated back to Hipparchus, who around 190 BC used the catalogue of his predecessors Timocharis and Aristillus to discover Earth's precession. In doing so, he developed the brightness scale still in use today. Hipparchus compiled a catalogue with their positions. Hipparchus's successor, included a catalogue of 1,022 stars in his work the Almagest, giving their location and brightness. In the 10th century, Abd al-Rahman al-Sufi carried out observations on the stars and described their positions and star color. Ibn Yunus observed more than 10,000 entries for the Sun's position for many years using a large astrolabe with a diameter of nearly 1.4 metres.
His observations on eclipses were still used centuries in Simon Newcomb's investigations on the motion of the Moon, while his other observations of the motions of the planets Jupiter and Saturn inspired Laplace's Obliquity of the Ecliptic and Inequalities of Jupiter and Saturn. In the 15th century, the Timurid astronomer Ulugh Beg compiled the Zij-i-Sultani, in which he catalogued 1,019 stars. Like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Beg's catalogue is estimated to have been precise to within 20 minutes of arc. In the 16th century, Tycho Brahe used improved instruments, including large mural instruments, to measure star positions more than with a precision of 15–35 arcsec. Taqi al-Din measured the right ascension of the stars at the Constantinople Observatory of Taqi ad-Din using the "observational clock" he invented; when telescopes became commonplace, setting circles sped measurements James Bradley first tried to measure stellar parallaxes in 1729. The stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light and the nutation of the Earth's axis.
His cataloguing of 3222 stars was refined in 1807 by Friedrich Bessel, the father of modern astrometry. He made the first measurement of stellar parallax: 0.3 arcsec for the binary star 61 Cygni. Being difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century by use of the filar micrometer. Astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated computer technology of the 1960s allowed more efficient compilation of star catalogues. In the 1980s, charge-coupled devices replaced photographic plates and reduced optical uncertainties to one milliarcsecond; this technology made astrometry less expensive. In 1989, the European Space Agency's Hipparcos satellite took astrometry into orbit, where it could be less affected by mechanical forces of the Earth and optical distortions from its atmosphere. Operated from 1989 to 1993, Hipparcos measured large and small angles on the sky with much greater precision than any previous optical telescopes.
During its 4-year run, the positions and proper motions of 118,218 stars were determined with an unprecedented degree of accuracy. A new "Tycho catalog" drew together a database of 1,058,332 to within 20-30 mas. Additional catalogues were compiled for the 23,882 double/multiple stars and 11,597 variable stars analyzed during the Hipparcos mission. Today, the catalogue most used is USNO-B1.0, an all-sky catalogue that tracks proper motions, positions and other characteristics for over one billion stellar objects. During the past 50 years, 7,435 Schmidt camera plates were used to complete several sky surveys that make the data in USNO-B1.0 accurate to within 0.2 arcsec. Apart from the fundamental function of providing astronomers with a reference frame to report their observations in, astrometry is fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. In observational astronomy, astrometric techniques help identify stellar objects by their unique motions, it is instrumental for keeping time, in that UTC is the atomic time synchronized to Earth's rotation by means of exact astronomical observations.
Astrometry is an important step in the cosmic distance ladder because it establishes parallax distance estimates for stars in the Milky Way. Astrometry has been used to support claims of extrasolar planet detection by measuring the displacement the proposed planets cause in their parent star's apparent position on the sky, due to their mutual orbit around the center of mass of the system. Astrometry is more accurate in space missions that are not affected by the distorting effects of the Earth's atmosphere. NASA's planned Space Interferometry Mission was to utilize astrometric techniques to detect terrestrial planets orbiting 200 or so of the nearest solar-type stars; the European Space Agency's Gaia Mission, launched in 2013, applies astrometric techniques in its stellar census. In addition to the detection of exoplanets, it can be used to determine their mass. Astrometric measurements are used by astrophysicists to constrain certain models in celestial mechanics. By measuring the velocities of pulsars, it is possible to put a limit on the asymmetry of supernova explosions.
A constellation is a group of stars that forms an imaginary outline or pattern on the celestial sphere representing an animal, mythological person or creature, a god, or an inanimate object. The origins of the earliest constellations go back to prehistory. People used them to relate stories of their beliefs, creation, or mythology. Different cultures and countries adopted their own constellations, some of which lasted into the early 20th century before today's constellations were internationally recognized. Adoption of constellations has changed over time. Many have changed in shape; some became popular. Others were limited to single nations; the 48 traditional Western constellations are Greek. They are given in Aratus' work Phenomena and Ptolemy's Almagest, though their origin predates these works by several centuries. Constellations in the far southern sky were added from the 15th century until the mid-18th century when European explorers began traveling to the Southern Hemisphere. Twelve ancient constellations belong to the zodiac.
The origins of the zodiac remain uncertain. In 1928, the International Astronomical Union formally accepted 88 modern constellations, with contiguous boundaries that together cover the entire celestial sphere. Any given point in a celestial coordinate system lies in one of the modern constellations; some astronomical naming systems include the constellation where a given celestial object is found to convey its approximate location in the sky. The Flamsteed designation of a star, for example, consists of a number and the genitive form of the constellation name. Other star patterns or groups called asterisms are not constellations per se but are used by observers to navigate the night sky. Examples of bright asterisms include the Pleiades and Hyades within the constellation Taurus or Venus' Mirror in the constellation of Orion.. Some asterisms, like the False Cross, are split between two constellations; the word "constellation" comes from the Late Latin term cōnstellātiō, which can be translated as "set of stars".
The Ancient Greek word for constellation is ἄστρον. A more modern astronomical sense of the term "constellation" is as a recognisable pattern of stars whose appearance is associated with mythological characters or creatures, or earthbound animals, or objects, it can specifically denote the recognized 88 named constellations used today. Colloquial usage does not draw a sharp distinction between "constellations" and smaller "asterisms", yet the modern accepted astronomical constellations employ such a distinction. E.g. the Pleiades and the Hyades are both asterisms, each lies within the boundaries of the constellation of Taurus. Another example is the northern asterism known as the Big Dipper or the Plough, composed of the seven brightest stars within the area of the IAU-defined constellation of Ursa Major; the southern False Cross asterism includes portions of the constellations Carina and Vela and the Summer Triangle.. A constellation, viewed from a particular latitude on Earth, that never sets below the horizon is termed circumpolar.
From the North Pole or South Pole, all constellations south or north of the celestial equator are circumpolar. Depending on the definition, equatorial constellations may include those that lie between declinations 45° north and 45° south, or those that pass through the declination range of the ecliptic or zodiac ranging between 23½° north, the celestial equator, 23½° south. Although stars in constellations appear near each other in the sky, they lie at a variety of distances away from the Earth. Since stars have their own independent motions, all constellations will change over time. After tens to hundreds of thousands of years, familiar outlines will become unrecognizable. Astronomers can predict the past or future constellation outlines by measuring individual stars' common proper motions or cpm by accurate astrometry and their radial velocities by astronomical spectroscopy; the earliest evidence for the humankind's identification of constellations comes from Mesopotamian inscribed stones and clay writing tablets that date back to 3000 BC.
It seems that the bulk of the Mesopotamian constellations were created within a short interval from around 1300 to 1000 BC. Mesopotamian constellations appeared in many of the classical Greek constellations; the oldest Babylonian star catalogues of stars and constellations date back to the beginning in the Middle Bronze Age, most notably the Three Stars Each texts and the MUL. APIN, an expanded and revised version based on more accurate observation from around 1000 BC. However, the numerous Sumerian names in these catalogues suggest that they built on older, but otherwise unattested, Sumerian traditions of the Early Bronze Age; the classical Zodiac is a revision of Neo-Babylonian constellations from the 6th century BC. The Greeks adopted the Babylonian constellations in the 4th century BC. Twenty Ptolemaic constellations are from the Ancient Near East. Another ten have the same stars but different names. Biblical scholar, E. W. Bullinger interpreted some of the creatures mentioned in the books of Ezekiel and Revelation as the middle signs of the four quarters of the Zodiac, with the Lion as Leo, the Bull as Taurus, the Man representing Aquarius and the Eagle standing in for Scorpio.
The biblical Book of Job also
Proper motion is the astronomical measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more distant stars. The components for proper motion in the equatorial coordinate system are given in the direction of right ascension and of declination, their combined value is computed as the total proper motion. It has dimensions of angle per time arcseconds per year or milliarcseconds per year. Knowledge of the proper motion and radial velocity allows calculations of true stellar motion or velocity in space in respect to the Sun, by coordinate transformation, the motion in respect to the Milky Way. Proper motion is not "proper", because it includes a component due to the motion of the Solar System itself. Over the course of centuries, stars appear to maintain nearly fixed positions with respect to each other, so that they form the same constellations over historical time.
Ursa Major or Crux, for example, looks nearly the same now. However, precise long-term observations show that the constellations change shape, albeit slowly, that each star has an independent motion; this motion is caused by the movement of the stars relative to the Solar System. The Sun travels in a nearly circular orbit about the center of the Milky Way at a speed of about 220 km/s at a radius of 8 kPc from the center, which can be taken as the rate of rotation of the Milky Way itself at this radius; the proper motion is a two-dimensional vector and is thus defined by two quantities: its position angle and its magnitude. The first quantity indicates the direction of the proper motion on the celestial sphere, the second quantity is the motion's magnitude expressed in arcseconds per year or milliarcsecond per year. Proper motion may alternatively be defined by the angular changes per year in the star's right ascension and declination, using a constant epoch in defining these; the components of proper motion by convention are arrived at.
Suppose an object moves from coordinates to coordinates in a time Δt. The proper motions are given by: μ α = α 2 − α 1 Δ t, μ δ = δ 2 − δ 1 Δ t; the magnitude of the proper motion μ is given by the Pythagorean theorem: μ 2 = μ δ 2 + μ α 2 ⋅ cos 2 δ, μ 2 = μ δ 2 + μ α ∗ 2, where δ is the declination. The factor in cos2δ accounts for the fact that the radius from the axis of the sphere to its surface varies as cosδ, for example, zero at the pole. Thus, the component of velocity parallel to the equator corresponding to a given angular change in α is smaller the further north the object's location; the change μα, which must be multiplied by cosδ to become a component of the proper motion, is sometimes called the "proper motion in right ascension", μδ the "proper motion in declination". If the proper motion in right ascension has been converted by cosδ, the result is designated μα*. For example, the proper motion results in right ascension in the Hipparcos Catalogue have been converted. Hence, the individual proper motions in right ascension and declination are made equivalent for straightforward calculations of various other stellar motions.
The position angle θ is related to these components by: μ sin θ = μ α cos δ = μ α ∗, μ cos θ = μ δ. Motions in equatorial coordinates can be converted to motions in galactic coordinates. For the majority of stars seen in the sky, the observed proper motions are small and unremarkable; such stars are either faint or are distant, have changes of below 10 milliarcseconds per year, do not appear to move appreciably over many millennia. A few do have significant motions, are called high-proper motion stars. Motions can be in seemingly random directions. Two or more stars, double stars or open star clusters, which are moving in similar directions, exhibit so-called shared or common proper motion, suggesting they may be gravitationally attached or share similar motion in space. Barnard's Star has the largest proper motion of all stars, moving at 10.3 seconds of arc per year. L
The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is used as an estimate of a body's surface temperature when the body's emissivity curve is not known; when the star's or planet's net emissivity in the relevant wavelength band is less than unity, the actual temperature of the body will be higher than the effective temperature. The net emissivity may be low due to surface or atmospheric properties, including greenhouse effect; the effective temperature of a star is the temperature of a black body with the same luminosity per surface area as the star and is defined according to the Stefan–Boltzmann law FBol = σTeff4. Notice that the total luminosity of a star is L = 4πR2σTeff4, where R is the stellar radius; the definition of the stellar radius is not straightforward. More rigorously the effective temperature corresponds to the temperature at the radius, defined by a certain value of the Rosseland optical depth within the stellar atmosphere.
The effective temperature and the bolometric luminosity are the two fundamental physical parameters needed to place a star on the Hertzsprung–Russell diagram. Both effective temperature and bolometric luminosity depend on the chemical composition of a star; the effective temperature of our Sun is around 5780 kelvins. Stars have a decreasing temperature gradient; the "core temperature" of the Sun—the temperature at the centre of the Sun where nuclear reactions take place—is estimated to be 15,000,000 K. The color index of a star indicates its temperature from the cool—by stellar standards—red M stars that radiate in the infrared to the hot blue O stars that radiate in the ultraviolet; the effective temperature of a star indicates the amount of heat that the star radiates per unit of surface area. From the warmest surfaces to the coolest is the sequence of stellar classifications known as O, B, A, F, G, K, M. A red star could be a tiny red dwarf, a star of feeble energy production and a small surface or a bloated giant or supergiant star such as Antares or Betelgeuse, either of which generates far greater energy but passes it through a surface so large that the star radiates little per unit of surface area.
A star near the middle of the spectrum, such as the modest Sun or the giant Capella radiates more energy per unit of surface area than the feeble red dwarf stars or the bloated supergiants, but much less than such a white or blue star as Vega or Rigel. To find the effective temperature of a planet, it can be calculated by equating the power received by the planet to the known power emitted by a blackbody of temperature T. Take the case of a planet at a distance D from the star, of luminosity L. Assuming the star radiates isotropically and that the planet is a long way from the star, the power absorbed by the planet is given by treating the planet as a disc of radius r, which intercepts some of the power, spread over the surface of a sphere of radius D; the calculation assumes the planet reflects some of the incoming radiation by incorporating a parameter called the albedo. An albedo of 1 means that all the radiation is reflected, an albedo of 0 means all of it is absorbed; the expression for absorbed power is then: P a b s = L r 2 4 D 2 The next assumption we can make is that the entire planet is at the same temperature T, that the planet radiates as a blackbody.
The Stefan–Boltzmann law gives an expression for the power radiated by the planet: P r a d = 4 π r 2 σ T 4 Equating these two expressions and rearranging gives an expression for the effective temperature: T = L 16 π σ D 2 4 Note that the planet's radius has cancelled out of the final expression. The effective temperature for Jupiter from this calculation is 88 K and 51 Pegasi b is 1,258 K. A better estimate of effective temperature for some planets, such as Jupiter, would need to include the internal heating as a power input; the actual temperature depends on atmosphere effects. The actual temperature from spectroscopic analysis for HD 209458 b is 1,130 K, but the effective temperature is 1,359 K; the internal heating within Jupiter raises the effective temperature to about 152 K. The surface temperature of a planet can be estimated by modifying the effective-temperature calculation to account for emissivity and temperature variation; the area of the planet that absorbs the power from the star is Aabs, some fraction of the total surface area Atotal = 4πr2, where r is the radius of the planet.
This area intercepts some of the power, spread over the surface of a sphere of radius D. We allow the planet to reflect some of the incoming radiation by incorporating a parameter a called the albedo. An albedo of 1 means that all the radiation is reflected, an albedo
A giant star is a star with larger radius and luminosity than a main-sequence star of the same surface temperature. They lie above the main sequence on the Hertzsprung–Russell diagram and correspond to luminosity classes II and III; the terms giant and dwarf were coined for stars of quite different luminosity despite similar temperature or spectral type by Ejnar Hertzsprung about 1905. Giant stars have radii up to a few hundred times the Sun and luminosities between 10 and a few thousand times that of the Sun. Stars still more luminous than giants are referred to as hypergiants. A hot, luminous main-sequence star may be referred to as a giant, but any main-sequence star is properly called a dwarf no matter how large and luminous it is. A star becomes a giant after all the hydrogen available for fusion at its core has been depleted and, as a result, leaves the main sequence; the behaviour of a post-main-sequence star depends on its mass. For a star with a mass above about 0.25 solar masses, once the core is depleted of hydrogen it contracts and heats up so that hydrogen starts to fuse in a shell around the core.
The portion of the star outside the shell expands and cools, but with only a small increase in luminosity, the star becomes a subgiant. The inert helium core continues to grow and increase temperature as it accretes helium from the shell, but in stars up to about 10-12 M☉ it does not become hot enough to start helium burning. Instead, after just a few million years the core reaches the Schönberg–Chandrasekhar limit collapses, may become degenerate; this causes the outer layers to expand further and generates a strong convective zone that brings heavy elements to the surface in a process called the first dredge-up. This strong convection increases the transport of energy to the surface, the luminosity increases and the star moves onto the red-giant branch where it will stably burn hydrogen in a shell for a substantial fraction of its entire life; the core continues to gain mass and increase in temperature, whereas there is some mass loss in the outer layers. § 5.9. If the star's mass, when on the main sequence, was below 0.4 M☉, it will never reach the central temperatures necessary to fuse helium.
P. 169. It will therefore remain a hydrogen-fusing red giant until it runs out of hydrogen, at which point it will become a helium white dwarf. § 4.1, 6.1. According to stellar evolution theory, no star of such low mass can have evolved to that stage within the age of the Universe. In stars above about 0.4 M☉ the core temperature reaches 108 K and helium will begin to fuse to carbon and oxygen in the core by the triple-alpha process.§ 5.9, chapter 6. When the core is degenerate helium fusion begins explosively, but most of the energy goes into lifting the degeneracy and the core becomes convective; the energy generated by helium fusion reduces the pressure in the surrounding hydrogen-burning shell, which reduces its energy-generation rate. The overall luminosity of the star decreases, its outer envelope contracts again, the star moves from the red-giant branch to the horizontal branch. Chapter 6; when the core helium is exhausted, a star with up to about 8 M☉ has a carbon–oxygen core that becomes degenerate and starts helium burning in a shell.
As with the earlier collapse of the helium core, this starts convection in the outer layers, triggers a second dredge-up, causes a dramatic increase in size and luminosity. This is the asymptotic giant branch analogous to the red-giant branch but more luminous, with a hydrogen-burning shell contributing most of the energy. Stars only remain on the AGB for around a million years, becoming unstable until they exhaust their fuel, go through a planetary nebula phase, become a carbon–oxygen white dwarf. § 7.1–7.4. Main-sequence stars with masses above about 12 M☉ are very luminous and they move horizontally across the HR diagram when they leave the main sequence becoming blue giants before they expand further into blue supergiants, they start core-helium burning before the core becomes degenerate and develop smoothly into red supergiants without a strong increase in luminosity. At this stage they have comparable luminosities to bright AGB stars although they have much higher masses, but will further increase in luminosity as they burn heavier elements and become a supernova.
Stars in the 8-12 M☉ range have somewhat intermediate properties and have been called super-AGB stars. They follow the tracks of lighter stars through RGB, HB, AGB phases, but are massive enough to initiate core carbon burning and some neon burning, they form oxygen–magnesium–neon cores, which may collapse in an electron-capture supernova, or they may leave behind an oxygen–neon white dwarf. O class main sequence stars are highly luminous; the giant phase for such stars is a brief phase of increased size and luminosity before developing a supergiant spectral luminosity class. Type O giants may be more than a hundred thousand times as luminous as the sun, brighter than many supergiants. Classification is complex and difficult with small differences between luminosity classes and a continuous range of intermediate forms; the most massive stars develop giant or supergiant spectral features while still burning hydrogen in their cores, due to mixing of heavy elements to the surface and high luminosity which produces a powerful stellar wind and causes the star's atmosphere to expand.
A star whose initial mass is less than 0.25 M☉ will not become a giant star at all. For most of th
The apparent magnitude of an astronomical object is a number, a measure of its brightness as seen by an observer on Earth. The magnitude scale is logarithmic. A difference of 1 in magnitude corresponds to a change in brightness by a factor of 5√100, or about 2.512. The brighter an object appears, the lower its magnitude value, with the brightest astronomical objects having negative apparent magnitudes: for example Sirius at −1.46. The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry. Apparent magnitudes are used to quantify the brightness of sources at ultraviolet and infrared wavelengths. An apparent magnitude is measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V filter band would be denoted either as mV or simply as V, as in "mV = 15" or "V = 15" to describe a 15th-magnitude object; the scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes.
The brightest stars in the night sky were said to be of first magnitude, whereas the faintest were of sixth magnitude, the limit of human visual perception. Each grade of magnitude was considered twice the brightness of the following grade, although that ratio was subjective as no photodetectors existed; this rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest and is believed to have originated with Hipparchus. In 1856, Norman Robert Pogson formalized the system by defining a first magnitude star as a star, 100 times as bright as a sixth-magnitude star, thereby establishing the logarithmic scale still in use today; this implies that a star of magnitude m is about 2.512 times as bright as a star of magnitude m + 1. This figure, the fifth root of 100, became known as Pogson's Ratio; the zero point of Pogson's scale was defined by assigning Polaris a magnitude of 2. Astronomers discovered that Polaris is variable, so they switched to Vega as the standard reference star, assigning the brightness of Vega as the definition of zero magnitude at any specified wavelength.
Apart from small corrections, the brightness of Vega still serves as the definition of zero magnitude for visible and near infrared wavelengths, where its spectral energy distribution approximates that of a black body for a temperature of 11000 K. However, with the advent of infrared astronomy it was revealed that Vega's radiation includes an Infrared excess due to a circumstellar disk consisting of dust at warm temperatures. At shorter wavelengths, there is negligible emission from dust at these temperatures. However, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale. Therefore, the magnitude scale was extrapolated to all wavelengths on the basis of the black-body radiation curve for an ideal stellar surface at 11000 K uncontaminated by circumstellar radiation. On this basis the spectral irradiance for the zero magnitude point, as a function of wavelength, can be computed. Small deviations are specified between systems using measurement apparatuses developed independently so that data obtained by different astronomers can be properly compared, but of greater practical importance is the definition of magnitude not at a single wavelength but applying to the response of standard spectral filters used in photometry over various wavelength bands.
With the modern magnitude systems, brightness over a wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30; the brightness of Vega is exceeded by four stars in the night sky at visible wavelengths as well as the bright planets Venus and Jupiter, these must be described by negative magnitudes. For example, the brightest star of the celestial sphere, has an apparent magnitude of −1.4 in the visible. Negative magnitudes for other bright astronomical objects can be found in the table below. Astronomers have developed other photometric zeropoint systems as alternatives to the Vega system; the most used is the AB magnitude system, in which photometric zeropoints are based on a hypothetical reference spectrum having constant flux per unit frequency interval, rather than using a stellar spectrum or blackbody curve as the reference. The AB magnitude zeropoint is defined such that an object's AB and Vega-based magnitudes will be equal in the V filter band.
As the amount of light received by a telescope is reduced by transmission through the Earth's atmosphere, any measurement of apparent magnitude is corrected for what it would have been as seen from above the atmosphere. The dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of 100. Therefore, the apparent magnitude m, in the spectral band x, would be given by m x = − 5 log 100 , more expressed in terms of common logarithms as m x