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; these are the most numerous true stars in the universe, include the Earth's Sun. After condensation and ignition of a star, it generates thermal energy in its dense core region through nuclear fusion of hydrogen into helium. During this stage of the star's lifetime, it is located on the main sequence at a position determined by its mass, but based upon its chemical composition and age; the cores of main-sequence stars are in hydrostatic equilibrium, where outward thermal pressure from the hot core is balanced by the inward pressure of gravitational collapse from the overlying layers. The strong dependence of the rate of energy generation on temperature and pressure helps to sustain this balance.
Energy generated at the core 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 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 uses atoms of carbon 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 radiative with convective zones near the surface. With decreasing stellar mass, the proportion of the star forming a convective envelope increases.
Main-sequence stars below 0.4 M☉ 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 a star is, 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, into a supergiant, red giant, or directly to a white dwarf. In the early part of the 20th century, information about the types and distances of stars became more available; the spectra of stars were shown to have distinctive features. 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 1901. 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. The following year he began studying star clusters, he published the first plots of color versus luminosity for these stars. These plots showed a 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, 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 followed the spectra-luminosity relationship discovered by Russell. However, the giant stars are much brighter than so do not follow the same relationship.
Russell proposed that the "giant stars must have low density or great surface-brightness, the reverse is true of dwarf stars". The same curve showed that there were 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. By this theorem, when a star's chemical composition and its position on the main sequence is known, so too is the star's mass and radius. A refined scheme for stellar classification was published in 1943 by William Wilson Morgan and Philip Childs 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 lett
The Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin is the base unit of temperature in the International System of Units; until 2018, the kelvin was defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. In other words, it was defined such that the triple point of water is 273.16 K. On 16 November 2018, a new definition was adopted, in terms of a fixed value of the Boltzmann constant. For legal metrology purposes, the new definition will come into force on 20 May 2019; the Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin, who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or written as a degree; the kelvin is the primary unit of temperature measurement in the physical sciences, but is used in conjunction with the degree Celsius, which has the same magnitude.
The definition implies that absolute zero is equivalent to −273.15 °C. In 1848, William Thomson, made Lord Kelvin, wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby "infinite cold" was the scale's null point, which used the degree Celsius for its unit increment. Kelvin calculated; this absolute scale is known today as the Kelvin thermodynamic temperature scale. Kelvin's value of "−273" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the accepted value. In 1954, Resolution 3 of the 10th General Conference on Weights and Measures gave the Kelvin scale its modern definition by designating the triple point of water as its second defining point and assigned its temperature to 273.16 kelvins. In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K. Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction 1/273.16 of the thermodynamic temperature of the triple point of water."In 2005, the Comité International des Poids et Mesures, a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the Kelvin thermodynamic temperature scale would refer to water having an isotopic composition specified as Vienna Standard Mean Ocean Water.
In 2018, Resolution A of the 26th CGPM adopted a significant redefinition of SI base units which included redefining the Kelvin in terms of a fixed value for the Boltzmann constant of 1.380649×10−23 J/K. When spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm; when reference is made to the "Kelvin scale", the word "kelvin"—which is a noun—functions adjectivally to modify the noun "scale" and is capitalized. As with most other SI unit symbols there is a space between the kelvin symbol. Before the 13th CGPM in 1967–1968, the unit kelvin was called a "degree", the same as with the other temperature scales at the time, it was distinguished from the other scales with either the adjective suffix "Kelvin" or with "absolute" and its symbol was °K. The latter term, the unit's official name from 1948 until 1954, was ambiguous since it could be interpreted as referring to the Rankine scale. Before the 13th CGPM, the plural form was "degrees absolute".
The 13th CGPM changed the unit name to "kelvin". The omission of "degree" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales, but rather an absolute unit of measure which can be manipulated algebraically. In science and engineering, degrees Celsius and kelvins are used in the same article, where absolute temperatures are given in degrees Celsius, but temperature intervals are given in kelvins. E.g. "its measured value was 0.01028 °C with an uncertainty of 60 µK." This practice is permissible because the degree Celsius is a special name for the kelvin for use in expressing relative temperatures, the magnitude of the degree Celsius is equal to that of the kelvin. Notwithstanding that the official endorsement provided by Resolution 3 of the 13th CGPM states "a temperature interval may be expressed in degrees Celsius", the practice of using both °C and K is widespread throughout the scientific world; the use of SI prefixed forms of the degree Celsius to express a temperature interval has not been adopted.
In 2005 the CIPM embarked on a programme to redefine the kelvin using a more experimentally rigorous methodology. In particular, the committee proposed redefining the kelvin such that Boltzmann's constant takes the exact value 1.3806505×10−23 J/K. The committee had hoped tha
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
Right ascension is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the point above the earth in question. When paired with declination, these astronomical coordinates specify the direction of a point on the celestial sphere in the equatorial coordinate system. An old term, right ascension refers to the ascension, or the point on the celestial equator that rises with any celestial object as seen from Earth's equator, where the celestial equator intersects the horizon at a right angle, it contrasts with oblique ascension, the point on the celestial equator that rises with any celestial object as seen from most latitudes on Earth, where the celestial equator intersects the horizon at an oblique angle. Right ascension is the celestial equivalent of terrestrial longitude. Both right ascension and longitude measure an angle from a primary direction on an equator. Right ascension is measured from the Sun at the March equinox i.e. the First Point of Aries, the place on the celestial sphere where the Sun crosses the celestial equator from south to north at the March equinox and is located in the constellation Pisces.
Right ascension is measured continuously in a full circle from that alignment of Earth and Sun in space, that equinox, the measurement increasing towards the east. As seen from Earth, objects noted to have 12h RA are longest visible at the March equinox. On those dates at midnight, such objects will reach their highest point. How high depends on their declination. Any units of angular measure could have been chosen for right ascension, but it is customarily measured in hours and seconds, with 24h being equivalent to a full circle. Astronomers have chosen this unit to measure right ascension because they measure a star's location by timing its passage through the highest point in the sky as the Earth rotates; the line which passes through the highest point in the sky, called the meridian, is the projection of a longitude line onto the celestial sphere. Since a complete circle contains 24h of right ascension or 360°, 1/24 of a circle is measured as 1h of right ascension, or 15°. A full circle, measured in right-ascension units, contains 24 × 60 × 60 = 86400s, or 24 × 60 = 1440m, or 24h.
Because right ascensions are measured in hours, they can be used to time the positions of objects in the sky. For example, if a star with RA = 1h 30m 00s is at its meridian a star with RA = 20h 00m 00s will be on the/at its meridian 18.5 sidereal hours later. Sidereal hour angle, used in celestial navigation, is similar to right ascension, but increases westward rather than eastward. Measured in degrees, it is the complement of right ascension with respect to 24h, it is important not to confuse sidereal hour angle with the astronomical concept of hour angle, which measures angular distance of an object westward from the local meridian. The Earth's axis rotates westward about the poles of the ecliptic, completing one cycle in about 26,000 years; this movement, known as precession, causes the coordinates of stationary celestial objects to change continuously, if rather slowly. Therefore, equatorial coordinates are inherently relative to the year of their observation, astronomers specify them with reference to a particular year, known as an epoch.
Coordinates from different epochs must be mathematically rotated to match each other, or to match a standard epoch. Right ascension for "fixed stars" near the ecliptic and equator increases by about 3.05 seconds per year on average, or 5.1 minutes per century, but for fixed stars further from the ecliptic the rate of change can be anything from negative infinity to positive infinity. The right ascension of Polaris is increasing quickly; the North Ecliptic Pole in Draco and the South Ecliptic Pole in Dorado are always at right ascension 18h and 6h respectively. The used standard epoch is J2000.0, January 1, 2000 at 12:00 TT. The prefix "J" indicates. Prior to J2000.0, astronomers used the successive Besselian epochs B1875.0, B1900.0, B1950.0. The concept of right ascension has been known at least as far back as Hipparchus who measured stars in equatorial coordinates in the 2nd century BC, but Hipparchus and his successors made their star catalogs in ecliptic coordinates, the use of RA was limited to special cases.
With the invention of the telescope, it became possible for astronomers to observe celestial objects in greater detail, provided that the telescope could be kept pointed at the object for a period of time. The easiest way to do, to use an equatorial mount, which allows the telescope to be aligned with one of its two pivots parallel to the Earth's axis. A motorized clock drive is used with an equatorial mount to cancel out the Earth's rotation; as the equatorial mount became adopted for observation, the equatorial coordinate system, which includes right ascension, was adopted at the same time for simplicity. Equatorial mounts could be pointed at objects with known right ascension and declination by the use of setting circles; the first star catalog to use right ascen
Minute and second of arc
A minute of arc, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn – it is for this reason that the Earth's circumference is exactly 21,600 nautical miles. A minute of arc is π/10800 of a radian. A second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, π/648000 of a radian; these units originated in Babylonian astronomy as sexagesimal subdivisions of the degree. To express smaller angles, standard SI prefixes can be employed; the number of square arcminutes in a complete sphere is 4 π 2 = 466 560 000 π ≈ 148510660 square arcminutes. The names "minute" and "second" have nothing to do with the identically named units of time "minute" or "second"; the identical names reflect the ancient Babylonian number system, based on the number 60. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted.
One arcminute is thus written 1′. It is abbreviated as arcmin or amin or, less the prime with a circumflex over it; the standard symbol for the arcsecond is the double prime, though a double quote is used where only ASCII characters are permitted. One arcsecond is thus written 1″, it is abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations, the preference being for degrees and decimals of a minute, for example, written as 42° 25.32′ or 42° 25.322′. This notation has been carried over into marine GPS receivers, which display latitude and longitude in the latter format by default; the full moon's average apparent size is about 31 arcminutes. An arcminute is the resolution of the human eye. An arcsecond is the angle subtended by a U. S. dime coin at a distance of 4 kilometres. An arcsecond is the angle subtended by an object of diameter 725.27 km at a distance of one astronomical unit, an object of diameter 45866916 km at one light-year, an object of diameter one astronomical unit at a distance of one parsec, by definition.
A milliarcsecond is about the size of a dime atop the Eiffel Tower. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth. A nanoarcsecond is about the size of a penny on Neptune's moon Triton as observed from Earth. Notable examples of size in arcseconds are: Hubble Space Telescope has calculational resolution of 0.05 arcseconds and actual resolution of 0.1 arcseconds, close to the diffraction limit. Crescent Venus measures between 66 seconds of arc. Since antiquity the arcminute and arcsecond have been used in astronomy. In the ecliptic coordinate system and longitude; the principal exception is right ascension in equatorial coordinates, measured in time units of hours and seconds. The arcsecond is often used to describe small astronomical angles such as the angular diameters of planets, the proper motion of stars, the separation of components of binary star systems, parallax, the small change of position of a star in the course of a year or of a solar system body as the Earth rotates.
These small angles may be written in milliarcseconds, or thousandths of an arcsecond. The unit of distance, the parsec, named from the parallax of one arc second, was developed for such parallax measurements, it is the distance at which the mean radius of the Earth's orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia, launched in 2013, can approximate star positions to 7 microarcseconds. Apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red giant with a diameter of 0.05 arcsecond. Because of the effects of atmospheric seeing, ground-based telescopes will smear the image of a star to an angular diameter of about 0.5 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond. Space telescopes are diffraction limited. For example, the Hubble Space Telescope can reach an angular size of stars down to about 0.1″. Techniques exist for improving seeing on the ground. Adaptive optics, for example, can produce images around 0.05 arcsecond on a 10 m class telescope.
Minutes and seconds of arc are used in cartography and navigation. At sea level one minute of arc
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
The horizontal branch is a stage of stellar evolution that follows the red giant branch in stars whose masses are similar to the Sun's. Horizontal-branch stars are powered by helium fusion in the core and by hydrogen fusion in a shell surrounding the core; the onset of core helium fusion at the tip of the red giant branch causes substantial changes in stellar structure, resulting in an overall reduction in luminosity, some contraction of the stellar envelope, the surface reaching higher temperatures. Horizontal branch stars were discovered with the first deep photographic photometric studies of globular clusters and were notable for being absent from all open clusters, studied up to that time; the horizontal branch is so named because in low-metallicity star collections like globular clusters, HB stars lie along a horizontal line in a Hertzsprung–Russell diagram. After exhausting their core hydrogen, stars leave the main sequence and begin fusion in a hydrogen shell around the helium core and become giants on the red giant branch.
In stars with masses up to 2.3 times the mass of the Sun the helium core becomes a region of degenerate matter that does not contribute to the generation of energy. It continues to grow and increase in temperature as the hydrogen fusion in the shell contributes more helium. If the star has more than about 0.5 solar masses, the core reaches the temperature necessary for the fusion of helium into carbon through the triple-alpha process. The initiation of helium fusion begins across the core region, which will cause an immediate temperature rise and a rapid increase in the rate of fusion. Within a few seconds the core becomes non-degenerate and expands, producing an event called helium flash. Non-degenerate cores initiate fusion more smoothly, without a flash; the output of this event is absorbed by the layers of plasma above, so the effects are not seen from the exterior of the star. The star now changes to a new equilibrium state, its evolutionary path switches from the red giant branch onto the horizontal branch of the Hertzsprung–Russell diagram.
Stars between about 2.3 M☉ and 8 M☉ have larger helium cores that do not become degenerate. Instead their cores reach the Schoenberg-Chandrasekhar mass at which they are no longer in hydrostatic or thermal equilibrium, they contract and heat up, which triggers helium fusion before the core becomes degenerate. These stars become hotter during core helium fusion, but they have different core masses and hence different luminosities from HB stars, they vary in temperature during core helium fusion and perform a blue loop before moving to the asymptotic giant branch. Stars more massive than about 8 M☉ ignite their core helium smoothly, go on to burn heavier elements as a red supergiant. Stars remain on the horizontal branch for around 100 million years, becoming more luminous in the same way that main sequence stars increase luminosity as the virial theorem shows; when their core helium is exhausted, they progress to helium shell burning on the asymptotic giant branch. On the AGB they become cooler and much more luminous.
Stars on the horizontal branch all have similar core masses, following the helium flash. This means that they have similar luminosities, on a Hertzsprung–Russell diagram plotted by visual magnitude the branch is horizontal; the size and temperature of an HB star depends on the mass of the hydrogen envelope remaining around the helium core. Stars with larger hydrogen envelopes are cooler; this creates the spread of stars along the horizontal branch at constant luminosity. The temperature variation effect is much stronger at lower metallicity, so old clusters have more pronounced horizontal branches. Although the horizontal branch is named because it consists of stars with the same absolute magnitude across a range of temperatures, lying in a horizontal bar on a color–magnitude diagrams, the branch is far from horizontal at the blue end; the horizontal branch ends in a "blue tail" with hotter stars having lower luminosity with a "blue hook" of hot stars. It is not horizontal when plotted by bolometric luminosity, with hotter horizontal branch stars being less luminous than cooler ones.
The hottest horizontal-branch stars, referred to as extreme horizontal branch, have temperatures of 20,000–30,000K. This is far beyond. Theories to explain these stars include binary interactions, "late thermal pulses", where a thermal pulse that Asymptotic giant branch stars experience occurs after fusion has ceased and the star has entered the superwind phase; these stars are "born again" with unusual properties. Despite the bizarre-sounding process, this is expected to occur for 10% or more of post-AGB stars, although it is thought that only late thermal pulses create extreme horizontal-branch stars, after the planetary nebular phase and when the central star is cooling towards a white dwarf. Globular cluster CMDs show horizontal branches that have a prominent gap in the HB; this gap in the CMD incorrectly suggests that the cluster has no stars in this region of its CMD. The gap occurs at the instability strip, so many stars in this region pulsate; these pulsating horizontal-branch stars are known as RR Lyrae variable stars and they are variable in brightness with periods of up to 1.2 days.
It requires an extended observing program to establish the star's true apparent color. Such a program is beyond the scope of an investigation of a cluster's color