Luminosity

In astronomy, luminosity is the total amount of energy emitted per unit of time by a star, galaxy, or other astronomical object.[1] As a term for energy emitted per unit time, luminosity is synonymous with power.[2][3][4][5]

In SI units luminosity is measured in joules per second or watts. Values for luminosity are often given in the terms of the luminosity of the Sun, L. Luminosity can also be given in terms of the astronomical magnitude system: the absolute bolometric magnitude (Mbol) of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band.

In contrast, the term brightness in astronomy is generally used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the luminosity of the object and the distance between the object and observer, and also on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness. The distance determined by luminosity measures can be somewhat ambiguous, and is thus sometimes called the luminosity distance.

Measuring luminosity

In astronomy, luminosity is the amount of electromagnetic energy a body radiates per unit of time.[6] When not qualified, the term "luminosity" means bolometric luminosity, which is measured either in the SI units, watts, or in terms of solar luminosities (L). A bolometer is the instrument used to measure radiant energy over a wide band by absorption and measurement of heating. A star also radiates neutrinos, which carry off some energy (about 2% in the case of our Sun), contributing to the star's total luminosity.[7] The IAU has defined a nominal solar luminosity of 3.828×1026 W to promote publication of consistent and comparable values in units of the solar luminosity.[8]

While bolometers do exist, they cannot be used to measure even the apparent brightness of a star because they are insufficiently sensitive across the electromagnetic spectrum and because most wavelengths do not reach the surface of the Earth. In practice bolometric magnitudes are measured by taking measurements at certain wavelengths and constructing a model of the total spectrum that is most likely to match those measurements. In some cases, the process of estimation is extreme, with luminosities being calculated when less than 1% of the energy output is observed, for example with a hot Wolf-Rayet star observed only in the infra-red. Bolometric luminosities can also be calculated using a bolometric correction to a luminosity in a particular passband.[9][10]

The term luminosity is also used in relation to particular passbands such as a visual luminosity of K-band luminosity.[11] These are not generally luminosities in the strict sense of an absolute measure of radiated power, but absolute magnitudes defined for a given filter in a photometric system. Several different photometric systems exist. Some such as the UBV or Johnson system are defined against photometric standard stars, while others such as the AB system are defined in terms of a spectral flux density.[12]

Stellar luminosity

Hertzsprung-Russel StarData
Hertzsprung–Russell diagram identifying stellar luminosity as a function of temperature for many stars in our solar neighborhood.

A star's luminosity can be determined from two stellar characteristics: size and effective temperature.[6] The former is typically represented in terms of solar radii, R, while the latter is represented in kelvins, but in most cases neither can be measured directly. To determine a star's radius, two other metrics are needed: the star's angular diameter and its distance from Earth. Both can be measured with great accuracy in certain cases, with cool supergiants often having large angular diameters, and some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI. However, for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty. Since the effective temperature is merely a number that represents the temperature of a black body that would reproduce the luminosity, it obviously cannot be measured directly, but it can be estimated from the spectrum.

An alternative way to measure stellar luminosity is to measure the star's apparent brightness and distance. A third component needed to derive the luminosity is the degree of interstellar extinction that is present, a condition that usually arises because of gas and dust present in the interstellar medium (ISM), the Earth's atmosphere, and circumstellar matter. Consequently, one of astronomy's central challenges in determining a star's luminosity is to derive accurate measurements for each of these components, without which an accurate luminosity figure remains elusive.[13] Extinction can only be measured directly if the actual and observed luminosities are both known, but it can be estimated from the observed colour of a star, using models of the expected level of reddening from the interstellar medium.

In the current system of stellar classification, stars are grouped according to temperature, with the massive, very young and energetic Class O stars boasting temperatures in excess of 30,000 K while the less massive, typically older Class M stars exhibit temperatures less than 3,500 K. Because luminosity is proportional to temperature to the fourth power, the large variation in stellar temperatures produces an even vaster variation in stellar luminosity.[14] Because the luminosity depends on a high power of the stellar mass, high mass luminous stars have much shorter lifetimes. The most luminous stars are always young stars, no more than a few million years for the most extreme. In the Hertzsprung–Russell diagram, the x-axis represents temperature or spectral type while the y-axis represents luminosity or magnitude. The vast majority of stars are found along the main sequence with blue Class O stars found at the top left of the chart while red Class M stars fall to the bottom right. Certain stars like Deneb and Betelgeuse are found above and to the right of the main sequence, more luminous or cooler than their equivalents on the main sequence. Increased luminosity at the same temperature, or alternatively cooler temperature at the same luminosity, indicates that these stars are larger than those on the main sequence and they are called giants or supergiants.

Blue and white supergiants are high luminosity stars somewhat cooler than the most luminous main sequence stars. A star like Deneb, for example, has a luminosity around 200,000 L, a spectral type of A2, and an effective temperature around 8,500 K, meaning it has a radius around 203 R. For comparison, the red supergiant Betelgeuse has a luminosity around 100,000 L, a spectral type of M2, and a temperature around 3,500 K, meaning its radius is about 1,000 R. Red supergiants are the largest type of star, but the most luminous are much smaller and hotter, with temperatures up to 50,000 K and more and luminosities of several million L, meaning their radii are just a few tens of R. For example, R136a1 has a temperature over 50,000 K and a luminosity of more than 8,000,000 L (mostly in the UV), it is only 35 R.

Radio luminosity

The luminosity of a radio source is measured in W Hz−1, to avoid having to specify a bandwidth over which it is measured. The observed strength, or flux density, of a radio source is measured in Jansky where 1 Jy = 10−26 W m−2 Hz−1.

For example, consider a 10W transmitter at a distance of 1 million metres, radiating over a bandwidth of 1 MHz. By the time that power has reached the observer, the power is spread over the surface of a sphere with area 4πr2 or about 1.26×1013 m2, so its flux density is 10 / 106 / 1.26×1013 W m−2 Hz−1 = 108 Jy.

More generally, for sources at cosmological distances, a k-correction must be made for the spectral index α of the source, and a relativistic correction must be made for the fact that the frequency scale in the emitted rest frame is different from that in the observer's rest frame. So the full expression for radio luminosity, assuming isotropic emission, is

where Lν is the luminosity in W Hz−1, Sobs is the observed flux density in W m−2 Hz−1, DL is the luminosity distance in metres, z is the redshift, α is the spectral index (in the sense , and in radio astronomy, assuming thermal emission the spectral index is typically equal to 2.)[15]

For example, consider a 1 Jy signal from a radio source at a redshift of 1, at a frequency of 1.4 GHz. Ned Wright's cosmology calculator calculates a luminosity distance for a redshift of 1 to be 6701 Mpc = 2×1026 m giving a radio luminosity of 10−26 × 4π(2×1026)2 / (1+1)(1+2) = 6×1026 W Hz−1.

To calculate the total radio power, this luminosity must be integrated over the bandwidth of the emission. A common assumption is to set the bandwidth to the observing frequency, which effectively assumes the power radiated has uniform intensity from zero frequency up to the observing frequency. In the case above, the total power is 4×1027 × 1.4×109 = 5.7×1036 W. This is sometimes expressed in terms of the total (i.e. integrated over all wavelengths) luminosity of the Sun which is 3.86×1026 W, giving a radio power of 1.5×1010 L.

Magnitude

Luminosity is an intrinsic measurable property of a star independent of distance. The concept of magnitude, on the other hand, incorporates distance. The apparent magnitude is a measure of the diminishing flux of light as a result of distance according to the inverse-square law.[16] The Pogson logarithmic scale is used to measure both apparent and absolute magnitudes, the latter corresponding to the brightness of a star or other celestial body as seen if it would be located at an interstellar distance of 10 parsecs .In addition to this brightness decrease from increased distance, there is an extra decrease of brightness due to extinction from intervening interstellar dust.[17]

By measuring the width of certain absorption lines in the stellar spectrum, it is often possible to assign a certain luminosity class to a star without knowing its distance. Thus a fair measure of its absolute magnitude can be determined without knowing its distance nor the interstellar extinction.

In measuring star brightnesses, absolute magnitude, apparent magnitude, and distance are interrelated parameters—if two are known, the third can be determined. Since the Sun's luminosity is the standard, comparing these parameters with the Sun's apparent magnitude and distance is the easiest way to remember how to convert between them, although officially, zero point values are defined by the IAU

Luminosity formulae

Inverse square law
Point source S is radiating light equally in all directions. The amount passing through an area A varies with the distance of the surface from the light.

The Stefan–Boltzmann equation applied to a black body gives the value for luminosity for a black body, an idealized object which is perfectly opaque and non-reflecting:[6]

,

where A is the surface area, T is the temperature (in Kelvins) and σ is the Stefan–Boltzmann constant, with a value of 5.670367(13)×10−8 W⋅m−2⋅K−4.[18]

Imagine a point source of light of luminosity that radiates equally in all directions. A hollow sphere centered on the point would have its entire interior surface illuminated. As the radius increases, the surface area will also increase, and the constant luminosity has more surface area to illuminate, leading to a decrease in observed brightness.

,

where

is the area of the illuminated surface.
is the flux density of the illuminated surface.

The surface area of a sphere with radius r is , so for stars and other point sources of light:

,

where is the distance from the observer to the light source.

For stars on the main sequence, luminosity is also related to mass:

.

Relationship to magnitude

The magnitude of a star, a unitless measure, is a logarithmic scale of observed visible brightness. The apparent magnitude is the observed visible brightness from Earth which depends on the distance of the object. The absolute magnitude is the apparent magnitude at a distance of 10 parsecs, therefore the bolometric absolute magnitude is a logarithmic measure of the bolometric luminosity.

The difference in bolometric magnitude between two objects is related to their luminosity ratio according to:

[19]

where:

is the bolometric magnitude of the first object
is the bolometric magnitude of the second object.
is the first object's bolometric luminosity
is the second object's bolometric luminosity

The zero point of the absolute magnitude scale is actually defined as a fixed luminosity of 3.0128×1028 W. Therefore, the absolute magnitude can be calculated from a luminosity in watts:

where L0 is the zero point luminosity 3.0128×1028 W

and the luminosity in watts can be calculated from an absolute magnitude (although absolute magnitudes are often not measured relative to an absolute flux):

See also

References

  1. ^ Hopkins, Jeanne (1980). Glossary of Astronomy and Astrophysics (2nd ed.). The University of Chicago Press. ISBN 978-0-226-35171-1.
  2. ^ "Luminosity | astronomy". Encyclopedia Britannica. Retrieved 2018-06-24.
  3. ^ "* Luminosity (Astronomy) - Definition,meaning - Online Encyclopedia". en.mimi.hu. Retrieved 2018-06-24.
  4. ^ "Brightest Stars: Luminosity & Magnitude". Space.com. Retrieved 2018-06-24.
  5. ^ http://www.astro.cornell.edu/academics/courses/a290/lectures/A2290_13%20(Flux%20and%20Magnitudes).pdf
  6. ^ a b c "Luminosity of Stars". Australia Telescope National Facility. 12 July 2004. Archived from the original on 9 August 2014.
  7. ^ Bahcall, John. "Solar Neutrino Viewgraphs". Institute for Advanced Study School of Natural Science. Retrieved 2012-07-03.
  8. ^ Mamajek, E. E.; Prsa, A.; Torres, G.; Harmanec, P.; Asplund, M.; Bennett, P. D.; Capitaine, N.; Christensen-Dalsgaard, J.; Depagne, E.; Folkner, W. M.; Haberreiter, M.; Hekker, S.; Hilton, J. L.; Kostov, V.; Kurtz, D. W.; Laskar, J.; Mason, B. D.; Milone, E. F.; Montgomery, M. M.; Richards, M. T.; Schou, J.; Stewart, S. G. (2015). "IAU 2015 Resolution B3 on Recommended Nominal Conversion Constants for Selected Solar and Planetary Properties". arXiv:1510.07674 [astro-ph.SR].
  9. ^ Nieva, M.-F (2013). "Temperature, gravity, and bolometric correction scales for non-supergiant OB stars". Astronomy & Astrophysics. 550: A26. arXiv:1212.0928. Bibcode:2013A&A...550A..26N. doi:10.1051/0004-6361/201219677.
  10. ^ Buzzoni, A; Patelli, L; Bellazzini, M; Pecci, F. Fusi; Oliva, E (2010). "Bolometric correction and spectral energy distribution of cool stars in Galactic clusters". Monthly Notices of the Royal Astronomical Society. 403 (3): 1592. arXiv:1002.1972. Bibcode:2010MNRAS.403.1592B. doi:10.1111/j.1365-2966.2009.16223.x.
  11. ^ "ASTR 5610, Majewski [SPRING 2016]. Lecture Notes". www.faculty.virginia.edu. Retrieved 2019-02-03.
  12. ^ Delfosse, X; Forveille, T; Ségransan, D; Beuzit, J.-L; Udry, S; Perrier, C; Mayor, M (2000). "Accurate masses of very low mass stars. IV. Improved mass-luminosity relations". Astronomy and Astrophysics. 364: 217. arXiv:astro-ph/0010586. Bibcode:2000A&A...364..217D.
  13. ^ Karttunen, Hannu (2003). Fundamental Astronomy. Springer-Verlag. p. 289. ISBN 978-3-540-00179-9.
  14. ^ Ledrew, Glenn (February 2001). "The Real Starry Sky" (PDF). Journal of the Royal Astronomical Society of Canada. 95: 32–33. Bibcode:2001JRASC..95...32L. Retrieved 2 July 2012.
  15. ^ Singal, J.; Petrosian, V.; Lawrence, A.; Stawarz, Ł. (20 December 2011). "ON THE RADIO AND OPTICAL LUMINOSITY EVOLUTION OF QUASARS". The Astrophysical Journal. 743 (2): 104. doi:10.1088/0004-637X/743/2/104.
  16. ^ Joshua E. Barnes (February 18, 2003). "The Inverse-Square Law". Institute for Astronomy - University of Hawaii. Retrieved 26 September 2012.
  17. ^ "Magnitude System". Astronomy Notes. 2 November 2010. Retrieved 2 July 2012.
  18. ^ "CODATA Value: Stefan–Boltzmann constant". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-25. 2014 CODATA recommended values
  19. ^ "Absolute Magnitude". csep10.phys.utk.edu. Retrieved 2019-02-02.

Further reading

External links

Absolute magnitude

Absolute magnitude is a measure of the luminosity of a celestial object, on a logarithmic astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly 10 parsecs (32.6 light-years), with no extinction (or dimming) of its light due to absorption by interstellar dust particles. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared on a magnitude scale. As with all astronomical magnitudes, the absolute magnitude can be specified for different wavelength ranges corresponding to specified filter bands or passbands; for stars a commonly quoted absolute magnitude is the absolute visual magnitude, which uses the visual (V) band of the spectrum (in the UBV photometric system). Absolute magnitudes are denoted by a capital M, with a subscript representing the filter band used for measurement, such as MV for absolute magnitude in the V band.

The more luminous an object, the smaller the numerical value of its absolute magnitude. A difference of 5 magnitudes between the absolute magnitudes of two objects corresponds to a ratio of 100 in their luminosities, and a difference of n magnitudes in absolute magnitude corresponds to a luminosity ratio of 100(n/5). For example, a star of absolute magnitude MV=3 would be 100 times more luminous than a star of absolute magnitude MV=8 as measured in the V filter band. The Sun has absolute magnitude MV=+4.83. Highly luminous objects can have negative absolute magnitudes: for example, the Milky Way galaxy has an absolute B magnitude of about −20.8.An object's absolute bolometric magnitude represents its total luminosity over all wavelengths, rather than in a single filter band, as expressed on a logarithmic magnitude scale. To convert from an absolute magnitude in a specific filter band to absolute bolometric magnitude, a bolometric correction is applied.

For Solar System bodies that shine in reflected light, a different definition of absolute magnitude (H) is used, based on a standard reference distance of one astronomical unit.

Apparent magnitude

The apparent magnitude (m) of an astronomical object is a number that is 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 (i.e. inverse relation), 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, visible, and infrared wavelengths. An apparent magnitude is usually 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 ("visual") filter band would be denoted either as mV or often simply as V, as in "mV = 15" or "V = 15" to describe a 15th-magnitude object.

Cepheid variable

A Cepheid variable () is a type of star that pulsates radially, varying in both diameter and temperature and producing changes in brightness with a well-defined stable period and amplitude.

A strong direct relationship between a Cepheid variable's luminosity and pulsation period established Cepheids as important indicators of cosmic benchmarks for scaling galactic and extragalactic distances. This robust characteristic of classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt after studying thousands of variable stars in the Magellanic Clouds. This discovery allows one to know the true luminosity of a Cepheid by simply observing its pulsation period. This in turn allows one to determine the distance to the star, by comparing its known luminosity to its observed brightness.

The term Cepheid originates from Delta Cephei in the constellation Cepheus, identified by John Goodricke in 1784, the first of its type to be so identified.

Cosmic distance ladder

The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement of an astronomical object is possible only for those objects that are "close enough" (within about a thousand parsecs) to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances and methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known luminosity.

The ladder analogy arises because no single technique can measure distances at all ranges encountered in astronomy. Instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next higher rung.

Eddington luminosity

The Eddington luminosity, also referred to as the Eddington limit, is the maximum luminosity a body (such as a star) can achieve when there is balance between the force of radiation acting outward and the gravitational force acting inward. The state of balance is called hydrostatic equilibrium. When a star exceeds the Eddington luminosity, it will initiate a very intense radiation-driven stellar wind from its outer layers. Since most massive stars have luminosities far below the Eddington luminosity, their winds are mostly driven by the less intense line absorption. The Eddington limit is invoked to explain the observed luminosity of accreting black holes such as quasars.

Originally, Sir Arthur Stanley Eddington took only the electron scattering into account when calculating this limit, something that now is called the classical Eddington limit. Nowadays, the modified Eddington limit also counts on other radiation processes such as bound-free and free-free radiation (see Bremsstrahlung) interaction.

Giant star

A giant star is a star with substantially larger radius and luminosity than a main-sequence (or dwarf) star of the same surface temperature. They lie above the main sequence (luminosity class V in the Yerkes spectral classification) 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 supergiants and hypergiants.

A hot, luminous main-sequence star may also be referred to as a giant, but any main-sequence star is properly called a dwarf no matter how large and luminous it is.

Hertzsprung–Russell diagram

The Hertzsprung–Russell diagram, abbreviated as H–R diagram, HR diagram or HRD, is a scatter plot of stars showing the relationship between the stars' absolute magnitudes or luminosities versus their stellar classifications or effective temperatures. More simply, it plots each star on a graph plotting the star's brightness against its temperature (color).

The diagram was created circa 1910 by Ejnar Hertzsprung and Henry Norris Russell and represents a major step towards an understanding of stellar evolution.

The related color–magnitude diagram (CMD) plots the apparent magnitudes of stars against their color, usually for a cluster so that the stars are all at the same distance.

Hypergiant

A hypergiant (luminosity class 0 or Ia+) is among the very rare kinds of stars that typically show tremendous luminosities and very high rates of mass loss by stellar winds. The term hypergiant is defined as luminosity class 0 (zero) in the MKK system. However, this is rarely seen in the literature or in published spectral classifications, except for specific well-defined groups such as the yellow hypergiants, RSG (red supergiants), or blue B(e) supergiants with emission spectra. More commonly, hypergiants may be classed as Ia-0 or Ia+, but red supergiants are rarely assigned these spectral classifications. Astronomers are mostly interested in these stars because they relate to understanding stellar evolution, especially with star formation, stability, and their expected demise as supernovae.

Kelvin–Helmholtz mechanism

The Kelvin–Helmholtz mechanism is an astronomical process that occurs when the surface of a star or a planet cools. The cooling causes the pressure to drop, and the star or planet shrinks as a result. This compression, in turn, heats the core of the star/planet. This mechanism is evident on Jupiter and Saturn and on brown dwarfs whose central temperatures are not high enough to undergo nuclear fusion. It is estimated that Jupiter radiates more energy through this mechanism than it receives from the Sun, but Saturn might not. The latter process causes Jupiter to shrink at a rate of two centimetres each year.The mechanism was originally proposed by Kelvin and Helmholtz in the late nineteenth century to explain the source of energy of the Sun. By the mid-nineteenth century, conservation of energy had been accepted, and one consequence of this law of physics is that the Sun must have some energy source to continue to shine. Because nuclear reactions were unknown, the main candidate for the source of solar energy was gravitational contraction.

However, it soon was recognized by Sir Arthur Eddington and others that the total amount of energy available through this mechanism only allowed the Sun to shine for millions of years rather than the billions of years that the geological and biological evidence suggested for the age of the Earth. (Kelvin himself had argued that the Earth was millions, not billions, of years old.) The true source of the Sun's energy remained uncertain until the 1930s, when it was shown by Hans Bethe to be nuclear fusion.

Luminosity Gaming

Luminosity Gaming is a professional esports video game organization. It has teams competing in Call of Duty, Hearthstone: Heroes of Warcraft, World of Warcraft, Counter-Strike: Global Offensive, Smite, Overwatch and Fortnite. The team was founded in Canada by Steve "Buyaka" Maida in 2015, and is based in Toronto, Ontario.

Luminosity function

A luminosity function or luminous efficiency function describes the average spectral sensitivity of human visual perception of brightness. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describe relative sensitivity to light of different wavelengths. It should not be considered perfectly accurate, but it is a good representation of visual sensitivity of the human eye and it is valuable as a baseline for experimental purposes. Different luminosity functions apply under different lighting condition, varying from photopic in brightly lit conditions through mesotopic to scotopic under low lighting conditions. Without qualification, the luminosity function generally refers to the photopic luminosity function.

The CIE photopic luminosity function y(λ) or V(λ) is a standard function established by the Commission Internationale de l'Éclairage (CIE) and may be used to convert radiant energy into luminous (i.e., visible) energy. It also forms the central color matching function in the CIE 1931 color space.

Luminous mind

Luminous mind (Skt: prabhāsvara-citta or ābhāsvara-citta, Pali: pabhassara citta; T. ’od gsal gyi sems; C. guangmingxin; J. kōmyōshin; K. kwangmyŏngsim) is a Buddhist term which appears in a sutta of the Pali Anguttara Nikaya as well as numerous Mahayana texts and Buddhist tantras. It is variously translated as "brightly shining mind", or "mind of clear light" while the related term luminosity (Skt. prabhāsvaratā; Tib.’od gsal ba; Ch. guāng míng; Jpn. kōmyō; Kor. kwangmyōng) is also translated as "clear light" in Tibetan Buddhist contexts or, "purity" in East Asian contexts. The term is usually used to describe the mind or consciousness in different ways.

This term is given no direct doctrinal explanation in the Pali discourses, but later Buddhist schools explained it using various concepts developed by them. The Theravada school identifies the "luminous mind" with the bhavanga, a concept first proposed in the Theravada Abhidhamma. The later schools of the Mahayana identify it with both the Mahayana concepts of bodhicitta and tathagatagarbha. The notion is of central importance in the philosophy and practice of Dzogchen.

Main sequence

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, and 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 primarily by its mass, but also 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 makes its way to the surface and is radiated away at the photosphere. The energy is carried by either radiation or convection, with the latter occurring in regions with steeper temperature gradients, higher opacity or both.

The main sequence is sometimes divided into upper and lower parts, based on the dominant process that a star uses to generate energy. Stars below about 1.5 times the mass of the Sun (1.5 M☉) primarily fuse hydrogen atoms together in a series of stages to form helium, a sequence called the proton–proton chain. Above this mass, in the upper main sequence, the nuclear fusion process mainly uses atoms of carbon, nitrogen and oxygen as intermediaries in the CNO cycle that produces helium from hydrogen atoms. Main-sequence stars with more than two solar masses undergo convection in their core regions, which acts to stir up the newly created helium and maintain the proportion of fuel needed for fusion to occur. Below this mass, stars have cores that are entirely radiative with convective zones near the surface. With decreasing stellar mass, the proportion of the star forming a convective envelope steadily increases. 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.

Solar luminosity

The solar luminosity, L☉, is a unit of radiant flux (power emitted in the form of photons) conventionally used by astronomers to measure the luminosity of stars, galaxies and other celestial objects in terms of the output of the Sun. One nominal solar luminosity is defined by the International Astronomical Union to be 3.828×1026 W. This does not include the solar neutrino luminosity, which would add 0.023 L☉. The Sun is a weakly variable star, and its actual luminosity therefore fluctuates. The major fluctuation is the eleven-year solar cycle (sunspot cycle) that causes a periodic variation of about ±0.1%. Other variations over the last 200–300 years are thought to be much smaller than this.

Star

A star is type of astronomical object consisting of a luminous spheroid of plasma held together by its own gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye from Earth during the night, appearing as a multitude of fixed luminous points in the sky due to their immense distance from Earth. Historically, the most prominent stars were grouped into constellations and asterisms, the brightest of which gained proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. However, most of the estimated 300 sextillion (3×1023) stars in the Universe are invisible to the naked eye from Earth, including all stars outside our galaxy, the Milky Way.

For at least a portion of its life, a star shines due to thermonuclear fusion of hydrogen into helium in its core, releasing energy that traverses the star's interior and then radiates into outer space. Almost all naturally occurring elements heavier than helium are created by stellar nucleosynthesis during the star's lifetime, and for some stars by supernova nucleosynthesis when it explodes. Near the end of its life, a star can also contain degenerate matter. Astronomers can determine the mass, age, metallicity (chemical composition), and many other properties of a star by observing its motion through space, its luminosity, and spectrum respectively. The total mass of a star is the main factor that determines its evolution and eventual fate. Other characteristics of a star, including diameter and temperature, change over its life, while the star's environment affects its rotation and movement. A plot of the temperature of many stars against their luminosities produces a plot known as a Hertzsprung–Russell diagram (H–R diagram). Plotting a particular star on that diagram allows the age and evolutionary state of that star to be determined.

A star's life begins with the gravitational collapse of a gaseous nebula of material composed primarily of hydrogen, along with helium and trace amounts of heavier elements. When the stellar core is sufficiently dense, hydrogen becomes steadily converted into helium through nuclear fusion, releasing energy in the process. The remainder of the star's interior carries energy away from the core through a combination of radiative and convective heat transfer processes. The star's internal pressure prevents it from collapsing further under its own gravity. A star with mass greater than 0.4 times the Sun's will expand to become a red giant when the hydrogen fuel in its core is exhausted. In some cases, it will fuse heavier elements at the core or in shells around the core. As the star expands it throws a part of its mass, enriched with those heavier elements, into the interstellar environment, to be recycled later as new stars. Meanwhile, the core becomes a stellar remnant: a white dwarf, a neutron star, or if it is sufficiently massive a black hole.

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. Stars can form part of a much larger gravitationally bound structure, such as a star cluster or a galaxy.

Stellar classification

In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting the rainbow of colors interspersed with spectral lines. Each line indicates a particular chemical element or molecule, with the line strength indicating the abundance of that element. The strengths of the different spectral lines vary mainly due to the temperature of the photosphere, although in some cases there are true abundance differences. The spectral class of a star is a short code primarily summarizing the ionization state, giving an objective measure of the photosphere's temperature.

Most stars are currently classified under the Morgan-Keenan (MK) system using the letters O, B, A, F, G, K, and M, a sequence from the hottest (O type) to the coolest (M type). Each letter class is then subdivided using a numeric digit with 0 being hottest and 9 being coolest (e.g. A8, A9, F0, and F1 form a sequence from hotter to cooler). The sequence has been expanded with classes for other stars and star-like objects that do not fit in the classical system, such as class D for white dwarfs and classes S and C for carbon stars.

In the MK system, a luminosity class is added to the spectral class using Roman numerals. This is based on the width of certain absorption lines in the star's spectrum, which vary with the density of the atmosphere and so distinguish giant stars from dwarfs. Luminosity class 0 or Ia+ is used for hypergiants, class I for supergiants, class II for bright giants, class III for regular giants, class IV for sub-giants, class V for main-sequence stars, class sd (or VI) for sub-dwarfs, and class D (or VII) for white dwarfs. The full spectral class for the Sun is then G2V, indicating a main-sequence star with a temperature around 5,800 K.

Subgiant

A subgiant is a star that is brighter than a normal main-sequence star of the same spectral class, but not as bright as true giant stars. The term subgiant is applied both to a particular spectral luminosity class and to a stage in the evolution of a star.

Supergiant star

Supergiants are among the most massive and most luminous stars. Supergiant stars occupy the top region of the Hertzsprung–Russell diagram with absolute visual magnitudes between about −3 and −8. The temperature range of supergiant stars spans from about 3,450 K to over 20,000 K.

Variable star

A variable star is a star whose brightness as seen from Earth (its apparent magnitude) fluctuates.

This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either:

Intrinsic variables, whose luminosity actually changes; for example, because the star periodically swells and shrinks.

Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes eclipses it.Many, possibly most, stars have at least some variation in luminosity: the energy output of our Sun, for example, varies by about 0.1% over an 11-year solar cycle.

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