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The math didn't add up. The sun is roughly correctly dated, and the total age is correct using the reference given. Thus, the math needs correcting. |
→Classification: {{Further}}. |
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A refined scheme for [[stellar classification]] was published in 1943 by [[William Wilson Morgan]] and [[Philip Childs Keenan]].<ref name=keenan_morgan43/> The MK classification assigned each star a spectral type—based on the Harvard classification—and a luminosity class. The Harvard classification had been developed by assigning a different letter to each star based on the strength of the hydrogen spectral line before the relationship between spectra and temperature was known. When ordered by temperature and when duplicate classes were removed, the [[spectral type]]s of stars followed, in order of decreasing temperature with colors ranging from blue to red, the sequence O, B, A, F, G, K, and M. (A popular [[mnemonic]] for memorizing this sequence of stellar classes is "Oh Be A Fine Girl/Guy, Kiss Me".) The luminosity class ranged from I to V, in order of decreasing luminosity. Stars of luminosity class V belonged to the main sequence.<ref name=tnc/>
In April 2018, astronomers reported the detection of the most distant "ordinary" (i.e., main sequence) [[star]], named [[Icarus (star)|Icarus]] (formally, [[MACS J1149 Lensed Star 1]]), at 9 billion light-years away from [[Earth]].<ref name="
== Formation and evolution ==
{{Star formation}}
{{Main|Star formation|Protostar|Pre-main-sequence star|Stellar evolution#Main sequence stellar mass objects}}
[[File:Zams and tracks.png|thumb|left|Zero age main sequence and evolutionary tracks]]
[[File:Hot and brilliant O stars in star-forming regions.jpg|thumb|left|upright=1.2|Hot and brilliant [[O-type main-sequence star]]s in star-forming regions. These are all regions of star formation that contain many hot young stars including several bright stars of spectral type O.<ref>{{cite news |title=The Brightest Stars Don't Live Alone |newspaper=ESO Press Release |url=https://www.eso.org/public/news/eso1230/ |access-date=27 July 2012}}</ref>]]▼
[[File:The violent youth of solar proxies.jpg|thumb|The violent youth of stars like the Sun]]
When a [[protostar]] is formed from the [[Jeans instability|collapse]] of a [[giant molecular cloud]] of gas and dust in the local [[interstellar medium]], the initial composition is homogeneous throughout, consisting of about 70% hydrogen, 28% helium, and trace amounts of other elements, by mass.<ref name=asr34_1/> The initial mass of the star depends on the local conditions within the cloud. (The mass distribution of newly formed stars is described empirically by the [[initial mass function]].)<ref name=science295_5552/> During the initial collapse, this [[pre-main-sequence star]] generates energy through gravitational contraction. Once sufficiently dense, stars begin converting hydrogen into helium and giving off energy through an [[exothermic]] [[nuclear fusion]] process.<ref name=tnc/>
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== Classification ==
▲[[File:Hot and brilliant O stars in star-forming regions.jpg|thumb
{{Further|OB star}}
Main sequence stars are divided into the following types:
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* [[K-type main-sequence star]]
* [[M-type main-sequence star]]
M-type (and, to a lesser extent, K-type)<ref
== Properties ==
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The mass, radius, and luminosity of a star are closely interlinked, and their respective values can be approximated by three relations. First is the Stefan–Boltzmann law, which relates the luminosity ''L'', the radius ''R'' and the surface temperature ''T''<sub>eff</sub>. Second is the [[mass–luminosity relation]], which relates the luminosity ''L'' and the mass ''M''. Finally, the relationship between ''M'' and ''R'' is close to linear. The ratio of ''M'' to ''R'' increases by a factor of only three over 2.5 [[orders of magnitude]] of ''M''. This relation is roughly proportional to the star's inner temperature ''T<sub>I</sub>'', and its extremely slow increase reflects the fact that the rate of energy generation in the core strongly depends on this temperature, whereas it has to fit the mass-luminosity relation. Thus, a too-high or too-low temperature will result in stellar instability.
A better approximation is to take {{nowrap|1=''ε'' = ''L''/''M''}}, the energy generation rate per unit mass, as ''ε'' is proportional to ''T<sub>I</sub>''<sup>15</sup>, where ''T<sub>I</sub>'' is the core temperature. This is suitable for stars at least as massive as the Sun, exhibiting the [[CNO cycle]], and gives the better fit {{nowrap|''R'' ∝ ''M''<sup>0.78</sup>}}.<ref
=== Sample parameters ===
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This relationship applies to main-sequence stars in the range {{solar mass|0.1–50}}.<ref name=rolfs_rodney88/>
The amount of fuel available for nuclear fusion is proportional to the mass of the star. Thus, the lifetime of a star on the main sequence can be estimated by comparing it to solar evolutionary models. The [[Sun]] has been a main-sequence star for about 4.5 billion years and it will
: <math>\tau_\text{MS} \approx
10^{10} \text{years} \left[ \frac{M}{M_\bigodot} \right] \left[ \frac{L_\bigodot}{L} \right] =
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where ''M'' and ''L'' are the mass and luminosity of the star, respectively, <math>M_\bigodot</math> is a [[solar mass]], <math>L_\bigodot</math> is the [[solar luminosity]] and <math>\tau_\text{MS}</math> is the star's estimated main-sequence lifetime.
Although more massive stars have more fuel to burn and might intuitively be expected to last longer, they also radiate a proportionately greater amount with increased mass. This is required by the stellar equation of state; for a massive star to maintain equilibrium, the outward pressure of radiated energy generated in the core not only must but ''will'' rise to match the titanic inward gravitational pressure of its envelope. Thus, the most massive stars may remain on the main sequence for only a few million years, while stars with less than a tenth of a solar mass may last for over a trillion years.<ref name=apj482
The exact mass-luminosity relationship depends on how efficiently energy can be transported from the core to the surface. A higher [[opacity (optics)|opacity]] has an insulating effect that retains more energy at the core, so the star does not need to produce as much energy to remain in [[hydrostatic equilibrium]]. By contrast, a lower opacity means energy escapes more rapidly and the star must burn more fuel to remain in equilibrium.<ref name=imamura07
In high-mass main-sequence stars, the opacity is dominated by [[electron scattering]], which is nearly constant with increasing temperature. Thus the luminosity only increases as the cube of the star's mass.<ref name="prialnik00"/> For stars below {{solar mass|10}}, the opacity becomes dependent on temperature, resulting in the luminosity varying approximately as the fourth power of the star's mass.<ref name=rolfs_rodney88
== Evolutionary tracks ==
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[[File:Evolutionary track 1m.svg|thumb|left|Evolutionary track of a star like the sun]]
When a main-sequence star has consumed the hydrogen at its core, the loss of energy generation causes its gravitational collapse to resume and the star evolves off the main sequence. The path which the star follows across the HR diagram is called an evolutionary track.<ref name="Iben2012"/>
[[File: Open cluster HR diagram ages.gif|right|thumb|upright=1.2|[[Hertzsprung–Russell diagram|H–R diagram]] for two open clusters: [[NGC 188]] (blue) is older and shows a lower turn off from the main sequence than [[Messier 67|M67]] (yellow). The dots outside the two sequences are mostly foreground and background stars with no relation to the clusters.]]
Stars with less than {{solar mass|0.23}}<ref name=romp69
In stars more massive than {{solar mass|0.23}}, the hydrogen surrounding the helium core reaches sufficient temperature and pressure to undergo fusion, forming a hydrogen-burning shell and causing the outer layers of the star to expand and cool. The stage as these stars move away from the main sequence is known as the [[subgiant branch]]; it is relatively brief and appears as a [[Hertzsprung gap|gap]] in the evolutionary track since few stars are observed at that point.
When the helium core of low-mass stars becomes degenerate, or the outer layers of intermediate-mass stars cool sufficiently to become opaque, their hydrogen shells increase in temperature and the stars start to become more luminous. This is known as the [[red-giant branch]]; it is a relatively long-lived stage and it appears prominently in H–R diagrams. These stars will eventually end their lives as white dwarfs.<ref name=pmss_atoe
The most massive stars do not become red giants; instead, their cores quickly become hot enough to fuse helium and eventually heavier elements and they are known as [[supergiant]]s. They follow approximately horizontal evolutionary tracks from the main sequence across the top of the H–R diagram. Supergiants are relatively rare and do not show prominently on most H–R diagrams. Their cores will eventually collapse, usually leading to a [[supernova]] and leaving behind either a [[neutron star]] or [[black hole]].<ref name=sitko00
When a [[star cluster|cluster of stars]] is formed at about the same time, the main-sequence lifespan of these stars will depend on their individual masses. The most massive stars will leave the main sequence first, followed in sequence by stars of ever lower masses. The position where stars in the cluster are leaving the main sequence is known as the [[turnoff point]]. By knowing the main-sequence lifespan of stars at this point, it becomes possible to estimate the age of the cluster.<ref name=science299_5603
== See also ==
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<ref name=padmanabhan01>{{cite book |first=Thanu |last=Padmanabhan |date=2001 |title=Theoretical Astrophysics |publisher=Cambridge University Press |isbn=978-0-521-56241-6}}</ref>
<ref name=apj128_3>{{cite journal |last=Wright |first=J. T. |title=Do We Know of Any Maunder Minimum Stars? |journal=The Astronomical Journal |date=2004 |volume=128 |issue=3 |pages=1273–1278
<ref name=tayler94>{{cite book |first=Roger John |last=Tayler |date=1994 |title=The Stars: Their Structure and Evolution |publisher=Cambridge University Press |isbn=978-0-521-45885-6}}</ref>
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<ref name=mnras113>{{cite journal |last=Sweet |first=I. P. A. |author2=Roy, A. E. |title=The structure of rotating stars |journal=[[Monthly Notices of the Royal Astronomical Society]] |date=1953 |volume=113 |issue=6 |pages=701–715 |bibcode=1953MNRAS.113..701S |doi=10.1093/mnras/113.6.701 |doi-access=free}}</ref>
<ref name=cwcs13>{{cite conference |last=Burgasser |first=Adam J. |author2=Kirkpatrick, J. Davy |author3=Lépine, Sébastien |title=Spitzer Studies of Ultracool Subdwarfs: Metal-poor Late-type M, L and T Dwarfs |work=Proceedings of the 13th Cambridge Workshop on Cool Stars, Stellar Systems and the Sun |page=237 |publisher=Dordrecht, D. Reidel Publishing Co |date=5–9 July 2004 |___location=Hamburg, Germany |bibcode=2005ESASP.560..237B
<ref name=green04>{{cite book |first=S. F. |last=Green |author2=Jones, Mark Henry |author3=Burnell, S. Jocelyn |date=2004 |title=An Introduction to the Sun and Stars |publisher=Cambridge University Press |isbn=978-0-521-54622-5}}</ref>
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<ref name=lecchini07>For a detailed historical reconstruction of the theoretical derivation of this relationship by Eddington in 1924, see: {{cite book |first=Stefano |last=Lecchini |date=2007 |title=How Dwarfs Became Giants. The Discovery of the Mass-Luminosity Relation |publisher=Bern Studies in the History and Philosophy of Science |isbn=978-3-9522882-6-9}}</ref>
<ref name=Hansen1999>{{
|title=Stellar Interiors: Physical Principles, Structure, and Evolution
|series=Astronomy and Astrophysics Library
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|year=1999 |isbn=978-0-387-94138-7 |page=39
|url=https://books.google.com/books?id=m-_6LYuUbUkC&pg=PA39}}</ref>
<ref name="NA-20180402">{{cite journal |author=Kelly, Patrick L. |display-authors=etal |title=Extreme magnification of an individual star at redshift 1.5 by a galaxy-cluster lens |date=2 April 2018 |journal=[[Nature (journal) |Nature]] |volume=2 |issue=4 |pages=334–342 |doi=10.1038/s41550-018-0430-3 |arxiv=1706.10279 |bibcode=2018NatAs...2..334K |s2cid=125826925}}</ref>
<ref name="SPC-20180402">{{cite web |last=Howell |first=Elizabeth |title=Rare Cosmic Alignment Reveals Most Distant Star Ever Seen |url=https://www.space.com/40171-cosmic-alignment-reveals-most-distant-star-yet.html |date=2 April 2018 |work=[[Space.com]] |access-date=2 April 2018}}</ref>
<ref name=eso>{{cite news |title=The Brightest Stars Don't Live Alone |newspaper=ESO Press Release |url=https://www.eso.org/public/news/eso1230/ |access-date=27 July 2012}}</ref>
<ref name=pettersen1989>{{cite journal |last1=Pettersen |first1=B. R. |last2=Hawley |first2=S. L. |date=1989-06-01 |title=A spectroscopic survey of red dwarf flare stars. |journal=Astronomy and Astrophysics |volume=217 |pages=187–200 |bibcode=1989A&A...217..187P |issn=0004-6361}}</ref>
<ref name=standrews>{{cite web |title=A course on stars' physical properties, formation and evolution |publisher=University of St. Andrews |url=http://www-star.st-and.ac.uk/~kw25/teaching/stars/STRUC4.pdf |access-date=2010-05-18 |archive-date=2020-12-02 |archive-url=https://web.archive.org/web/20201202003201/http://www-star.st-and.ac.uk/~kw25/teaching/stars/STRUC4.pdf |url-status=dead }}</ref>
<ref name=apj418>{{cite journal |last=Sackmann |first=I.-Juliana |author2=Boothroyd, Arnold I. |author3=Kraemer, Kathleen E. |title=Our Sun. III. Present and Future |journal=Astrophysical Journal |date=November 1993 |volume=418 |pages=457–468 |doi=10.1086/173407 |bibcode=1993ApJ...418..457S|doi-access=free }}</ref>
<ref name=hansen_kawaler94>{{cite book |first=Carl J. |last=Hansen |author2=Kawaler, Steven D. |date=1994 |title=Stellar Interiors: Physical Principles, Structure, and Evolution |page=[https://archive.org/details/stellarinteriors00hans/page/28 28] |publisher=Birkhäuser |isbn=978-0-387-94138-7 |url-access=registration |url=https://archive.org/details/stellarinteriors00hans/page/28}}</ref>
<ref name=apj482>{{cite journal |last=Laughlin |first=Gregory |author2=Bodenheimer, Peter |author3=Adams, Fred C. |title=The End of the Main Sequence |journal=The Astrophysical Journal |date=1997 |volume=482 |issue=1 |pages=420–432 |doi=10.1086/304125 |bibcode=1997ApJ...482..420L |doi-access=free}}</ref>
<ref name=imamura07>{{cite web |last=Imamura |first=James N. |date=7 February 1995 |url=http://zebu.uoregon.edu/~imamura/208/feb6/mass.html |title=Mass-Luminosity Relationship |publisher=University of Oregon |access-date=8 January 2007 |archive-url=https://web.archive.org/web/20061214065335/http://zebu.uoregon.edu/~imamura/208/feb6/mass.html |archive-date=14 December 2006}}</ref>
<ref name=rolfs_rodney88>{{cite book |first=Claus E. |last=Rolfs |author2=Rodney, William S. |date=1988 |title=Cauldrons in the Cosmos: Nuclear Astrophysics |publisher=University of Chicago Press |isbn=978-0-226-72457-7}}</ref>
<ref name=science295_5552>{{cite journal |last=Kroupa |first=Pavel |title=The Initial Mass Function of Stars: Evidence for Uniformity in Variable Systems |journal=Science |date=2002 |volume=295 |issue=5552 |pages=82–91 |doi=10.1126/science.1067524 |pmid=11778039 |arxiv=astro-ph/0201098 |bibcode=2002Sci...295...82K |s2cid=14084249}}</ref>
<ref name="Iben2012">{{cite book |author=Icko Iben |title=Stellar Evolution Physics |url=https://books.google.com/books?id=IU357EiecWwC&pg=PA1481 |date=29 November 2012 |publisher=Cambridge University Press |isbn=978-1-107-01657-6 |pages=1481–}}</ref>
<ref name=martins2021>{{cite journal
| title=Spectroscopic evolution of massive stars near the main sequence at low metallicity
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| journal=Astronomy & Astrophysics
| volume=645 | at=id. A67 | date=January 2021
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<ref name=pmss_atoe>{{cite web |author=Staff |date=12 October 2006 |url=http://outreach.atnf.csiro.au/education/senior/astrophysics/stellarevolution_postmain.html |title=Post-Main Sequence Stars |publisher=Australia Telescope Outreach and Education |access-date=2008-01-08 |archive-url=https://web.archive.org/web/20130120215215/http://outreach.atnf.csiro.au/education/senior/astrophysics/stellarevolution_postmain.html |archive-date=20 January 2013 }}</ref>
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<ref name=science299_5603>{{cite journal |last=Krauss |first=Lawrence M. |author2=Chaboyer, Brian |title=Age Estimates of Globular Clusters in the Milky Way: Constraints on Cosmology |journal=Science |date=2003 |volume=299 |issue=5603 |pages=65–69 |doi=10.1126/science.1075631 |pmid=12511641 |bibcode=2003Sci...299...65K |s2cid=10814581 }}</ref>
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