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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>{{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>
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>{{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
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 10 {{solar mass}}, 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>{{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> For very low-mass stars, molecules in the atmosphere also contribute to the opacity. Below about 0.5 {{solar mass}}, the luminosity of the star varies as the mass to the power of 2.3, producing a flattening of the slope on a graph of mass versus luminosity. Even these refinements are only an approximation, however, and the mass-luminosity relation can vary depending on a star's composition.<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 |url=https://www.science.org/doi/10.1126/science.1067524 |access-date=2007-12-03 |doi=10.1126/science.1067524 |pmid=11778039 |arxiv=astro-ph/0201098 |bibcode=2002Sci...295...82K |s2cid=14084249}}</ref>
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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>{{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
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>{{cite web |last=Sitko |first=Michael L. |date=24 March 2000 |url=http://www.physics.uc.edu/~sitko/Spring00/4-Starevol/starevol.html |title=Stellar Structure and Evolution |publisher=University of Cincinnati |access-date=2007-12-05
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>{{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 |url=https://semanticscholar.org/paper/4bae7262b55da8fc7d8ff28be71052c8a6bc0289}}</ref>
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<ref name=apj129>{{cite journal |author1=Luck, R. Earle |author2=Heiter, Ulrike |title=Stars within 15 Parsecs: Abundances for a Northern Sample |journal=The Astronomical Journal |date=2005 |volume=129 |issue=2 |pages=1063–1083 |bibcode=2005AJ....129.1063L |doi=10.1086/427250 |doi-access=free}}</ref>
<ref name=recons>{{cite web |author=Staff |date=1 January 2008 |url=http://www.chara.gsu.edu/RECONS/TOP100.posted.htm |title=List of the Nearest Hundred Nearest Star Systems |publisher=Research Consortium on Nearby Stars |access-date=2008-08-12
<ref name=brainerd>{{cite web |last=Brainerd |first=Jerome James |date=16 February 2005 |url=https://www.astrophysicsspectator.com/topics/stars/MainSequence.html |title=Main-Sequence Stars |publisher=The Astrophysics Spectator |access-date=2007-12-04}}</ref>
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<ref name=aaa102_1>{{cite journal |author1=Bressan, A. G. |author2=Chiosi, C. |author3=Bertelli, G. |title=Mass loss and overshooting in massive stars |journal=Astronomy and Astrophysics |date=1981 |volume=102 |issue=1 |pages=25–30 |bibcode=1981A&A...102...25B}}</ref>
<ref name=lockner06>{{cite web |last=Lochner |first=Jim |author2=Gibb, Meredith |author3=Newman, Phil |date=6 September 2006 |url=http://imagine.gsfc.nasa.gov/docs/science/know_l2/stars.html |title=Stars |publisher=NASA |access-date=2007-12-05
<ref name=sp74>{{cite journal |last=Gough |first=D. O. |title=Solar interior structure and luminosity variations |journal=Solar Physics |date=1981 |volume=74 |issue=1 |pages=21–34 |bibcode=1981SoPh...74...21G |doi=10.1007/BF00151270 |s2cid=120541081}}</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 |
<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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|first1=Carl J. |last1=Hansen |first2=Steven D. |last2=Kawaler
|publisher=Springer Science & Business Media
|year=1999 |isbn={{Format ISBN|978-0387941387}} |page=39
|url=https://books.google.com/books?id=m-_6LYuUbUkC&pg=PA39}}</ref>
}}
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===Technical===
* {{cite book |last=Arnett |first=David |title=Supernovae and Nucleosynthesis |publisher=[[Princeton University Press]] |___location=Princeton |year=1996}}
* {{cite book |last=Bahcall |first=John N. |title=Neutrino Astrophysics |url=https://archive.org/details/neutrinoastrophy0000bahc |url-access=registration |publisher=[[Cambridge University Press]] |___location=Cambridge |year=1989 |isbn={{Format ISBN|9780521379755}}}}
* {{cite journal |last1=Bahcall |first1=John N. |last2=Pinsonneault |first2=M.H. |last3=Basu |first3=Sarbani |title=Solar Models: Current Epoch and Time Dependences, Neutrinos, and Helioseismological Properties |journal=The Astrophysical Journal |volume=555 |pages=990–1012 |number=2 |year=2001 |arxiv=astro-ph/0010346 |doi=10.1086/321493 |bibcode=2001ApJ...555..990B |s2cid=13798091}}
* {{cite book |editor1-last=Barnes |editor1-first=C. A. |editor2-last=Clayton |editor2-first=D. D. |editor3-last=Schramm |editor3-first=D. N. |title=Essays in Nuclear Astrophysics |publisher=Cambridge University Press |___location=Cambridge |year=1982}}
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* {{cite journal |last1=Chabrier |first1=Gilles |last2=Baraffe |first2=Isabelle |title=Theory of Low-Mass Stars and Substellar Objects |journal=Annual Review of Astronomy and Astrophysics |volume=38 |pages=337–377 |year=2000 |arxiv=astro-ph/0006383 |doi=10.1146/annurev.astro.38.1.337 |bibcode=2000ARA&A..38..337C |s2cid=59325115}}
* {{cite book |last=Chandrasekhar |first=S. |author-link=Subramanyam Chandrasekhar |title=An Introduction to the study of stellar Structure |publisher=Dover |___location=New York |year=1967}}
* {{cite book |last=Clayton |first=Donald D. |title=Principles of Stellar Evolution and Nucleosynthesis |url=https://archive.org/details/principlesofstel0000clay |url-access=registration |publisher=University of Chicago |___location=[[Chicago]] |year=1983 |isbn={{Format ISBN|9780226109527}}}}
* {{cite book |last1=Cox |first1=J. P. |last2=Giuli |first2=R. T. |title=Principles of Stellar Structure |publisher=Gordon and Breach |___location=[[New York City]] |year=1968}}
* {{cite journal |last1=Fowler |first1=William A. |author-link1=William A. Fowler |last2=Caughlan |first2=Georgeanne R. |author-link2=Georgeanne R. Caughlan |last3=Zimmerman |first3=Barbara A. |title=Thermonuclear Reaction Rates, I |journal=Annual Review of Astronomy and Astrophysics |volume=5 |page=525 |year=1967 |doi=10.1146/annurev.aa.05.090167.002521 |bibcode=1967ARA&A...5..525F}}
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* {{cite book |last1=Hansen |first1=Carl J. |last2=Kawaler |first2=Steven D. |last3=Trimble |first3=Virginia |title=Stellar Interiors: Physical Principles, Structure, and Evolution, Second Edition |publisher=Springer-Verlag |___location=New York |year=2004}}
* {{cite journal |last1=Harris |first1=Michael J. |last2=Fowler |first2=William A. |last3=Caughlan |first3=Georgeanne R. |last4=Zimmerman |first4=Barbara A. |title=Thermonuclear Reaction Rates, III |journal=Annual Review of Astronomy and Astrophysics |volume=21 |page=165 |year=1983 |doi=10.1146/annurev.aa.21.090183.001121 |bibcode=1983ARA&A..21..165H}}
* {{cite journal |last1=Iben |first1=Icko
* {{cite journal |last1=Iglesias |first1=Carlos A. |last2=Rogers |first2=Forrest J. |title=Updated Opal Opacities |journal=The Astrophysical Journal |volume=464 |page=943 |year=1996 |doi=10.1086/177381 |bibcode=1996ApJ...464..943I}}
* {{cite book |last1=Kippenhahn |first1=Rudolf |last2=Weigert |first2=Alfred |title=Stellar Structure and Evolution |publisher=[[Springer-Verlag]] |___location=Berlin |year=1990}}
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