Main sequence
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2008-07-16T22:59:36Z
RJHall
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[[Image:H-R diagram.svg|thumb|270px|A Hertzsprung-Russell diagram plots the actual brightness (or [[absolute magnitude]]) of a star against its [[color index]] (represented as B-V). The main sequence is visible as a prominent diagonal band that runs from the upper left to the lower right.]]
The '''main sequence''' is the name for a continuous and distinctive band of stars that appear on a plot of stellar [[Color index|color]] versus brightness. These color-[[absolute magnitude|magnitude]] plots are known as [[Hertzsprung-Russell diagram]]s after their co-developers, [[Ejnar Hertzsprung]] and [[Henry Norris Russell]]. Stars on this band are known as '''main-sequence stars''' or '''dwarf stars'''.
After a star has formed, it generates energy at the hot, dense core region through the [[nuclear fusion]] of [[hydrogen]] atoms into [[helium]]. During this stage of the star's lifetime, it is located along the main sequence at a position determined primarily by its mass, but also based upon its chemical composition and other factors. In general, the more massive the star 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.
The main sequence is sometimes divided into upper and lower parts, based on the processes that stars use to generate energy. Stars below about 1.5 times the [[Solar mass|mass of the Sun]] (or 1.5 solar masses) 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 can instead use atoms of [[carbon]], [[nitrogen]] and [[oxygen]] as intermediaries in the production of helium from hydrogen atoms.
Because there is a temperature gradient between the core of a star and its surface, energy is steadily transported upward through the intervening layers until it is radiated away at the [[photosphere]]. The two mechanisms used to carry this energy through the star are [[radiation]] and [[convection]], with the type used depending on the local conditions. Convection tends to occur in regions with steeper temperature gradients, higher opacity or both. When convection occurs in the core region it acts to stir up the helium ashes, thus maintaining the proportion of fuel needed for fusion to occur.
== History ==
In the early part of the [[twentieth century]], information about the types and distances of [[star]]s became more readily available. The [[spectra]] of stars were shown to have distinctive features, which allowed them to be categorized. [[Annie Jump Cannon]] and [[Edward C. Pickering]] at [[Harvard College Observatory]] had developed a method of categorization that became known as the Harvard classification scheme. This scheme was published in the ''Harvard Annals'' in 1901.<ref>{{cite book
| first=Malcolm S. | last=Longair | year=2006
| title=The Cosmic Century: A History of Astrophysics and Cosmology
| publisher=Cambridge University Press
| id=ISBN 0-521-47436-1 }}</ref>
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 "giant" and "dwarf" stars. The following year he began studying [[star cluster]]s; large groupings of stars that are co-located at approximately the same distance. He published the first plots of color versus luminosity for these stars. These plots showed a prominent and continuous sequence of stars, which he named the main sequence.<ref name=brown>{{cite book
| first=Laurie M.
| coauthors=Pais, Abraham; Pippard, A. B.
| last=Brown
| authorlink=Patrick Moore
| year=1995
| title=Twentieth Century Physics
| publisher=CRC Press
| id=ISBN 0-7503-0310-7 }}</ref>
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 which had been 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.<ref name=obs36>{{cite journal
| last=Russell | first=H. N.
| title="Giant" and "dwarf" stars
| journal=The Observatory
| year=1913 | volume=36 | pages=324–329
| url=http://adsabs.harvard.edu/abs/1913Obs....36..324R
| accessdate=2007-12-02 }}</ref>
Of the red stars observed by Hertzsprung, the dwarf stars also followed the spectra-luminosity relationship discovered by Russell. However, the giant stars are much brighter than dwarfs and so do not follow the same relationship. Russell proposed that the "giant stars must have low density or great surface-brightness, and the reverse is true of dwarf stars". The same curve also showed that there were very few faint white stars.<ref name=obs36/>
In 1933, [[Bengt Strömgren]] introduced the term Hertzsprung-Russell diagram to denote a luminosity-spectral class diagram.<ref>{{cite journal
| last=Strömgren | first=Bengt
| title=On the Interpretation of the Hertzsprung-Russell-Diagram
| journal=Zeitschrift für Astrophysik
| year=1933 | volume=7 | pages=222–248
| url=http://adsabs.harvard.edu/abs/1933ZA......7..222S
| accessdate=2008-05-23 }}</ref> This name reflected the parallel development of this technique by both Hertzsprung and Russell earlier in the century.<ref name=brown/>
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 is known, there is a unique solution determining the star's radius and luminosity. This became known as the [[Vogt-Russell theorem]]; named after Heinrich Vogt and Henry Norris Russell. By this theorem, once a star's chemical composition and its position on the main sequence is known, so too is the star's mass and radius. (However, it was subsequently discovered that the theorem breaks down somewhat for stars of non-uniform composition.)<ref>{{cite book
| first=Evry L. | last=Schatzman | year=1993
| coauthors=Praderie, Francoise
| title=The Stars | publisher=Springer
| id=ISBN 3-540-54196-9 }}</ref>
A refined scheme for [[stellar classification]] was published in 1943 by W. W. Morgan and P. C. Keenan.<ref>{{cite book
| first=W. W. | last=Morgan
| coauthors=Keenan, P. C.; Kellman, E. | year=1943
| title=An atlas of stellar spectra, with an outline of spectral classification
| publisher=The University of Chicago press
| location=Chicago, Illinois }}</ref> The MK classification assigned each star a spectral type—based on the Harvard classification—and a luminosity class. For historical reasons, 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>{{cite book
| first=Albrecht | last=Unsöld | year=1969
| title=The New Cosmos | pages=p. 268
| publisher=Springer-Verlag New York Inc. }}</ref>
== Characteristics ==
Main sequence stars have been extensively studied through stellar models, allowing their formation and evolutionary history to be relatively well understood. The position of the star on the main sequence provides information about its physical properties.
The [[temperature]] of a star can be approximately determined by treating it as an idealized energy radiator known as a [[black body]]. In this case, the luminosity ''L'' and radius ''R'' are related to the temperature ''T'' by the [[Stefan-Boltzmann Law]]:
:<math>L = 4\pi \sigma R^2 T^4</math>
where ''σ'' is the [[Stefan–Boltzmann constant]]. The temperature and composition of a star's [[photosphere]] determines the energy emission at different wavelengths. The [[color index]], or ''B'' − ''V'', measures the difference in this energy emission by means of filters that capture the star's [[apparent magnitude|magnitude]] in blue (''B'') and green-yellow (''V'') light. (By measuring the difference between these values, this eliminates the need to correct the magnitudes for distance.) Thus the position of a star on the HR diagram can be used to estimate its radius and temperature.<ref>{{cite web
| url=http://astro.unl.edu/naap/hr/hr_background3.html
| title=Origin of the Hertzsprung-Russell Diagram
| publisher=University of Nebraska
| accessdate=2007-12-06
}}</ref> By modifying the physical properties of the [[plasma]] in the photosphere, the temperature of a star also determines its [[spectral type]].
=== Formation ===
When a [[protostar]] is formed from the 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>{{cite journal
| last=Gloeckler | first=George
| coauthors=Geissc, Johannes
| title=Composition of the local interstellar medium as diagnosed with pickup ions
| journal=Advances in Space Research
| year=2004 | volume=34 | issue=1 | pages=53–60
| url=http://adsabs.harvard.edu/abs/2004AdSpR..34...53G
| accessdate=2007-12-09
| doi=10.1016/j.asr.2003.02.054
}}</ref> During the initial collapse, this [[pre-main sequence star]] generates energy through gravitational contraction. Upon reaching a suitable density, energy generation is begun at the core using an exothermic [[nuclear fusion]] process that converts hydrogen into helium.<ref name=tnc/>
{{star nav}}
Once nuclear fusion of hydrogen becomes the dominant energy production process and the excess energy gained from gravitational contraction has been lost,<ref>{{cite journal
| last=Schilling | first=Govert
| title=New Model Shows Sun Was a Hot Young Star
| journal=Science | year=2001 | volume=293
| issue=5538 | pages=2188–2189
| url=http://www.sciencemag.org/cgi/content/full/293/5538/2188
| accessdate=2007-02-04
| doi=10.1126/science.293.5538.2188
| pmid=11567116 }}</ref> the star lies along a [[curve]] on the [[Hertzsprung-Russell diagram]] (or HR diagram) called the standard main sequence. Astronomers will sometimes refer to this stage as "zero age main sequence", or ZAMS.<ref>{{cite web
| url=http://astronomy.swin.edu.au/cms/astro/cosmos/Z/Zero+Age+Main+Sequence
| title=Zero Age Main Sequence
| work=The SAO Encyclopedia of Astronomy
| publisher=Swinburne University
| accessdate=2007-12-09
}}</ref> This curve is calculated using computer models of stellar properties at the point when stars begin hydrogen fusion; the brightness and surface temperature of stars typically increase from this point with age.<ref name=Clayton>{{cite book
| first=Donald D. | last=Clayton | year=1983
| title=Principles of Stellar Evolution and Nucleosynthesis
| publisher=University of Chicago Press
| id=ISBN 0-226-10953-4 }}</ref>
A star remains near its initial position on the main sequence until a significant amount of hydrogen in the core has been consumed, then begins to evolve into a more luminous star. (On the HR diagram, the evolving star moves up and to the right of the main sequence.) Thus the main sequence represents the primary hydrogen-burning stage of a star's lifetime.<ref name=tnc/>
The majority of stars on a typical HR diagram lie along the main sequence curve. This line is so pronounced because both the [[stellar classification|spectral type]] and the [[luminosity]] depend only on a star's mass, at least to [[zeroth order approximation]], as long as it is fusing hydrogen at its core—and that is what almost all stars spend most of their "active" life doing.<ref>{{cite web
| url=http://outreach.atnf.csiro.au/education/senior/astrophysics/stellarevolution_mainsequence.html
| title=Main Sequence Stars
| publisher=Australia Telescope Outreach and Education
| accessdate=2007-12-04 }}</ref> These main-sequence (and therefore "normal") stars are called dwarf stars. This is not because they are unusually small, but instead comes from their smaller radii and lower luminosity as compared to the other main category of stars, the [[giant star]]s.<ref>{{cite book
| first=Patrick | last=Moore | authorlink=Patrick Moore
| year=2006 | title=The Amateur Astronomer
| publisher=Springer | id=ISBN 1-85233-878-4 }}</ref> [[White dwarfs]] are a different kind of star that are much smaller than main sequence stars—being roughly the size of the [[Earth]]. These represent the final evolutionary stage of many main sequence stars.<ref>{{cite web
| url=http://astronomy.swin.edu.au/cosmos/W/White+Dwarf
| title=White Dwarf
| work=COSMOS—The SAO Encyclopedia of Astronomy
| publisher=Swinburne University
| accessdate=2007-12-04 }}</ref>
=== Energy generation ===
[[Image:PPvsCNO.png|right|280px|thumb|This graph shows the relative energy output for the [[Proton-proton chain reaction|proton-proton]] (PP), [[CNO cycle|CNO]] and [[Triple-alpha process|triple-α ]] fusion processes at different temperatures. At the Sun's core temperature, the PP process is more efficient.]]
All main sequence stars have a core region where energy is generated by nuclear fusion. The temperature and density of this core are at the levels necessary to sustain the energy production needed to support the remainder of the star. A reduction of energy production would cause the overlaying mass to compress, increasing the temperature and pressure needed for fusion. Likewise an increase in energy production would cause the star to expand, lowering the pressure at the core. Thus the star forms a self-regulating system in [[hydrostatic equilibrium]] that is stable over the course of its main sequence lifetime.<ref name=brainerd>{{cite web
| last=Brainerd | first=Jim | date=[[February 16]], [[2005]]
| url=http://www.astrophysicsspectator.com/topics/stars/MainSequence.html
| title=Main-Sequence Stars
| publisher=The Astrophysics Spectator
| accessdate=2007-12-04 }}</ref>
Astronomers divide the main sequence into upper and lower parts, based on the type of fusion process at the core. Stars in the upper main sequence have sufficient mass to use the [[CNO cycle]] to fuse hydrogen into helium. This process uses atoms of [[carbon]], [[nitrogen]] and [[oxygen]] as intermediaries in the fusion process. In the lower main sequence, energy is generated as the result of the [[proton-proton chain]], which directly fuses hydrogen together in a series of stages to produce helium.<ref name=hannu>{{cite book
| first=Hannu | last=Karttunen | year=2003
| title=Fundamental Astronomy | publisher=Springer
| id=ISBN 3-540-00179-4 }}</ref>
At a stellar core temperature of 18 million [[kelvin]]s, both fusion processes are equally efficient. This is the core temperature of a star with 1.5 solar masses. Hence the upper main sequence consists of stars above this mass. The apparent upper limit for a main sequence star is 120-200 solar masses.<ref>{{cite journal
| last=Oey | first=M. S.
| coauthors=Clarke, C. J.
| title=Statistical Confirmation of a Stellar Upper Mass Limit
| journal=The Astrophysical Journal
| year=2005 | volume=620
| issue=1 | pages=L43–L46
| url=http://adsabs.harvard.edu/abs/2005ApJ...620L..43O
| accessdate=2007-12-05
| doi=10.1086/428396 }}</ref> The lower limit for sustained nuclear fusion is about 0.08 solar masses.<ref name=hannu/>
=== Structure ===
[[Image:Solar internal structure.svg|right|280px|thumb|This diagram shows a cross-section of a Sun-like star, showing the internal structure.]]
Because there is a temperature difference between the core and the surface, or [[photosphere]], energy is transported outward. The two modes for transporting this energy are [[radiation]] and [[convection]]. A [[radiation zone]], where energy is transported by [[radiation]], is stable against convection and there is very little mixing of the plasma. By contrast, in a [[convection zone]] the energy is transported by bulk movement of plasma, with hotter material rising and cooler material descending. Convection is a more efficient mode for carrying energy than radiation, but it will only occur under conditions that create a steep temperature gradient.<ref>{{cite book
| first=Lawrence H.
| last=Aller
| year=1991
| title=Atoms, Stars, and Nebulae
| publisher=Cambridge University Press
| id=ISBN 0-521-31040-7 }}</ref><ref name=brainerd/>
In massive stars, the rate of energy generation by the CNO cycle is very sensitive to temperature, so the fusion is highly concentrated at the core. Consequently, there is a high temperature gradient at the core, which results in a convection zone for more efficient energy transport.<ref name=hannu/> The mixing of material around the core removes the helium ashes from the hydrogen burning region, allowing more of the hydrogen in the star to be burned. The outer regions of a massive star transport energy by radiation, with little or no convection.<ref name=brainerd/>
Intermediate mass, class A stars such as [[Sirius]] may transport energy entirely by radiation.<ref>{{cite web
| last=Lochner | first=Jim
| coauthors=Gibb, Meredith; Newman, Phil
| date=[[September 6]], [[2006]]
| url=http://imagine.gsfc.nasa.gov/docs/science/know_l2/stars.html
| title=Stars | publisher=NASA
| accessdate=2007-12-05 }}</ref> Medium-sized, low mass stars like the Sun have a core region that is stable against convection and a convection zone near the surface. This produces mixing of the outer layers, but a less efficient burning of the hydrogen in the star. The eventual result is the buildup of a helium-rich core, surrounded by a hydrogen-rich region. By contrast, cool, low-mass stars are convective throughout. The helium produced at the core is distributed across the star, producing a relatively uniform atmosphere.<ref name=brainerd/>
=== Luminosity-color variation ===
As non-fusing helium ash accumulates in the core, the reduction in the abundance of hydrogen per unit mass results in a gradual lowering of the fusion rate within that mass. To compensate, the core temperature and pressure slowly increase, which actually causes a net increase in the overall fusion rate (to support the greater density of the inner star). This produces a steady increase in the luminosity and radius of the star over time.<ref name=Clayton/> Thus, for example, the luminosity of the early Sun was only about 70% of its current value.<ref>{{cite journal
| last=Gough | first=D. O.
| title=Solar interior structure and luminosity variations
| journal=Solar Physics | year=1981 | volume=74 | pages=21–34
| url=http://adsabs.harvard.edu/abs/1981SoPh...74...21G
| accessdate=2007-12-06
| doi=10.1007/BF00151270 }}</ref> The luminosity increase of a star changes its position on the HR diagram; resulting in a broadening of the main sequence band because stars are observed at random stages in their lifetime.<ref>{{cite book
| first=Thanu | last=Padmanabhan | year=2001
| title=Theoretical Astrophysics
| publisher=Cambridge University Press
| id=ISBN 0-521-56241-4 }}</ref>
The stars in the main sequence do not lie upon a narrow curve on the HR diagram. This is primarily because of the observational uncertainties that mainly affect the distance of the star in question, but also because of factoring in unresolved [[binary star]]s. However, even perfect observations would lead to a fuzzy main sequence, because mass is not a star's only parameter. In addition to variations in [[Metallicity|chemical composition]]—both because of the initial abundances and the star's [[Stellar evolution|evolutionary status]],<ref>{{cite journal
| last=Wright | first=J. T.
| title=Do We Know of Any Maunder Minimum Stars?
| journal=The Astronomical Journal
| year=2004 | volume=128 | issue=3 | pages=1273–1278
| url=http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:astro-ph/0406338
| accessdate=2007-12-06
| doi=10.1086/423221 }}</ref> the presence of a [[Binary star|close companion]],<ref>{{cite book
| first=Roger John | last=Tayler | year=1994
| title=The Stars: Their Structure and Evolution
| publisher=Cambridge University Press
| id=ISBN 0-521-45885-4 }}</ref> [[Stellar rotation|rapid rotation]],<ref>{{cite journal
| last=Sweet | coauthors=Roy, A. E. | first=I. P. A.
| title=The structure of rotating stars
| journal=Monthly Notices of the Royal Astronomical Society
| year=1953 | volume=113 | pages=701–715
| url=http://adsabs.harvard.edu/abs/1953MNRAS.113..701S
| accessdate=2007-12-06 }}</ref> or a [[Stellar magnetic field|magnetic field]] can also move a star slightly on the main sequence, to name just a few factors. For example, there are stars with a very low abundance of elements with higher atomic numbers than helium—known as [[metal-poor]] stars—that lie just below the main sequence. Also known as [[subdwarf]]s, these stars are also fusing hydrogen in their core and so they mark the lower edge of the main sequence's fuzziness due to chemical composition.<ref>{{cite conference
| last=Burgasser | first=Adam J.
| coauthors=Kirkpatrick, J. Davy; Lepine, Sebastien
| title=Spitzer Studies of Ultracool Subdwarfs: Metal-poor Late-type M, L and T Dwarfs
| booktitle=Proceedings of the 13th Cambridge Workshop on Cool Stars, Stellar Systems and the Sun
| pages=p. 237
| publisher=Dordrecht, D. Reidel Publishing Co.
| date=July 5-9, 2004
| location=Hamburg, Germany
| url=http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:astro-ph/0409178
| accessdate=2007-12-06 }}</ref>
A nearly vertical region of the HR diagram is known as the [[instability strip]] and is occupied by pulsating [[variable star]]s. These stars vary in magnitude at regular intervals, giving them a pulsating appearance. The strip intersects the upper part of the main sequence in the region of class A and F stars; between one and two solar masses. However, main sequence stars in this region experience only small variations in magnitude and so are hard to detect.<ref>{{cite book
| first=S. F.
| last=Green
| coauthors=Jones, Mark Henry; Burnell, S. Jocelyn
| year=2004 | title=An Introduction to the Sun and Stars
| publisher=Cambridge University Press
| id=ISBN 0-521-54622-2 }}</ref>
=== Lifetime ===
The lifespan that a star spends on the main sequence is governed by two factors. The total amount of energy that can be generated through nuclear fusion of hydrogen is limited by the amount of available hydrogen fuel that can be consumed at the core. For a star in equilibrium, the energy generated at the core must be at least equal to the energy radiated at the surface. Since the luminosity gives the amount of energy radiated per unit time, the total life span can be estimated, to first approximation, as the total energy produced divided by the star's luminosity.<ref>{{cite web
| last=Richmond | first=Michael
| date=[[November 10]], [[2004]]
| url=http://spiff.rit.edu/classes/phys230/lectures/star_age/star_age.html
| title=Stellar evolution on the main sequence
| publisher=Rochester Institute of Technology
| accessdate=2007-12-03 }}</ref>
Our [[Sun]] has been a main sequence star for about 4.5 billion years and will continue to be one for another 5.5 billion years, for a total main sequence lifetime of 10<sup>10</sup> years. After the hydrogen supply in the core is exhausted, it will expand to become a [[red giant]] and fuse [[helium]] atoms to form [[carbon]]. As the
energy output of the helium fusion process per unit mass is
only about a tenth the energy output of the hydrogen process, this stage will only last for about 10% of a star's total active lifetime. Thus, on average, about 90% of the observed stars will be on the main sequence.<ref>{{cite book
| first=David | last=Arnett | year=1996
| title=Supernovae and Nucleosynthesis: An Investigation of the History of Matter, from the Big Bang to the Present
| publisher=Princeton University Press
| id=ISBN 0-691-01147-8 }}—Hydrogen fusion produces 8×10<sup>18</sup> [[erg]]/[[gram|g]] while helium fusion produces 8×10<sup>17</sup> erg/g.</ref>
On average, main sequence stars are known to follow an empirical mass-luminosity relationship.<ref>For a detailed historical reconstruction of the theoretical derivation of this relationship by Eddington in 1924, see: {{cite book
| first=Stefano | last=Lecchini | year=2007
| title=How Dwarfs Became Giants. The Discovery of the Mass-Luminosity Relation
| url=http://www.amazon.de/Dwarfs-Giants-Discovery-Mass-Luminosity-Relation/dp/3952288268
| publisher=Bern Studies in the History and Philosophy of Science
| id=ISBN 3-9522882-6-8}}</ref> The luminosity (''L'') of the star is approximately related to the total mass (''M'') as the following [[power law]]:
:<math>\begin{smallmatrix}L\ \propto\ M^{3.5}\end{smallmatrix}</math>
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 the Sun:<ref>{{cite web
| last = Richmond | first = Michael
| url = http://spiff.rit.edu/classes/phys230/lectures/star_age/star_age.html
| title = Stellar evolution on the main sequence
| accessdate = 2006-08-24 }}</ref>
:<math>\begin{smallmatrix} \tau_{ms}\ \sim \ 10^{10} \text{years} \cdot \left[ \frac{M}{M_{\bigodot}} \right] \cdot \left[ \frac{L_{\bigodot}}{L} \right]\ =\ 10^{10} \text{years} \cdot \left[ \frac{M_{\bigodot}}{M} \right]^{2.5} \end{smallmatrix}</math>
where ''M'' and ''L'' are the mass and luminosity of the star, respectively, <math>\begin{smallmatrix}M_{\bigodot}\end{smallmatrix}</math> is a solar mass, <math>\begin{smallmatrix}L_{\bigodot}\end{smallmatrix}</math> is the [[solar luminosity]] and <math>\tau_{ms}</math> is the star's estimated main sequence lifetime.
[[Image:Isochrone ZAMS Z2pct.png|360px|right|thumb|This plot gives an example of the mass-luminosity relationship for zero-age main sequence stars. The mass and luminosity are relative to the present-day Sun.]]
This is a counter-intuitive result, as more massive stars have more fuel to burn and might be expected to last longer. Instead, the lightest stars, of less than a tenth of a solar mass, may last over a trillion years.<ref>{{cite journal
| last=Laughlin | first=Gregory
| coauthors=Bodenheimer, Peter; Adams, Fred C.
| title=The End of the Main Sequence
| journal=The Astrophysical Journal
| year=1997 | volume=482 | pages=420–432
| doi= 10.1086/304125 }}</ref> For the heaviest stars, however, this mass-luminosity relationship poorly matches the estimated lifetime, which last at least a few million years. A more accurate representation gives a different function for various ranges of mass.
The 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>{{cite web
| last=Imamura | first=James N.
| date=[[February 7]], [[1995]]
| url=http://zebu.uoregon.edu/~imamura/208/feb6/mass.html
| title=Mass-Luminosity Relationship
| publisher=University of Oregon
| accessdate=2007-01-08 }}</ref> Note, however, that a sufficiently high opacity can result in energy transport via [[convection]], which changes the conditions needed to remain in equilibrium.<ref>{{cite book
| first=Donald D. | last=Clayton | year=1983
| title=Principles of Stellar Evolution and Nucleosynthesis
| publisher=University of Chicago Press
| id=ISBN 0-226-10953-4 }}</ref>
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>{{cite book
| first=Dina | last=Prialnik | year=2000
| title=An Introduction to the Theory of Stellar Structure and Evolution
| publisher=Cambridge UniversityPress | id=ISBN 0-521-65937-X }}</ref> For stars below 10 times the solar mass, the opacity becomes dependent on temperature, resulting in the luminosity varying approximately as the fourth power of the star's mass.<ref>{{cite book
| first=Claus E. | last=Rolfs
| coauthors=Rodney, William S. | year=1988
| title=Cauldrons in the Cosmos: Nuclear Astrophysics
| publisher=University of Chicago Press | id=ISBN 0-226-72457-3 }}</ref> For very low mass stars, molecules in the atmosphere also contribute to the opacity. Below about 0.5 solar masses, 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>{{cite journal
| last=Kroupa | first=Pavel
| title=The Initial Mass Function of Stars: Evidence for Uniformity in Variable Systems
| journal=Science | year=2002 | volume=295
| issue=5552 | pages=82–91
| url=http://www.sciencemag.org/cgi/content/full/295/5552/82
| accessdate=2007-12-03
| doi=10.1126/science.1067524
| pmid=11778039 }}</ref>
=== Evolutionary tracks ===
Once a main sequence star consumes the hydrogen at its core, the loss of energy generation causes gravitational collapse to resume. The hydrogen surrounding the core reaches sufficient temperature and pressure to undergo fusion, forming a hydrogen-burning shell surrounding a helium core. In consequence of this change, the outer envelope of the star expands and decreases in temperature, turning it into a [[red giant]]. At this point the star is evolving off the main sequence and entering the giant branch. (The path the star now follows across the HR diagram is called an evolutionary track.) The helium core of the star continues to collapse until it is entirely supported by [[electron degeneracy pressure]]—a [[quantum mechanics|quantum mechanical]] effect that restricts how closely matter can be compacted. For stars of more than about 0.5 [[solar mass]]es,<ref>{{cite journal
| author= Fynbo, Hans O. U. ''et al''
| title=Revised rates for the stellar triple-α process from measurement of 12C nuclear resonances
| journal=Nature | year=2004 | volume=433 | pages=136–139
| doi=10.1038/nature03219 }}</ref> the core can reach a temperature where it becomes hot enough to burn helium into carbon via the [[triple alpha process]].<ref>{{cite web
| last=Sitko | first=Michael L.
| date=[[March 24]], [[2000]]
| url=http://www.physics.uc.edu/~sitko/Spring00/4-Starevol/starevol.html
| title=Stellar Structure and Evolution
| publisher=University of Cincinnati
| accessdate=2007-12-05 }}</ref><ref>{{cite web
| author=Staff | date=[[October 12]], [[2006]]
| url=http://outreach.atnf.csiro.au/education/senior/astrophysics/stellarevolution_postmain.html
| title=Post-Main Sequence Stars
| publisher=Australia Telescope Outreach and Education
| accessdate=2008-01-08 }}</ref>
[[Image:Open cluster HR diagram ages.gif|right|thumb|250px|This shows the [[Hertzsprung-Russell diagram]]s for two open clusters. [[NGC 188]] is older, and shows a lower turn off from the main sequence than that seen in [[Messier 67|M67]].]]
When a [[star cluster|cluster of stars]] is formed at about the same time, the life span of these stars will depend on their individual masses. The most massive stars will leave the main sequence first, followed steadily in sequence by stars of ever lower masses. Thus the stars will evolve in order of their position on the main sequence, proceeding from the most massive at the left toward the right of the HR diagram. The current position where stars in this cluster are leaving the main sequence is known as the turn-off point. By knowing the main sequence lifespan of stars at this point, it becomes possible to estimate the age of the cluster.<ref>{{cite journal
| last=Krauss | first=Lawrence M.
| coauthors=Chaboyer, Brian
| title=Age Estimates of Globular Clusters in the Milky Way: Constraints on Cosmology
| journal=Science
| year=2003 | volume=299
| issue=5603 | pages=65–69
| doi= 10.1126/science.1075631
| pmid=12511641 }}</ref>
== Stellar parameters ==
The table below shows typical values for stars along the main sequence. The values of [[luminosity]] (L), [[radius]] (R) and [[mass]] (M) are relative to the Sun—a dwarf star with a spectral classification of G2 V. The actual values for a star may vary by as much as 20-30% from the values listed below.<ref>{{cite web
| last=Siess | first=Lionel | date=2000
| url=http://www-astro.ulb.ac.be/~siess/server/iso.html
| title=Computation of Isochrones
| publisher=Institut d'Astronomie et d'Astrophysique, Université libre de Bruxelles
| accessdate=2007-12-06 }}—Compare, for example, the model isochrones generated for a ZAMS of 1.1 solar masses. This is listed in the table as 1.26 times the [[solar luminosity]]. At metallicity Z=0.01 the luminosity is 1.34 times solar luminosity. At metallicity Z=0.04 the luminosity is 0.89 times the solar luminosity.</ref> The coloration of the stellar class column gives an approximate representation of the star's photographic color, which is a function of the effective surface [[temperature]].
<!-- Please include a solid reference if you try to fill in additional values on this table. -->
:{| border="1" cellspacing="0" cellpadding="4"
|+ Table of main sequence stellar parameters<ref name=zombeck>{{cite book
| first=Martin V. | last=Zombeck | year=1990
| title=Handbook of Space Astronomy and Astrophysics
| publisher=Cambridge University Press
| edition=2nd edition
| url=http://ads.harvard.edu/books/hsaa/toc.html
| access-date=2007-12-06 | id=ISBN 0-521-34787-4 }}</ref>
|- bgcolor="#FFFFCC"
!rowspan="2" style="font-size: smaller;"|[[Stellar classification|Stellar<br />Class]]
!style="font-size: smaller;"|[[Radius]]
!style="font-size: smaller;"|Mass
!style="font-size: smaller;"|Luminosity
!style="font-size: smaller;"|Temperature
!rowspan="2"|Examples
|- bgcolor="#FFFFEE"
|align="center"|R/[[solar radius|R<sub>☉</sub>]]
|align="center"|M/[[solar mass|M<sub>☉</sub>]]
|align="center"|L/[[solar luminosity|L<sub>☉</sub>]]
|align="center"|[[kelvin|K]]
|-
|align="center" bgcolor="#3e6cff"|O5
|align="center"|18
|align="center"|40
|align="center"|500,000
|align="center"|38,000
|Sanduleak −66° 41, [[Zeta Puppis]]
|-
|align="center" bgcolor="#4472ff"|B0
|align="center"|7.4
|align="center"|18
|align="center"|20,000
|align="center"|30,000
|[[Phi Orionis|Phi<sup>1</sup> Orionis]]
|-
|align="center" bgcolor="#5785ff"|B5
|align="center"|3.8
|align="center"|6.5
|align="center"|800
|align="center"|16,400
|[[Pi Andromedae|Pi Andromedae A]]
|-
|align="center" bgcolor="#7ca5ff"|A0
|align="center"|2.5
|align="center"|3.2
|align="center"|80
|align="center"|10,800
|[[Alpha Coronae Borealis|Alpha Coronae Borealis A]]
|-
|align="center" bgcolor="#9cbdff"|A5
|align="center"|1.7
|align="center"|2.1
|align="center"|20
|align="center"|8,620
|[[Beta Pictoris]]
|-
|align="center" bgcolor="#b1ccff"|F0
|align="center"|1.4
|align="center"|1.7
|align="center"|6
|align="center"|7,240
|[[Gamma Virginis]]
|-
|align="center" bgcolor="#d4e4ff"|F5
|align="center"|1.2
|align="center"|1.29
|align="center"|2.5
|align="center"|6,540
|[[Eta Arietis]]
|-
|align="center" bgcolor="#edf4ff"|G0
|align="center"|1.05
|align="center"|1.10
|align="center"|1.26
|align="center"|6,000
|[[Beta Comae Berenices]]
|-
|align="center" bgcolor="#fdfeff"|G2
|align="center"| 1.00<ref name=bydef>The Sun is a typical type G2V star.</ref>
|align="center"| 1.00<ref name=bydef/>
|align="center"| 1.00<ref name=bydef/>
|align="center"|5,920
|[[Sun]], [[Alpha Centauri A]]
|-
|align="center" bgcolor="#fff6e9"|G5
|align="center"|0.93
|align="center"|0.93
|align="center"|0.79
|align="center"|5,610
|[[Alpha Mensae]]
|-
|align="center" bgcolor="#ffe9cb"|K0
|align="center"|0.85
|align="center"|0.78
|align="center"|0.40
|align="center"|5,150
|[[70 Ophiuchi|70 Ophiuchi A]]
|-
|align="center" bgcolor="#ffcb91"|K5
|align="center"|0.74
|align="center"|0.69
|align="center"|0.16
|align="center"|—
|[[61 Cygni|61 Cygni A]]
|-
|align="center" bgcolor="#ffae62"|M0
|align="center"|0.63
|align="center"|0.47
|align="center"|0.063
|align="center"|3,920
|Gliese 185
|-
|align="center" bgcolor="#ff8a38"|M5
|align="center"|0.32
|align="center"|0.21
|align="center"|0.0079
|align="center"|3,120
|[[EZ Aquarii|EZ Aquarii A]]
|-
|align="center" bgcolor="#f00000"|M8
|align="center"|0.13
|align="center"|0.10
|align="center"|0.0008
|align="center"|—
|Van Biesbroeck's star
|}
== See also ==
* [[Hertzsprung-Russell diagram]]
* [[Hydrogen burning process]]
== References ==
{{reflist|2}}
== External links ==
* [http://www.io.com/~iareth/mainsequence.html Table of Features of the "Life Zones" of Main Sequence Stars]
* [http://instruct1.cit.cornell.edu/courses/astro101/java/evolve/evolve.htm A java based applet for stellar evolution.]
{{Star}}
[[Category:Hertzsprung-Russell classifications]]
[[Category:Main sequence stars|*]]
[[Category:Stellar evolution]]
[[cs:Hlavní posloupnost]]
[[de:Hauptreihe]]
[[es:Secuencia principal]]
[[fa:رشته اصلی]]
[[gl:Secuencia principal]]
[[ko:주계열성]]
[[hr:Glavni niz]]
[[id:Deret utama]]
[[it:Sequenza principale]]
[[he:הסדרה הראשית]]
[[lv:Galvenās secības zvaigzne]]
[[lt:Pagrindinė seka]]
[[nl:Hoofdreeks]]
[[ja:主系列星]]
[[no:Hovedserien]]
[[nn:Hovudserien]]
[[pl:Ciąg główny]]
[[pt:Sequência principal]]
[[ru:Главная последовательность]]
[[sk:Hlavná postupnosť]]
[[sr:Главни низ]]
[[fi:Pääsarja]]
[[sv:Huvudserien]]
[[zh:主序星]]