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.

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. This plot shows 22,000 stars from the Hipparcos Catalogue together with 1,000 low-luminosity stars (red and white dwarfs) from the Gliese Catalogue of Nearby Stars.


Hot and brilliant O stars in star-forming regions
Hot and brilliant O-type main-sequence stars 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.[1]

In the early part of the 20th century, information about the types and distances of stars 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 developed a method of categorization that became known as the Harvard Classification Scheme, published in the Harvard Annals in 1901.[2]

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 clusters; 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.[3]

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.[4]

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.[4]

In 1933, Bengt Strömgren introduced the term Hertzsprung–Russell diagram to denote a luminosity-spectral class diagram.[5] This name reflected the parallel development of this technique by both Hertzsprung and Russell earlier in the century.[3]

As evolutionary models of stars were developed during the 1930s, it was shown that, for stars of a uniform chemical composition, a relationship exists between a star's mass and its luminosity and radius. That is, for a given mass and composition, there is a unique solution for determining the star's radius and luminosity. This became known as the Vogt–Russell theorem; named after Heinrich Vogt and Henry Norris Russell. By this theorem, when a star's chemical composition and its position on the main sequence is known, so too is the star's mass and radius. (However, it was subsequently discovered that the theorem breaks down somewhat for stars of non-uniform composition.)[6]

A refined scheme for stellar classification was published in 1943 by William Wilson Morgan and Philip Childs Keenan.[7] 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 types 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.[8]

In April 2018, astronomers reported the detection of the most distant "ordinary" (i.e., main sequence) star, named Icarus (formally, MACS J1149 Lensed Star 1), at 9 billion light-years away from Earth.[9][10]

Formation and evolution

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.[11] 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.)[12] 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.[8]


When nuclear fusion of hydrogen becomes the dominant energy production process and the excess energy gained from gravitational contraction has been lost,[13] 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.[14][15] The ZAMS curve can be calculated using computer models of stellar properties at the point when stars begin hydrogen fusion. From this point, the brightness and surface temperature of stars typically increase with age.[16]

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.[8]


The majority of stars on a typical HR diagram lie along the main-sequence curve. This line is pronounced because both the 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" lives doing.[17]

The temperature of a star determines its spectral type via its effect on the physical properties of plasma in its photosphere. A star's energy emission as a function of wavelength is influenced by both its temperature and composition. A key indicator of this energy distribution is given by the color index, B − V, which measures the star's magnitude in blue (B) and green-yellow (V) light by means of filters.[note 1] This difference in magnitude provides a measure of a star's temperature.

Dwarf terminology

Main-sequence stars are called dwarf stars,[18][19] but this terminology is partly historical and can be somewhat confusing. For the cooler stars, dwarfs such as red dwarfs, orange dwarfs, and yellow dwarfs are indeed much smaller and dimmer than other stars of those colors. However, for hotter blue and white stars, the size and brightness difference between so-called "dwarf" stars that are on the main sequence and the so-called "giant" stars that are not becomes smaller; for the hottest stars it is not directly observable. For those stars the terms "dwarf" and "giant" refer to differences in spectral lines which indicate if a star is on the main sequence or off it. Nevertheless, very hot main-sequence stars are still sometimes called dwarfs, even though they have roughly the same size and brightness as the "giant" stars of that temperature.[20]

The common use of "dwarf" to mean main sequence is confusing in another way, because there are dwarf stars which are not main-sequence stars. For example, a white dwarf is the dead core of a star that is left after the star has shed its outer layers, that is much smaller than a main-sequence star, roughly the size of Earth. These represent the final evolutionary stage of many main-sequence stars.[21]


Morgan-Keenan spectral classification
Comparison of main sequence stars of each spectral class

By treating the star as an idealized energy radiator known as a black body, the luminosity L and radius R can be related to the effective temperature Teff by the Stefan–Boltzmann law:

where σ is the Stefan–Boltzmann constant. As the position of a star on the HR diagram shows its approximate luminosity, this relation can be used to estimate its radius.[22]

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 Teff. 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 TI, 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 ε = L/M, the energy generation rate per unit mass, as ε is proportional to TI15, where TI 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 RM0.78.[23]

Sample 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.[24]

Table of main-sequence stellar parameters[25]
Radius Mass Luminosity Temp. Examples[26]
O6 18 40 500,000 38,000 Theta1 Orionis C
B0 07.4 18 020,000 30,000 Phi1 Orionis
B5 03.8 06.5 000,800 16,400 Pi Andromedae A
A0 02.5 03.2 000,080 10,800 Alpha Coronae Borealis A
A5 01.7 02.1 000,020 08,620 Beta Pictoris
F0 01.3 01.7 000,006 07,240 Gamma Virginis
F5 01.2 01.3 000,002.5 06,540 Eta Arietis
G0 01.05 01.10 000,001.26 05,920 Beta Comae Berenices
G2 01.00 01.00 000,001.00 05,780 Sun[note 2]
G5 00.93 00.93 000,000.79 05,610 Alpha Mensae
K0 00.85 00.78 000,000.40 05,240 70 Ophiuchi A
K5 00.74 00.69 000,000.16 04,410 61 Cygni A[27]
M0 00.51 00.60 000,000.072 03,800 Lacaille 8760
M5 00.32 00.21 000,000.0079 03,120 EZ Aquarii A
M8 00.13 00.10 000,000.0008 02,660 Van Biesbroeck's star[28]

Energy generation

Nuclear energy generation
Logarithm of the relative energy output (ε)
Proton-Proton (PP), CNO and Triple-α fusion processes at different temperatures:
The dashed line shows the combined energy generation of the PP and CNO processes within a star. 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 that will support the remainder of the star. A reduction of energy production would cause the overlaying mass to compress the core, resulting in an increase in the fusion rate because of higher temperature and pressure. 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.[29]

Main-sequence stars employ two types of hydrogen fusion processes, and the rate of energy generation from each type depends on the temperature in the core region. Astronomers divide the main sequence into upper and lower parts, based on which of the two is the dominant fusion process. In the lower main sequence, energy is primarily generated as the result of the proton-proton chain, which directly fuses hydrogen together in a series of stages to produce helium.[30] Stars in the upper main sequence have sufficiently high core temperatures to efficiently use the CNO cycle. (See the chart.) This process uses atoms of carbon, nitrogen and oxygen as intermediaries in the process of fusing hydrogen into helium.

At a stellar core temperature of 18 million Kelvin, the PP process and CNO cycle are equally efficient, and each type generates half of the star's net luminosity. As this is the core temperature of a star with about 1.5 M, the upper main sequence consists of stars above this mass. Thus, roughly speaking, stars of spectral class F or cooler belong to the lower main sequence, while A-type stars or hotter are upper main-sequence stars.[16] The transition in primary energy production from one form to the other spans a range difference of less than a single solar mass. In the Sun, a one solar-mass star, only 1.5% of the energy is generated by the CNO cycle.[31] By contrast, stars with 1.8 M or above generate almost their entire energy output through the CNO cycle.[32]

The observed upper limit for a main-sequence star is 120–200 M.[33] The theoretical explanation for this limit is that stars above this mass can not radiate energy fast enough to remain stable, so any additional mass will be ejected in a series of pulsations until the star reaches a stable limit.[34] The lower limit for sustained proton–proton nuclear fusion is about 0.08 M or 80 times the mass of Jupiter.[30] Below this threshold are sub-stellar objects that can not sustain hydrogen fusion, known as brown dwarfs.[35]


Solar internal structure
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.[29][36]

In massive stars (above 10 M)[37] 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 in the core region, which results in a convection zone for more efficient energy transport.[30] This mixing of material around the core removes the helium ash from the hydrogen-burning region, allowing more of the hydrogen in the star to be consumed during the main-sequence lifetime. The outer regions of a massive star transport energy by radiation, with little or no convection.[29]

Intermediate-mass stars such as Sirius may transport energy primarily by radiation, with a small core convection region.[38] Medium-sized, low-mass stars like the Sun have a core region that is stable against convection, with a convection zone near the surface that mixes the outer layers. This results in a steady buildup of a helium-rich core, surrounded by a hydrogen-rich outer region. By contrast, cool, very low-mass stars (below 0.4 M) are convective throughout.[12] Thus the helium produced at the core is distributed across the star, producing a relatively uniform atmosphere and a proportionately longer main sequence lifespan.[29]

Luminosity-color variation

The Sun is the most familiar example of a main-sequence star

As non-fusing helium ash accumulates in the core of a main-sequence star, the reduction in the abundance of hydrogen per unit mass results in a gradual lowering of the fusion rate within that mass. Since it is the outflow of fusion-supplied energy that supports the higher layers of the star, the core is compressed, producing higher temperatures and pressures. Both factors increase the rate of fusion thus moving the equilibrium towards a smaller, denser, hotter core producing more energy whose increased outflow pushes the higher layers further out. Thus there is a steady increase in the luminosity and radius of the star over time.[16] For example, the luminosity of the early Sun was only about 70% of its current value.[39] As a star ages this luminosity increase changes its position on the HR diagram. This effect results in a broadening of the main sequence band because stars are observed at random stages in their lifetime. That is, the main sequence band develops a thickness on the HR diagram; it is not simply a narrow line.[40]

Other factors that broaden the main sequence band on the HR diagram include uncertainty in the distance to stars and the presence of unresolved binary stars that can alter the observed stellar parameters. However, even perfect observation would show a fuzzy main sequence because mass is not the only parameter that affects a star's color and luminosity. Variations in chemical composition caused by the initial abundances, the star's evolutionary status,[41] interaction with a close companion,[42] rapid rotation,[43] or a magnetic field can all slightly change a main-sequence star's HR diagram position, to name just a few factors. As an example, there are metal-poor stars (with a very low abundance of elements with higher atomic numbers than helium) that lie just below the main sequence and are known as subdwarfs. These stars are fusing hydrogen in their cores and so they mark the lower edge of main sequence fuzziness caused by variance in chemical composition.[44]

A nearly vertical region of the HR diagram, known as the instability strip, is occupied by pulsating variable stars known as Cepheid variables. 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, which are between one and two solar masses. Pulsating stars in this part of the instability strip that intersects the upper part of the main sequence are called Delta Scuti variables. Main-sequence stars in this region experience only small changes in magnitude and so this variation is difficult to detect.[45] Other classes of unstable main-sequence stars, like Beta Cephei variables, are unrelated to this instability strip.


Isochrone ZAMS Z2pct
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.

The total amount of energy that a star can generate through nuclear fusion of hydrogen is limited by the amount of 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.[46]

For a star with at least 0.5 M, when the hydrogen supply in its core is exhausted and it expands to become a red giant, it can start to fuse helium atoms to form carbon. The energy output of the helium fusion process per unit mass is only about a tenth the energy output of the hydrogen process, and the luminosity of the star increases.[47] This results in a much shorter length of time in this stage compared to the main sequence lifetime. (For example, the Sun is predicted to spend 130 million years burning helium, compared to about 12 billion years burning hydrogen.)[48] Thus, about 90% of the observed stars above 0.5 M will be on the main sequence.[49] On average, main-sequence stars are known to follow an empirical mass-luminosity relationship.[50] The luminosity (L) of the star is roughly proportional to the total mass (M) as the following power law:

This relationship applies to main-sequence stars in the range 0.1–50 M.[51]

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 become a red giant in 6.5 billion years,[52] for a total main sequence lifetime of roughly 1010 years. Hence:[53]

where M and L are the mass and luminosity of the star, respectively, is a solar mass, is the solar luminosity and 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.[54]

The exact mass-luminosity relationship depends on how efficiently energy can be transported from the core to the surface. A higher 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.[55] Note, however, that a sufficiently high opacity can result in energy transport via convection, which changes the conditions needed to remain in equilibrium.[16]

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.[47] For stars below 10 M, the opacity becomes dependent on temperature, resulting in the luminosity varying approximately as the fourth power of the star's mass.[51] For very low-mass stars, molecules in the atmosphere also contribute to the opacity. Below about 0.5 M, 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.[12]

Evolutionary tracks

Evolutionary track 1m
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.[56]

Stars with less than 0.23 M,[57] are predicted to directly become white dwarfs when energy generation by nuclear fusion of hydrogen at their core comes to a halt although no stars are old enough for this to have occurred.

Open cluster HR diagram ages
H-R Diagram for two open clusters: NGC 188 (blue) is older and shows a lower turn off from the main sequence than M67 (yellow). The dots outside the two sequences are mostly foreground and background stars with no relation to the clusters.

In stars more massive than 0.23 M, 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 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.[58][59]

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 supergiants. 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.[60]

When a 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.[61]


  1. ^ By measuring the difference between these values, this eliminates the need to correct the magnitudes for distance. However, see extinction.
  2. ^ The Sun is a typical type G2V star.


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Further reading


  • Kippenhahn, Rudolf, 100 Billion Suns, Basic Books, New York, 1983.


  • Arnett, David (1996). Supernovae and Nucleosynthesis. Princeton: Princeton University Press.
  • Bahcall, John N. (1989). Neutrino Astrophysics. Cambridge: Cambridge University Press.
  • Bahcall, John N.; Pinsonneault, M.H.; Basu, Sarbani (2001). "Solar Models: Current Epoch and Time Dependences, Neutrinos, and Helioseismological Properties". The Astrophysical Journal. 555 (2).
  • Barnes, C. A.; Clayton, D. D.; Schramm, D. N., eds. (1982). Essays in Nuclear Astrophysics. Cambridge: Cambridge University Press.
  • Bowers, Richard L.; Deeming, Terry (1984). Astrophysics I: Stars. Boston: Jones and Bartlett.
  • Carroll, Bradley W. & Ostlie, Dale A. (2007). An Introduction to Modern Astrophysics. San Francisco: Person Education Addison-Wesley. ISBN 978-0-8053-0402-2.
  • Chabrier, Gilles; Baraffe, Isabelle (2000). "Theory of Low-Mass Stars and Substellar Objects". Annual Review of Astronomy and Astrophysics. 38: 337.
  • Chandrasekhar, S. (1967). An Introduction to the study of stellar Structure. New York: Dover.
  • Clayton, Donald D. (1983). Principles of Stellar Evolution and Nucleosynthesis. Chicago: University of Chicago.
  • Cox, J. P.; Giuli, R. T. (1968). Principles of Stellar Structure. New York City: Gordon and Breach.
  • Fowler, William A.; Caughlan, Georgeanne R.; Zimmerman, Barbara A. (1967). "Thermonuclear Reaction Rates, I". Annual Review of Astronomy and Astrophysics. 5: 525.
  • Fowler, William A.; Caughlan, Georgeanne R.; Zimmerman, Barbara A. (1975). "Thermonuclear Reaction Rates, II". Annual Review of Astronomy and Astrophysics. 13: 69.
  • Hansen, Carl J.; Kawaler, Steven D.; Trimble, Virginia (2004). Stellar Interiors: Physical Principles, Structure, and Evolution, Second Edition. New York: Springer-Verlag.
  • Harris, Michael J.; Fowler, William A.; Caughlan, Georgeanne R.; Zimmerman, Barbara A. (1983). "Thermonuclear Reaction Rates, III". Annual Review of Astronomy and Astrophysics. 21: 165.
  • Iben, Icko, Jr (1967). "Stellar Evolution Within and Off the Main Sequence". Annual Review of Astronomy and Astrophysics. 5: 571.
  • Iglesias, Carlos A.; Rogers, Forrest J. (1996). "Updated Opal Opacities". The Astrophysical Journal. 464: 943.
  • Kippenhahn, Rudolf; Weigert, Alfred (1990). Stellar Structure and Evolution. Berlin: Springer-Verlag.
  • Liebert, James; Probst, Ronald G. (1987). "Very Low Mass Stars". Annual Review of Astronomy and Astrophysics. 25: 437.
  • Novotny, Eva (1973). Introduction to Stellar Atmospheres and Interior. New York City: Oxford University Press.
  • Padmanabhan, T. (2002). Theoretical Astrophysics. Cambridge: Cambridge University Press.
  • Prialnik, Dina (2000). An Introduction to the Theory of Stellar Structure and Evolution. Cambridge: Cambridge University Press.
  • Shore, Steven N. (2003). The Tapestry of Modern Astrophysics. Hoboken: John Wiley and Sons.
A-type main-sequence star

An A-type main-sequence star (A V) or A dwarf star is a main-sequence (hydrogen-burning) star of spectral type A and luminosity class V. These stars have spectra which are defined by strong hydrogen Balmer absorption lines. They have masses from 1.4 to 2.1 times the mass of the Sun and surface temperatures between 7600 and 10,000 K.

Bright and nearby examples are Altair (A7 V), Sirius A (A1 V), and Vega (A0 V). A-type stars don't have a convective zone and thus aren't expected to harbor a magnetic dynamo. As a consequence, because they don't have strong stellar winds they lack a means to generate X-ray emission.

B-type main-sequence star

A B-type main-sequence star (B V) is a main-sequence (hydrogen-burning) star of spectral type B and luminosity class V. These stars have from 2 to 16 times the mass of the Sun and surface temperatures between 10,000 and 30,000 K. B-type stars are extremely luminous and blue. Their spectra have neutral helium, which are most prominent at the B2 subclass, and moderate hydrogen lines. Examples include Regulus and Algol A.This class of stars was introduced with the Harvard sequence of stellar spectra and published in the Revised Harvard photometry catalogue. The definition of type B-type stars was the presence of non-ionized helium lines with the absence of singly ionized helium in the blue-violet portion of the spectrum. All of the spectral classes, including the B type, were subdivided with a numerical suffix that indicated the degree to which they approached the next classification. Thus B2 is 1/5 of the way from type B (or B0) to type A.Later, however, more refined spectra showed lines of ionized helium for stars of type B0. Likewise, A0 stars also show weak lines of non-ionized helium. Subsequent catalogues of stellar spectra classified the stars based on the strengths of absorption lines at specific frequencies, or by comparing the strengths of different lines. Thus, in the MK Classification system, the spectral class B0 has the line at wavelength 439 nm being stronger than the line at 420 nm. The Balmer series of hydrogen lines grows stronger through the B class, then peak at type A2. The lines of ionized silicon are used to determine the sub-class of the B-type stars, while magnesium lines are used to distinguish between the temperature classes.Type-B stars don't have a corona and lack a convection zone in their outer atmosphere. They have a higher mass loss rate than smaller stars such as the Sun, and their stellar wind has velocities of about 3,000 km/s. The energy generation in main-sequence B-type stars comes from the CNO cycle of thermonuclear fusion. Because the CNO cycle is very temperature sensitive, the energy generation is heavily concentrated at the center of the star, which results in a convection zone about the core. This results in a steady mixing of the hydrogen fuel with the helium byproduct of the nuclear fusion. Many B-type stars have a rapid rate of rotation, with an equatorial rotation velocity of about 200 km/s.

Dwarf star

A dwarf star is a star of relatively small size and low luminosity. Most main sequence stars are dwarf stars. The term was originally coined in 1906 when 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. They are either much brighter than the Sun, or much fainter. To distinguish these groups, he called them "giant" and "dwarf" stars, the dwarf stars being fainter and the giants being brighter than the Sun. Most stars are currently classified under the Morgan Keenan System using the letters O, B, A, F, G, K, and M, a sequence from the hottest: O type, to the coolest: M type. The scope of the term "dwarf" was later expanded to include the following:

Dwarf star alone generally refers to any main-sequence star, a star of luminosity class V: main-sequence stars (dwarfs). Example: Achernar (B6Vep)Red dwarfs are low-mass main-sequence stars.

Yellow dwarfs are main-sequence (dwarf) stars with masses comparable to that of the Sun.

Orange dwarfs are K-type main-sequence stars.

A blue dwarf is a hypothesized class of very-low-mass stars that increase in temperature as they near the end of their main-sequence lifetime.

A white dwarf is a star composed of electron-degenerate matter, thought to be the final stage in the evolution of stars not massive enough to collapse into a neutron star or black hole—stars less massive than roughly 9 solar masses.

A black dwarf is a white dwarf that has cooled sufficiently such that it no longer emits any visible light.

A brown dwarf is a substellar object not massive enough to ever fuse hydrogen into helium, but still massive enough to fuse deuterium—less than about 0.08 solar masses and more than about 13 Jupiter masses.

F-type main-sequence star

An F-type main-sequence star (F V) is a main-sequence, hydrogen-fusing compact star of spectral type F and luminosity class V. These stars have from 1.0 to 1.4 times the mass of the Sun and surface temperatures between 6,000 and 7,600 K.Tables VII and VIII. This temperature range gives the F-type stars a yellow-white hue. Because a main-sequence star is referred to as a dwarf star, this class of star may also be termed a yellow-white dwarf. Famous examples include Procyon A, Gamma Virginis A and B, and KIC 8462852.

G-type main-sequence star

A G-type main-sequence star (Spectral type: G-V), often (and imprecisely) called a yellow dwarf, or G dwarf star, is a main-sequence star (luminosity class V) of spectral type G. Such a star has about 0.84 to 1.15 solar masses and surface temperature of between 5,300 and 6,000 K., Tables VII, VIII. Like other main-sequence stars, a G-type main-sequence star is converting the element hydrogen to helium in its core by means of nuclear fusion. The Sun, the star to which the Earth is gravitationally bound in the Solar System and the object with the largest apparent magnitude, is an example of a G-type main-sequence star (G2V type). Each second, the Sun fuses approximately 600 million tons of hydrogen to helium, converting about 4 million tons of matter to energy. Besides the Sun, other well-known examples of G-type main-sequence stars include Alpha Centauri A, Tau Ceti, and 51 Pegasi.The term yellow dwarf is a misnomer, because G-type stars actually range in color from white, for more luminous types like the Sun, to only very slightly yellow for the less massive and luminous G-type main-sequence stars. The Sun is in fact white, and its spectrum peaks in blue and green light, but it can often appear yellow, orange or red through Earth's atmosphere due to atmospheric Rayleigh scattering, especially at sunrise and sunset. In addition, although the term "dwarf" is used to contrast yellow main-sequence stars from giant stars, yellow dwarfs like the Sun outshine 90% of the stars in the Milky Way (which are largely much dimmer orange dwarfs, red dwarfs, and white dwarfs, the last being a stellar remnant).

A G-type main-sequence star will fuse hydrogen from a few billion years to approximately 20 billion years, until it is exhausted at the center of the star. For example a star like the Sun will live on the main sequence for 10 billion years. When this happens, the star expands to many times its previous size and becomes a red giant, such as Aldebaran (or Alpha Tauri). Eventually the red giant sheds its outer layers of gas, which become a planetary nebula, while the core rapidly cools and contracts into a compact, dense white dwarf.

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.

Habitability of K-type main-sequence star systems

K-type main-sequence stars may be candidates for supporting extraterrestrial life. These stars are known as "Goldilocks stars" as they emit enough radiation in the non-UV ray spectrum to provide a temperature that allows liquid water to exist on the surface of a planet; they also remain stable in the main phase longer than the Sun, allowing more time for life to form on a planet around a K-type main-sequence star. The planet's habitable zone, ranging from 0.1–0.4 to 0.3–1.3 astronomical units (AU), depending on the size of the star, is often far enough from the star so as not to be tidally locked to the star, and to have a sufficiently low solar flare activity not to be lethal to life. In comparison, red dwarf stars have too much solar activity and quickly tidally lock the planets in their habitable zones, making them less suitable for life. The odds of intelligent life arising may be better on planets around K-type main-sequence stars than around Sun-like stars, given the extra time available for it to evolve. Few planets thus far have been found around K-type main-sequence stars, but those that have are potential candidates for extraterrestrial life.

Herbig Ae/Be star

A Herbig Ae/Be star (HAeBe) is a pre-main-sequence star – a young (<10Myr) star of spectral types A or B. These stars are still embedded in gas-dust envelopes and are sometimes accompanied by circumstellar disks. Hydrogen and calcium emission lines are observed in their spectra. They are 2-8 Solar mass (M☉) objects, still existing in the star formation (gravitational contraction) stage and approaching the main sequence (i.e. they are not burning hydrogen in their center). In the Hertzsprung–Russell diagram these stars are located to the right of the main sequence. They are named after the American astronomer George Herbig, who first distinguished them from other stars in 1960.

The original Herbig criteria were:

Spectral type earlier than F0 (in order to exclude T Tauri stars),

Balmer emission lines in the stellar spectrum (in order to be similar to T Tauri stars),

Projected location within the boundaries of a dark interstellar cloud (in order to select really young stars near their birthplaces),

Illumination of a nearby bright reflection nebula (in order to guarantee physical link with star formation region).There are now several known isolated Herbig Ae/Be stars (i.e. not connected with dark clouds or nebulae). Thus the most reliable criteria now can be:

Spectral type earlier than F0,

Balmer emission lines in the stellar spectrum,

Infrared radiation excess (in comparison with normal stars) due to circumstellar dust (in order to distinguish from classical Be stars, which have infrared excess due to free-free emission).Sometimes Herbig Ae/Be stars show significant brightness variability. They are believed to be due to clumps (protoplanets and planetesimals) in the circumstellar disk. In the lowest brightness stage the radiation from the star becomes bluer and linearly polarized (when the clump obscures direct star light, scattered from disk light relatively increases – it is the same effect as the blue color of our sky).

Analogs of Herbig Ae/Be stars in the smaller mass range (<2 M☉) – F, G, K, M spectral type pre-main-sequence stars – are called T Tauri stars. More massive (>8 M☉) stars in pre-main-sequence stage are not observed, because they evolve very quickly: when they become visible (i.e. disperses surrounding circumstellar gas and dust cloud), the hydrogen in the center is already burning and they are main-sequence objects.

K-type main-sequence star

A K-type main-sequence star (K V), also referred to as a K dwarf, is a main-sequence (hydrogen-burning) star of spectral type K and luminosity class V. These stars are intermediate in size between red M-type main-sequence stars ("red dwarfs") and yellow G-type main-sequence stars. They have masses between 0.5 and 0.8 times the mass of the Sun and surface temperatures between 3,900 and 5,200 K., Tables VII, VIII. Better known examples include Alpha Centauri B (K1 V) and Epsilon Indi.These stars are of particular interest in the search for extraterrestrial life because they are stable on the main sequence for a very long time (20 to 75 billion years, compared to 10 billion for the Sun). Like M-type stars, they tend to have a very small mass, leading to their extremely long lifespan that offers plenty of time for life to develop on orbiting Earth-like, terrestrial planets. In addition, K-type stars emit less ultraviolet radiation (which can damage DNA and thus hamper the emergence of nucleic acid based life) than G-type stars like the Sun. K-type main-sequence stars are also about three to four times as abundant as G-type main-sequence stars, making planet searches easier. While M-type stars are also very abundant, they are more likely to have tidally locked planets in orbit and are more prone to produce solar flares that would more easily strike nearby rocky planets, making it much harder for life to develop. Due to their greater heat, the habitable zones of K-type stars are also much wider than those of M-type stars. For all of these reasons, they may be the most favorable stars to focus on in the search for exoplanets and extraterrestrial life in the universe, especially if they are cooler (K6V–K9V, specifically those of the stellar class K7.5V temperate).

O-type main-sequence star

An O-type main-sequence star (O V) is a main-sequence (core hydrogen-burning) star of spectral type O and luminosity class V. These stars have between 15 and 90 times the mass of the Sun and surface temperatures between 30,000 and 50,000 K. They are between 40,000 and 1,000,000 times as luminous as the Sun.

Pre-main-sequence star

A pre-main-sequence star (also known as a PMS star and PMS object) is a star in the stage when it has not yet reached the main sequence. Earlier in its life, the object is a protostar that grows by acquiring mass from its surrounding envelope of interstellar dust and gas. After the protostar blows away this envelope, it is optically visible, and appears on the stellar birthline in the Hertzsprung-Russell diagram. At this point, the star has acquired nearly all of its mass but has not yet started hydrogen burning (i.e. nuclear fusion of hydrogen). The star then contracts, its internal temperature rising until it begins hydrogen burning on the zero age main sequence. This period of contraction is the pre-main sequence stage. An observed PMS object can either be a T Tauri star, if it has fewer than 2 solar masses (M☉), or else a Herbig Ae/Be star, if it has 2 to 8 M☉. Yet more massive stars have no pre-main-sequence stage because they contract too quickly as protostars. By the time they become visible, the hydrogen in their centers is already fusing and they are main-sequence objects.

The energy source of PMS objects is gravitational contraction, as opposed to hydrogen burning in main-sequence stars. In the Hertzsprung–Russell diagram, pre-main-sequence stars with more than 0.5 M☉ first move vertically downward along Hayashi tracks, then leftward and horizontally along Henyey tracks, until they finally halt at the main sequence. Pre-main-sequence stars with less than 0.5 M☉ contract vertically along the Hayashi track for their entire evolution.

PMS stars can be differentiated empirically from main-sequence stars by using stellar spectra to measure their surface gravity. A PMS object has a larger radius than a main-sequence star with the same stellar mass and thus has a lower surface gravity. Although they are optically visible, PMS objects are rare relative to those on the main sequence, because their contraction lasts for only 1 percent of the time required for hydrogen fusion. During the early portion of the PMS stage, most stars have circumstellar disks, which are the sites of planet formation.


A protostar is a very young star that is still gathering mass from its parent molecular cloud. The protostellar phase is the earliest one in the process of stellar evolution. For a low mass star (i.e. that of the Sun or lower), it lasts about 500,000 years The phase begins when a molecular cloud fragment first collapses under the force of self-gravity and an opaque, pressure supported core forms inside the collapsing fragment. It ends when the infalling gas is depleted, leaving a pre-main-sequence star, which contracts to later become a main-sequence star at the onset of Hydrogen fusion.

Red dwarf

A red dwarf (or M dwarf) is a small and cool star on the main sequence, of M spectral type. Red dwarfs range in mass from about 0.075 to about 0.50 solar mass and have a surface temperature of less than 4,000 K. Sometimes K-type main-sequence stars, with masses between 0.50-0.8 solar mass, are also included.

Red dwarfs are by far the most common type of star in the Milky Way, at least in the neighborhood of the Sun, but because of their low luminosity, individual red dwarfs cannot be easily observed. From Earth, not one is visible to the naked eye. Proxima Centauri, the nearest star to the Sun, is a red dwarf (Type M5, apparent magnitude 11.05), as are fifty of the sixty nearest stars.

According to some estimates, red dwarfs make up three-quarters of the stars in the Milky Way.Stellar models indicate that red dwarfs less than 0.35 M☉ are fully convective. Hence the helium produced by the thermonuclear fusion of hydrogen is constantly remixed throughout the star, avoiding helium buildup at the core, thereby prolonging the period of fusion. Red dwarfs therefore develop very slowly, maintaining a constant luminosity and spectral type for trillions of years, until their fuel is depleted. Because of the comparatively short age of the universe, no red dwarfs exist at advanced stages of evolution.

Red giant

A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses (M☉)) in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius large and the surface temperature around 5,000 K (4,700 °C; 8,500 °F) or lower. The appearance of the red giant is from yellow-orange to red, including the spectral types K and M, but also class S stars and most carbon stars.

The most common red giants are stars on the red-giant branch (RGB) that are still fusing hydrogen into helium in a shell surrounding an inert helium core. Other red giants are the red-clump stars in the cool half of the horizontal branch, fusing helium into carbon in their cores via the triple-alpha process; and the asymptotic-giant-branch (AGB) stars with a helium burning shell outside a degenerate carbon–oxygen core, and a hydrogen burning shell just beyond that.


A star is an 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.

Stellar evolution

Stellar evolution is the process by which a star changes over the course of time. Depending on the mass of the star, its lifetime can range from a few million years for the most massive to trillions of years for the least massive, which is considerably longer than the age of the universe. The table shows the lifetimes of stars as a function of their masses. All stars are born from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, becoming what is known as a main-sequence star.

Nuclear fusion powers a star for most of its life. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star. Later, as the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core. This process causes the star to gradually grow in size, passing through the subgiant stage until it reaches the red giant phase. Stars with at least half the mass of the Sun can also begin to generate energy through the fusion of helium at their core, whereas more-massive stars can fuse heavier elements along a series of concentric shells. Once a star like the Sun has exhausted its nuclear fuel, its core collapses into a dense white dwarf and the outer layers are expelled as a planetary nebula. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into an extremely dense neutron star or black hole. Although the universe is not old enough for any of the smallest red dwarfs to have reached the end of their lives, stellar models suggest they will slowly become brighter and hotter before running out of hydrogen fuel and becoming low-mass white dwarfs.Stellar evolution is not studied by observing the life of a single star, as most stellar changes occur too slowly to be detected, even over many centuries. Instead, astrophysicists come to understand how stars evolve by observing numerous stars at various points in their lifetime, and by simulating stellar structure using computer models.


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.

T Tauri star

T Tauri stars (TTS) are a class of variable stars associated with youth. They are less than about ten million years old. This class is named after the prototype, T Tauri, a young star in the Taurus star-forming region. They are found near molecular clouds and identified by their optical variability and strong chromospheric lines. T Tauri stars are pre-main-sequence stars in the process of contracting to the main sequence along the Hayashi track, a luminosity–temperature relationship obeyed by infant stars of less than 3 solar masses (M☉) in the pre-main-sequence phase of stellar evolution. It ends when a star of 0.5 M☉ develops a radiative zone, or when a larger star commences nuclear fusion on the main sequence.

Luminosity class
Star systems
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