Main sequence

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 sequence of stars that appear on a plot of color versus brightness for groups of stars. 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.

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. These factors also determine how much time a star remains on the main sequence, although, in general, the more massive the star the briefer its lifespan. 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 sections, based on the process used to generate energy. Stars below about 1.5 times the mass of the Sun fuse hydrogen atoms together in a series of stages to form helium, a sequence called the proton-proton chain. In the upper main sequence, the nuclear fusion process can 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 the surface, energy is transported upward through the intervening layers until it is finally radiated away at the photosphere. The two mechanisms used to carry the energy are radiation and convection, with the type used depending on the interior conditions. Convection tends to occur in regions with steeper tempereture gradients or higher opacity. When convection occurs in the core region, it acts to stir up the helium ashes, thus maintaining the fuel needed for fusion to occur.

History

In the early part of the twentieth century, information about the types and distances of stars became more readily available. The spectra of stars were show 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.

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.

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.

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 a lower density or higher surface-brightness than dwarfs. The same curve also showed that there were very few faint white stars.

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

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.)

A refined scheme for stellar classification was published in 1943 by W. W. Morgan and P. C. Keenan. The MK classification assigned each star a spectral type—based on the Harvard classification—and a luminosity class. For historical reasons, the spectral types of stars followed, with colors ranging from blue to red, the sequence O, B, A, F, G, K and M. The luminosity class ranged from I to V, in order of decreasing luminosity. Stars of luminosity class V belonged to the main sequence.

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:

$L=4\pi \sigma R^{2}T^{4}$

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 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.) By this means, the position of a star on the HR diagram can be used to estimate its radius and temperature.

Formation

When a protostar is formed from the collapse of a giant molecular cloud of gas and dust, the initial composition is homogeneous throughout, consisting of about 70% hydrogen, 28% helium and trace amounts of other elements, by mass. 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.

Hertzsprung–Russell diagram

Spectral type

O

B

A

F

G

K

M

L

T

Brown dwarfs

White dwarfs

Red dwarfs

Subdwarfs

Main sequence
("dwarfs")

Subgiants

Giants

Red giants

Blue giants

Bright giants

Supergiants

Red supergiant

Hypergiants

absolute
magni-
tude
(M_V)

Once nuclear fusion of hydrogen becomes the dominant energy production process and the excess energy gained from gravitational contraction has been lost, the star lies along a curve on the Hertzsprung-Russell diagram (or HR diagram) called the standard main sequence. The star remains near its initial position on this line 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.

The majority of stars on a typical HR diagram lie along the main sequence curve. This line is so 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—and that is what almost all stars spend most of their "active" life doing. These main-sequence (and therefore "normal") stars are called dwarf stars. This is not because they are unusually small, but instead they have smaller radii and are less luminous than the other main type of stars, the giant stars. White dwarfs are a different kind of star which are smaller than main sequence stars—roughly the size of the Earth. These represent the final evolutionary stage of many main sequence stars.

Astronomers will sometimes refer to the "zero age main sequence", or ZAMS. This is a line calculated by computer models of where a star will be when it begins hydrogen fusion; its brightness and surface temperature typically increase from this point with age. Stars usually enter and leave the main sequence from about when they are born or when they are starting to die, respectively.

Energy generation

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.

Astronomers divide the main sequence into upper and lower parts, based on the method of 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.

At a stellar core temperature of 18 million kelvins, both fusion processes are equally efficient. This is the core temperature of a star with 1.5 times the mass of the Sun. 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. The lower limit for sustained nuclear fusion is about 0.08 solar masses.

Structure

Cross-section of a Sun-like star, showing the different regions.

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.

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. 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.

Intermediate mass, spectral class A stars such as Sirius may transport energy entirely by radiation. 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.

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. Thus, for example, the luminosity of the early Sun was only about 70% of its current value. 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.

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 stars. 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 chemical composition—both because of the initial abundances and the star's evolutionary status, the presence of a close companion, rapid rotation, or a magnetic field can also move a star slightly on the main sequence, to name just a few factors. For example, there are very metal-poor stars—known as subdwarfs—that lie just below the main sequence. These stars are also fusing hydrogen in their core, thus marking the lower edge of the main sequence's fuzziness due to chemical composition.

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.

Our Sun is a main sequence star—it has been one 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 10¹⁰ 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.

On average, main sequence stars are known to follow an empirical mass-luminosity relationship. The luminosity (L) of the star is approximately related to the total mass (M) as the following power law:

${\begin{smallmatrix}L\ \propto \ M^{3.5}\end{smallmatrix}}$

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:

${\begin{smallmatrix}\tau _{ms}\ \sim \ 10^{10}{\text{years}}\cdot \left[{\frac {M}{M_{\bigodot }}}\right]\cdot \left[{\frac {L_{\bigodot }}{L}}\right]\ =\ 10^{10}{\text{years}}\cdot \left[{\frac {M_{\bigodot }}{M}}\right]^{2.5}\end{smallmatrix}}$

where ${\begin{smallmatrix}M_{\bigodot }\end{smallmatrix}}$ is the mass of the Sun, $M$ is the mass of the star and $\tau _{ms}$ is the star's estimated main sequence lifetime in years.

Example of the mass-luminosity relationship for zero-age main sequence stars. 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. 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 has an insulating effect that retains more energy at the core, so the star doesn't 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. Note, however, that a sufficiently high opacity can result in energy transport via convection, which changes the conditions needed to remain in equilibrium.

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. For stars below 10 times the mass of the Sun, the opacity becomes dependent on temperature, resulting in the luminosity varying approximately as the fourth power of the star's mass. 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 stars composition.

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 mechanical effect that restricts how closely matter can be compacted. For intermediate-mass stars of more than 2 solar masses, the core can reach a temperature where it becomes hot enough to burn helium into carbon via the triple alpha process.

This shows the Hertzsprung-Russell diagrams for two open clusters. NGC 188 is older, and shows a lower turn off from the main sequence than that seen in M67.

When a 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.

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. The coloration of the stellar class column gives an approximate representation of the star's photographic color, which is a function of the surface temperature. A popular mnemonic for memorizing the sequence of stellar classes is "Oh Be A Fine Girl/Guy, Kiss Me".

Stellar Class	Radius	Mass	Luminosity	Temperature	Example
	R/R☉	M/M☉	L/L☉	K
O2	16	158	2,000,000	54,000	Sanduleak −71° 51
O5	14	58	800,000	46,000	Sanduleak −66° 41
B0	5.7	16	16,000	29,000	Phi1 Orionis
B5	3.7	5.4	750	15,200	Pi Andromedae A
A0	2.3	2.6	63	9,600	Vega
A5	1.8	1.9	24	8,700	Beta Pictoris
F0	1.5	1.6	9.0	7,200	Gamma Virginis
F5	1.2	1.35	4.0	6,400	Eta Arietis
G0	1.05	1.08	1.45	6,000	Beta Comae Berenices
G2	1.0	1.0	1.0	5,700	Sun
G5	0.98	0.95	0.70	5,500	Alpha Mensae
K0	0.89	0.83	0.36	5,150	70 Ophiuchi A
K5	0.75	0.62	0.18	4,450	61 Cygni A
M0	0.64	0.47	0.075	3,850	Gliese 185
M5	0.36	0.25	0.013	3,200	EZ Aquarii A
M8	0.15	0.10	0.0008	2,500	Van Biesbroeck's star
M9.5	0.10	0.08	0.0001	1,900	LP 647-013

See also

• Hydrogen burning process
• Instability

External links

• Table of Features of the "Life Zones" of Main Sequence Stars
• A java based applet for stellar evolution.