Main sequence

The main sequence is formed in astronomy through the stars, which release their energy radiation by hydrogen burning in the core. The name comes from the fact that the majority of the observed stars are those stars and form a densely populated line in the Hertzsprung -Russell ( HR ) and similar diagrams. A star remains for the longest period of its development on the main sequence. At the beginning of hydrogen burning the star is located on the zero age main sequence (zero age main sequence, ZAMS ) and through in the hydrogen burning to the final age - main-sequence (terminal age main sequence, TAMS ) which he exhaustion of the hydrogen is depleted in the core with increasing completes development speed. The main sequence is the reference for the classification of stars in luminosity classes.


The main sequence is recognizable as such because stars are there for the longest time of their lives ( during the hydrogen burning in the core ) in a stable equilibrium. The energy released in the core of the star fusion energy is continuously transported outwards until it is eventually radiated to the stellar surface, see stellar structure.

The equilibrium in this so-called main sequence phase hardly dependent on the chemical composition, which can be different for the star formation already and changed over the course of the hydrogen burning, very sensitive, however, of the mass of the star. The mass affects both easily observable state variables surface temperature and brightness in the same sense. Thus, the main sequence extends in the Hertzsprung -Russell diagrams and similar diagonal of bright and blue ( hot) top left to faint and red ( cool ) at the bottom right. The surface temperature, however, the brightness varied only over one order of magnitude well, more than seven orders of magnitude. This is partly because the radiation density to the fourth power of the temperature increase, on the other hand, the radius and thus the radiant surface to the luminosity.

Stars move during their main sequence phase, a little to the upper left. While going out of the hydrogen - burning core and the onset of shell burning, the star left the main sequence with increasing speed up to the right and become red giants. However, you can use the main sequence in the later stages, for example on the development path to the white dwarf, traverse, which of course they no longer take account of the characteristics of typical main-sequence stars. The location of a star in the HR diagram relative to the main sequence is specified as a luminosity class, with the main sequence occupies the class V, below are the classes VI and VII, above classes to 0 ( hypergiants ).

The main sequence has at its hot end, with the spectral classes O and B, a greater thickness and there also includes the luminosity classes IV and III. This is due to that the local mass stars have a non- convective outer shell so that the metallicity via the opacity has a greater impact on the transport of energy. In addition, massive stars have a much shorter life, so that a greater part of them is about to transition to the stage of a red giant.

The star at the other end of the main sequence, however, are all youthful, as they consume their hydrogen very slowly. Unlike, the few red dots in the diagram on the right suspect they are much more numerous than the hot star ( just not as much visible) and dominate with their large number, the average of the stellar mass, which at about 0.6 solar masses (M ☉ ) lies. Here, the Sun is on the main sequence slightly to the right below the center.

The subdivision of the main sequence stars generally takes place after the ZAMS mass and depends on various properties of the stellar interior, or stellar evolution. Which division is elected depends on the purpose. The division into a " lower " and " upper " range is based on the processes by which energy is released in stars. Stars below 1.5 M ☉ fuse hydrogen atoms into helium ( proton-proton reaction). Above this mass ( in the upper main sequence ) is dominated by the Bethe- Weizsäcker cycle. Another division into " high ", "medium " and " low " mass based on the energy transport mechanisms within the star: star low-mass (< 0.5 M ☉ ) are vollkonvektiv, Intermediate-mass stars ( 0.5-1.5 M ☉ ) have a radiative radiative transfer zone in the core and a convective envelope, massive stars (> 1.5 M ☉ ) have a convective core and a radiative envelope. Alternatively, however, you can start at a limit of about 8M ☉ between "high" and "medium" masses as develop higher star ZAMS mass for a supernova that such lower mass white dwarfs.


The Danish astronomer Ejnar Hertzsprung discovered in 1906 in Potsdam that the reddest stars - classified as K and M stars - different groups can be divided into two. These stars are either much brighter than the sun or much weaker. To distinguish these groups, he called them "giants" and " dwarfs ". The following year he began the study of star clusters, large groupings of stars that are all about the same distance. He published his first charts that compared the color with the luminosity of these stars. These plots showed a prominent, continuous series of stars, which he called main sequence.

At Princeton University, Henry Norris Russell pursued a similar idea. He examined the relationship between the spectral classification of stars and their absolute magnitudes, ie brightness regardless of the distance. For this purpose he used a selection of stars that have reliable parallaxes and which have already been categorized into Harvard. After aufgezeichntet the spectral types of these stars against their absolute magnitude, he found that dwarf stars followed a distinct relationship. This allowed us to predict the true brightness of a dwarf star with sufficient accuracy.

For the red stars observed by Hertzsprung, followed by the red dwarf star of spectral - luminosity relation of Russell. The giant stars, however, were much brighter than the dwarves and therefore not subject to the same relationship. Russell suggested that the "giant stars must have low density or a high surface brightness, and the opposite is true for the dwarf stars. " The same curve showed that there are very few white weak stars.

In 1933, Bengt Strömgren the concept Hertzsprung -Russell diagram to denote a spectral luminosity diagram. This name reflects the parallel development of this technique of Hertzsprung and Russell beginning of the century.

Have been developed as models of development of stars during the 1930s, was for stars with uniform chemical composition of a relationship between the mass of the star on the one hand and its luminosity and its radius on the other. That is, when the mass and composition of a star is known, the radius and the luminance can be calculated. This relationship became known as the Vogt- Russell theorem, named after Heinrich Vogt and Henry Norris Russell. ( In retrospect, it was discovered that this theorem does not apply to stars with non-uniform composition).

A refined scheme for stellar classification was in 1943 by WW Morgan and P. C. Keenan published. The MK classification assigned each star a spectral type - based on the Harvard classification - and a light class. The spectral types of the sequence followed descending temperatures with colors from blue to red These were historical reasons with O, B, A, F, G, K and M respectively. The luminosity classes ranging from I to V according decreasing luminosity. Stars of luminosity class V belonged to the main sequence.


Main-sequence stars have been extensively studied by stellar models, so that their formation and evolution history are relatively well understood. The position of stars on the main sequence provides information about their physical properties.

The temperature of a star can be approximated by treating him as an ideal radiator, a blackbody. In this case, the luminance L and the radius R depend on the temperature T by the Stefan- Boltzmann law:

Where σ is the Stefan -Boltzmann constant. The temperature and composition of the photosphere of a star determines the energy radiation into different wavelengths. The color index or B - V measures the difference in these energy emissions with the help of filters, which measure the apparent brightness of the star in the blue (B) and green - yellow (V ) light. ( By measuring the difference eliminates the need for correcting the brightness on the basis of distance. ) Thus, the position of the star in the HR diagram used to estimate the radius and the temperature. As the temperature changes the physical properties of the plasma in the photosphere, the temperature also determines the spectral type.


Once a protostar forms from the collapse of a giant molecular cloud of gas and dust in the local interstellar medium, its original composition is homogeneous and consists of 70 % hydrogen, 28 % helium and traces of other elements. During this first collapse of the pre-main sequence star generates energy through gravitational contraction. When a suitable density is reached, the energy production begins in the nucleus by an exothermic process (nuclear fusion ) that converts the hydrogen into helium.

Once the nuclear fusion of hydrogen, the dominant energy production process and the excess energy is gone from the gravitational contraction of the star reached a curve in the Hertzsprung -Russell diagram, the main sequence. Astronomers call this stage sometimes called zero - age main sequence ( "zero age main sequence", ZAMS ). This curve was calculated by computer models (from the date on which a star with the helium production begins ); increase its brightness and its surface temperature is usually with age from that point on.

The star remains close to its initial position in the main series, has been converted into helium to about 10 percent of the originally present in the core hydrogen amount. This phase is the longest in a star life, as all other phases ( the so-called helium burning, the carbon burning and other phases) run much faster. From then on, he begins to develop a more luminous star. ( In the HR diagram moves the developing star to the top and right of the main sequence ). This represents the main sequence stage of the primary hydrogen - burning of a star's life dar.

The majority of the stars of a typical HR diagram lie along the main sequence line. This line is so pronounced because the spectral type and the luminosity depend only on the stellar mass, as long as the core hydrogen is fused - and do almost all stars spend most of their "active" life. The stars of the main sequence are called dwarf stars. This is not because they were unusually small, but because they are smaller in diameter and less luminous vigorously than the other main type of stars that are giants. White dwarfs are a different star style, which are smaller than the stars of the main sequence - about the size of Earth. They represent the end stage of many stars of the main sequence.


All main sequence stars have a core region is generated in the energy through nuclear fusion. The temperature and density of this core are necessary at this level to maintain an energy production to support the rest of the star. A reduction in energy production would cause to contract the overlying mass, and temperature and pressure for nuclear fusion would be increased again. Similarly, an increase in energy production would cause the star expands and the pressure on the core decreases. Thus the star forms a self-regulating system in hydrostatic equilibrium, which is stable throughout the main sequence time.

Astronomers divide the main sequence into an upper and lower range, based on the type of fusion processes in the nucleus. Stars in the upper part of the main sequence have enough mass for the CNO cycle to convert hydrogen into helium. This process uses carbon, nitrogen and oxygen as a catalyst in the fusion process. In the lower part of the main sequence, the energy produced as a result of the proton -proton process is directly fused into helium in the hydrogen.

At a core temperature of about 18 million Kelvin both fusion processes are equally efficient. This is the core temperature of a star with 1.5 solar masses. Therefore, the upper part of the main series of stars above that mass. The upper mass limit for main sequence stars is apparently 120-200 solar masses. The lower limit for a sustained nuclear fusion is about 0.08 solar masses.


By the temperature difference between the core and the surface energy is transported to the outside. The energy is transported either by convection or by radiation. A radiant zone in which the energy is transferred by radiation, convection, and is stable to the plasma is mixed there is little. In the convection zone the energy is, however, distributed by mass transport from plasma by rising material hotter and colder material sinks. Convection is more efficient than mode radiation to transfer power, but only occur under conditions in which a steep temperature gradient occurs.

In massive stars, the rate of energy production by the CNO cycle versus temperature is very sensitive, so that the fusion highly concentrated in the nucleus. Consequently, there is a high temperature gradient in the core, creating a convection for better energy transfer occurs. The mixing of material around the core removes the helium ash from the hydrogen-producing region, allowing more hydrogen can be burned in the star. The outer regions of massive star transport energy by radiation without convection.

Class A - Intermediate-mass stars such as Sirius can transport the energy completely by radiation. Stars of average size and small mass as the Sun have a core region that is stable against convection, and a surrounding convection zone near the surface. This results in a good mixing of the outer layers, but also a less efficient burning of hydrogen in the star. The possible result is the construction of a helium-rich core surrounded by a hydrogen-rich region. In contrast, cold and low-mass stars are fully convective. The produced in the core helium is distributed throughout the star, forming a relatively uniform atmosphere.

Changes in color and brightness

Because not fusionable helium ash accumulates in the nucleus, the reduction of hydrogen per unit mass leads to a gradual reduction in the rate of nuclear fusion within this mass. To compensate to increase the core temperature and the pressure slowly, which causes an increase of the total fusion rate. This results in a steady increase in the luminance and the radius of the star in the course of time. For example, was the luminosity of the young Sun in only about 70 % of its current value, the luminosity increase changes the position of the star in the HR diagram, which means that the main sequence band broadened, because the stars are observed at different stages of their lives. The stars in the main sequence are not on a tight curve in the HR diagram. This is mainly due to observation inaccuracies that affect the distance determination of the star, and on the assumption of unresolved binary stars. However, would also be perfect observations lead to a broadened main sequence, since the mass is not the only parameter of a star.

In addition to variations in chemical composition - because of the initial frequencies and stage of development of the star - can the presence of a nearby companion star, a rapid rotation and a stellar magnetic field cause a star on the main sequence moves, to name just a few factors.

There are, for example, stars with a very low frequency of elements with higher atomic mass than helium - known as metal-poor stars - which are slightly below the main sequence. This sub- dwarfs merge hydrogen in its core and so mark the lower limit of the broadened main sequence due to the chemical composition.

A nearly vertical region of the HR diagram is known as the instability strip and is occupied by pulsating variable stars. These stars change their brightness at regular intervals. This strip intersects the main sequence in the upper range in the region of class A and F stars, with a mass of one to two solar masses. However, main sequence stars in this region experience only small changes in brightness and are therefore difficult to detect.


The lifetime spent by a star on the main sequence is determined by two factors. The total amount of energy that can be generated by nuclear fusion of hydrogen is limited by the amount of available hydrogen which may be processed in the core. For a star in equilibrium, the energy generated in the core must be at least equal to the energy that is emitted from the surface. Since the luminance of the amount of energy emitted per unit time is calculated, the lifetime can be estimated to a first approximation be divided by the total energy produced by the luminosity of the star.

Our Sun is a main sequence star for about 4.6 billion years and will continue for another 6.4 billion years. This results in an entire lifetime on the main sequence of 11 × 109 years. After hydrogen is exhausted in the core, it will expand to a red giant and thereby merge helium atoms to carbon. Because the energy output of helium fusion per unit mass is only one- tenth of the energy output of the hydrogen process, this stage will be only 10 % of the active lifetime of the star. Therefore, on average, about 90 % of the observed stars on the main sequence. On average, the main-sequence stars follow an empirical mass-luminosity law..

The luminosity (L ) of a star depends approximately together with the total mass (M ) as shown in the following equation:

The amount of fuel that is available for fusion is, proportional to the mass of the star. Therefore, the life of a star of the main sequence can be estimated by comparing it with the sun:

Where M and L, the mass and the luminosity of the star is, or is one solar mass, the sun luminosity and is the estimated lifetime of the star on the main sequence.

This is an unexpected result, because massive stars have more fuel and therefore one might assume that they burn longer. Instead, the lightest stars live with a mass of one-tenth of the sun over a trillion years. For the most massive stars, this mass - luminosity relation hardly the estimated life, which is only a few million years fits. A more accurate representation results in a different function for different mass ranges.

The mass - brightness relationship is dependent on how efficiently energy can be transported to the surface of the core. A higher opacity has an insulating effect so that more power remains in the core. So do not spend so much energy the star to remain in hydrostatic equilibrium. In contrast, leads to a lower opacity that energy escapes faster and the star must consume more fuel in order to stay in balance. Note, however, that a sufficiently high opacity means that the energy transport by convection takes place and thereby change the conditions to remain in balance. In a high-mass main sequence star, the opacity is dominated by the scattering of electrons, which remains approximately constant with increasing temperature. Therefore, the luminosity increases only to the cube of the star's mass. For stars below a tenth of a solar mass, the opacity is dependent on the temperature, so that the luminosity behaves almost to the fourth power of the mass of the star. For very low mass stars also carry molecules in the stellar atmosphere in the opacity. Below half a solar mass, the luminosity changed to 2.3. Power of the mass, resulting in a flattening of the graphs in the diagram. However, these improvements are still only an approximation of reality, and the luminosity -mass relationship may also change depending on the neutral composition.

Development paths

Once a main sequence star has burned its hydrogen in the core, is resumed by the loss of energy of the gravitational collapse. The core surrounds the hydrogen reaches the necessary temperature and pressure to fuse. Thus, a hydrogen- burning shell around the helium core is formed. As a result of these changes, the outer shell expands, the temperature drops and the star turns into a red giant. From this point, the star leaves the main sequence and reaches the giant branch. ( The path of a star in the HR diagram is called the path of development ). The helium core of the star is contracted to continue until it is stopped by the so-called degenerate electron pressure - a quantum mechanical effect, which limits the extent to which matter can be compressed.

For stars with more than half of the mass of the sun can reach a core temperature at which it is possible that carbon is generated from helium through the three alpha - process.

Once a cluster is formed at a certain time, the lifetime of the star depends on their individual mass. The most massive stars will leave the main sequence first, followed by the stars with less mass. This is a function of their position in the HR diagram, starting on the left and continuing to the bottom right. The position of the stars of this group, which left the main sequence here, is known as a branch point. Once you know the lifespan of stars at this point of the main sequence, one can estimate the age of this cluster.