Secuencia principal

A continuous band of stars that appears on plots of stellar color versus brightness

Para el caballo de carreras, consulte Secuencia principal (caballo) .

Un diagrama de Hertzsprung-Russell traza la luminosidad (o magnitud absoluta ) de una estrella contra su índice de color (representado como B − V). La secuencia principal es visible como una banda diagonal prominente que va desde la parte superior izquierda a la inferior derecha. Este gráfico muestra 22.000 estrellas del Catálogo Hipparcos junto con 1.000 estrellas de baja luminosidad (enanas rojas y blancas) del Catálogo Gliese de Estrellas Cercanas .

Formación de estrellas
Clases de objetos
Medio interestelar Nube molecular Glóbulo de Bok Nebulosa oscura Objeto estelar joven Protoestrella Estrella previa a la secuencia principal Estrella T Tauri Herbig Ae / Be estrella Objeto Herbig – Haro
Conceptos teóricos
Acreción Función de masa inicial Inestabilidad de los jeans Mecanismo de Kelvin-Helmholtz Hipótesis nebular Migración planetaria
v t mi

En astronomía , la secuencia principal es una banda continua y distintiva de estrellas que aparece en gráficos de color estelar versus brillo . Estas gráficas de magnitud de color se conocen como diagramas de Hertzsprung-Russell en honor a sus co-desarrolladores, Ejnar Hertzsprung y Henry Norris Russell . Las estrellas de esta banda se conocen como estrellas de secuencia principal o estrellas enanas . Estas son las estrellas verdaderas más numerosas del universo e incluyen el Sol de la Tierra .

Después de la condensación y la ignición de una estrella, genera energía térmica en su densa región central a través de la fusión nuclear de hidrógeno en helio . Durante esta etapa de la vida de la estrella, se ubica en la secuencia principal en una posición determinada principalmente por su masa, pero también basada en su composición química y edad. Los núcleos de las estrellas de la secuencia principal están en equilibrio hidrostático , donde la presión térmica exterior del núcleo caliente se equilibra con la presión interior del colapso gravitacional.de las capas superpuestas. La fuerte dependencia de la tasa de generación de energía de la temperatura y la presión ayuda a mantener este equilibrio. La energía generada en el núcleo llega a la superficie y se irradia en la fotosfera . La energía es transportada por radiación o convección , y esta última ocurre en regiones con gradientes de temperatura más pronunciados, mayor opacidad o ambas.

La secuencia principal a veces se divide en partes superior e inferior, según el proceso dominante que utiliza una estrella para generar energía. Las estrellas por debajo de aproximadamente 1,5 veces la masa del Sol (1,5  M _☉ ) fusionan principalmente átomos de hidrógeno en una serie de etapas para formar helio, una secuencia llamada cadena protón-protón . Por encima de esta masa, en la secuencia principal superior, el proceso de fusión nuclear utiliza principalmente átomos de carbono , nitrógeno y oxígeno como intermediarios en el ciclo de CNO.que produce helio a partir de átomos de hidrógeno. Las estrellas de la secuencia principal con más de dos masas solares se someten a convección en sus regiones centrales, lo que actúa para agitar el helio recién creado y mantener la proporción de combustible necesaria para que se produzca la fusión. Por debajo de esta masa, las estrellas tienen núcleos que son completamente radiativos con zonas convectivas cerca de la superficie. Con la masa estelar decreciente, la proporción de la estrella que forma una envoltura convectiva aumenta constantemente. Las estrellas de la secuencia principal por debajo de 0,4  M _☉ experimentan convección en toda su masa. Cuando no se produce la convección del núcleo, se desarrolla un núcleo rico en helio rodeado por una capa exterior de hidrógeno.

En general, cuanto más masiva es una estrella, más corta es su vida útil en la secuencia principal. Una vez que se ha consumido el combustible de hidrógeno en el núcleo, la estrella evoluciona alejándose de la secuencia principal en el diagrama HR, hacia una supergigante , gigante roja o directamente a una enana blanca .

Historia

Estrellas de secuencia principal de tipo O calientes y brillantes en regiones de formación estelar. Todas estas son regiones de formación estelar que contienen muchas estrellas jóvenes calientes, incluidas varias estrellas brillantes de tipo espectral O. ^[1]

A principios del siglo XX, la información sobre los tipos y distancias de las estrellas se volvió más disponible. Se demostró que los espectros de las estrellas tienen características distintivas que les permiten ser categorizados. Annie Jump Cannon y Edward C. Pickering en el Observatorio de la Universidad de Harvard desarrollaron un método de categorización que se conoció como el Esquema de Clasificación de Harvard , publicado en los Anales de Harvard en 1901. ^[2]

En Potsdam, en 1906, el astrónomo danés Ejnar Hertzsprung notó que las estrellas más rojas, clasificadas como K y M en el esquema de Harvard, podían dividirse en dos grupos distintos. Estas estrellas son mucho más brillantes que el Sol o mucho más tenues. Para distinguir estos grupos, los llamó estrellas "gigantes" y "enanas". Al año siguiente comenzó a estudiar cúmulos estelares ; grandes agrupaciones de estrellas que se colocan aproximadamente a la misma distancia. Publicó las primeras gráficas de color versus luminosidad para estas estrellas. Estos gráficos mostraban una secuencia de estrellas prominente y continua, a la que llamó Secuencia Principal. ^[3]

En la Universidad de Princeton , Henry Norris Russell estaba siguiendo un curso de investigación similar. Estaba estudiando la relación entre la clasificación espectral de las estrellas y su brillo real corregido por la distancia, su magnitud absoluta . Para ello utilizó un conjunto de estrellas que tenían paralaje fiables y muchas de las cuales habían sido categorizadas en Harvard. Cuando trazó los tipos espectrales de estas estrellas frente a su magnitud absoluta, descubrió que las estrellas enanas seguían una relación distinta. Esto permitió predecir el brillo real de una estrella enana con una precisión razonable. ^[4]

De las estrellas rojas observadas por Hertzsprung, las estrellas enanas también siguieron la relación espectro-luminosidad descubierta por Russell. Sin embargo, las estrellas gigantes son mucho más brillantes que las enanas y, por lo tanto, no siguen la misma relación. Russell propuso que "las estrellas gigantes deben tener baja densidad o gran brillo superficial, y lo contrario es cierto para las estrellas enanas". La misma curva también mostró que había muy pocas estrellas blancas tenues. ^[4]

En 1933, Bengt Strömgren introdujo el término diagrama de Hertzsprung-Russell para denotar un diagrama de clases de luminosidad-espectral. ^[5] Este nombre refleja el desarrollo paralelo de esta técnica tanto por Hertzsprung como por Russell a principios de siglo. ^[3]

A medida que se desarrollaron modelos evolutivos de estrellas durante la década de 1930, se demostró que, para las estrellas de composición química uniforme, existe una relación entre la masa de una estrella y su luminosidad y radio. Es decir, para una masa y composición determinadas, existe una solución única para determinar el radio y la luminosidad de la estrella. Esto se conoció como el teorema de Vogt-Russell ; nombrado en honor a Heinrich Vogt y Henry Norris Russell. Según este teorema, cuando se conoce la composición química de una estrella y su posición en la secuencia principal, también se conoce la masa y el radio de la estrella. (Sin embargo, posteriormente se descubrió que el teorema se descompone un poco para las estrellas de composición no uniforme). ^[6]

En 1943, William Wilson Morgan y Philip Childs Keenan publicaron un esquema refinado para la clasificación estelar . ^[7] La clasificación MK asignó a cada estrella un tipo espectral, basado en la clasificación de Harvard, y una clase de luminosidad. La clasificación de Harvard se desarrolló asignando una letra diferente a cada estrella en función de la fuerza de la línea espectral del hidrógeno, antes de que se conociera la relación entre los espectros y la temperatura. Cuando se ordenaron por temperatura y cuando se eliminaron las clases duplicadas, los tipos espectrales de estrellas siguieron, en orden de temperatura decreciente con colores que iban del azul al rojo, la secuencia O, B, A, F, G, K y M. (Un popular mnemotécnicopara memorizar esta secuencia de clases estelares es "Oh, sé una buena chica / chico, bésame".) La clase de luminosidad varió de I a V, en orden de luminosidad decreciente. Las estrellas de clase de luminosidad V pertenecían a la secuencia principal. ^[8]

En abril de 2018, los astrónomos informaron de la detección de la estrella "ordinaria" (es decir, secuencia principal) más distante , llamada Ícaro (formalmente, MACS J1149 Lensed Star 1 ), a 9 mil millones de años luz de distancia de la Tierra . ^{[9] [10]}

Formación y evolución

Artículos principales: Formación estelar , Protoestrella , Estrella previa a la secuencia principal y Evolución estelar § Secuencia principal

Cuando se forma una protoestrella a partir del colapso de una nube molecular gigante de gas y polvo en el medio interestelar local , la composición inicial es homogénea en su totalidad, y consta de aproximadamente 70% de hidrógeno, 28% de helio y trazas de otros elementos, en masa. ^[11] La masa inicial de la estrella depende de las condiciones locales dentro de la nube. (La distribución de masa de las estrellas recién formadas se describe empíricamente mediante la función de masa inicial ). ^[12] Durante el colapso inicial, esta estrella anterior a la secuencia principal generates energy through gravitational contraction. Once sufficiently dense, stars begin converting hydrogen into helium and giving off energy through an exothermic nuclear fusion process.^[8]

Hertzsprung–Russell diagram

Spectral type

Brown dwarfs

White dwarfs

Red dwarfs

Subdwarfs

Main sequence("dwarfs")

Subgiants

Giants

Bright giants

Supergiants

Hypergiants

absolutemagni-tude(MV)

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]

Properties

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 difference in size and brightness between so-called "dwarf" stars that are on the main sequence and so-called "giant" stars that are not, becomes smaller. For the hottest stars the difference is not directly observable and for these stars the terms "dwarf" and "giant" refer to differences in spectral lines which indicate whether a star is on or off the main sequence. 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 left over after a star has shed its outer layers, and 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]

Parameters

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 T_eff by the Stefan–Boltzmann law:

${\displaystyle L=4\pi \sigma R^{2}T_{eff}^{4}}$

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 T_eff. 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 T_I, 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 T_I¹⁵, where T_I 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 R ∝ M^0.78.^[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]

StellarClass	Radius	Mass	Luminosity	Temp.	Examples[26]
	R/R☉	M/M☉	L/L☉	K
O2	012	100	800,000	50,000	BI 253
O6	09.80	35	180,000	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	0.18	0.15	000,000.0027	03,120	EZ Aquarii A
M8	0.11	0.08	000,000.0004	2,650	Van Biesbroeck's star[28]
L1	0.09	0.07	000,000.00017	2,200	2MASS J0523−1403

Energy generation

See also: Stellar nucleosynthesis

Logarithm of the relative energy output (ε) of proton–proton (PP), CNO and Triple-α fusion processes at different temperatures (T). 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 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]

Structure

Main article: Stellar 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.

Lifetime

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 thermal 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:

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

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]

${\displaystyle {\begin{smallmatrix}\tau _{\rm {MS}}\ \approx \ 10^{10}{\text{years}}\cdot \left[{\frac {M}{M_{\bigodot }}}\right]\cdot \left[{\frac {L_{\bigodot }}{L}}\right]\ =\ 10^{10}{\text{years}}\cdot \left[{\frac {M}{M_{\bigodot }}}\right]^{-2.5}\end{smallmatrix}}}$

where M and L are the mass and luminosity of the star, respectively, ${\displaystyle {\begin{smallmatrix}M_{\bigodot }\end{smallmatrix}}}$ is a solar mass, ${\displaystyle {\begin{smallmatrix}L_{\bigodot }\end{smallmatrix}}}$ is the solar luminosity and ${\displaystyle \tau _{\rm {MS}}}$ 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] 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

Main article: Stellar evolution

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]

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.

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.

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]

Notes

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

References

1. "The Brightest Stars Don't Live Alone". ESO Press Release. Retrieved 27 July 2012.
2. Longair, Malcolm S. (2006). The Cosmic Century: A History of Astrophysics and Cosmology. Cambridge University Press. pp. 25–26. ISBN 978-0-521-47436-8.
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Further reading

General

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

Technical

• 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): 990–1012. arXiv:astro-ph/0010346. Bibcode:2001ApJ...555..990B. doi:10.1086/321493. S2CID 13798091.
• 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: 337–377. arXiv:astro-ph/0006383. Bibcode:2000ARA&A..38..337C. doi:10.1146/annurev.astro.38.1.337. S2CID 59325115.
• 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. Bibcode:1967ARA&A...5..525F. doi:10.1146/annurev.aa.05.090167.002521.
• Fowler, William A.; Caughlan, Georgeanne R.; Zimmerman, Barbara A. (1975). "Thermonuclear Reaction Rates, II". Annual Review of Astronomy and Astrophysics. 13: 69. Bibcode:1975ARA&A..13...69F. doi:10.1146/annurev.aa.13.090175.000441.
• 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. Bibcode:1983ARA&A..21..165H. doi:10.1146/annurev.aa.21.090183.001121.
• Iben, Icko, Jr (1967). "Stellar Evolution Within and Off the Main Sequence". Annual Review of Astronomy and Astrophysics. 5: 571. Bibcode:1967ARA&A...5..571I. doi:10.1146/annurev.aa.05.090167.003035.
• Iglesias, Carlos A.; Rogers, Forrest J. (1996). "Updated Opal Opacities". The Astrophysical Journal. 464: 943. Bibcode:1996ApJ...464..943I. doi:10.1086/177381.
• 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. Bibcode:1987ARA&A..25..473L. doi:10.1146/annurev.aa.25.090187.002353.
• 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.