Chapter 11. Stars

11.1 Stars and elements

The problem of how stars are fuelled was solved in the early 20th century. In 1925, British-American astronomer Cecilia Payne-Gaposchkin used spectroscopy (discussed in Book II) to show that the majority of the Sun’s mass is made of hydrogen and helium.[1]

British physicist Robert d’Escourt Atkinson and Dutch-Austrian-German physicist Fritz Houtermans first suggested that a large amount of energy could be released by fusing hydrogen nuclei together in 1929,[2] and a decade later, German-American physicist Hans Bethe[3] and Indian-American physicist Subrahmanyan Chandrasekhar[4] showed that stars are fuelled by nuclear fusion (discussed in Book II).

Before stars existed, there were only four elements in the universe, hydrogen and helium, and some trace amounts of lithium and beryllium. Heavier elements were first created in the first generation of stars, which formed about 200 million years after the big bang, before the formation of galaxies.[5] In 1954, British astronomer Fred Hoyle showed that massive stars can synthesise all of the elements up to iron, after which, they explode in a supernova, which creates even heavier elements.[6]

Planets began to form after the most massive first-generation stars exploded in supernovae, spreading heavy elements across the universe.[7] This would have occurred after a few million years. The Sun is at least a second-generation star, having formed about 4.6 billion years ago.[8]

11.2 The solar nebular disc model

The first explanations for how the Solar System formed appeared in the 1700s. In 1734, Swedish natural philosopher Emanuel Swedenborg suggested that the Sun and the planets could have once originated from the same mass[9] and, in 1755, German philosopher Immanuel Kant suggested that the Solar System had once been a large cloud of gas, a nebula.[10] French mathematician Pierre-Simon Laplace popularised this theory in 1796.[11]

Russian astronomer Viktor Safronov eventually adapted the Laplacian model to form the currently accepted model - the solar nebular disc model (SNDM). Safronov’s work was publicised after it was translated into English in 1972.[12]

The SNDM suggests that stars form in regions known as stellar nurseries. These are massive, dense clouds of gas that are mostly made of molecular hydrogen - H2. Shockwaves can cause the clouds to become unstable, with matter falling together to make dense clumps. The densest region may become a protostar, and eventually, a star.

Shock waves are produced by the arms of spiral galaxies or by supernova explosions. The first stars may have formed because of slight asymmetries in the distribution of matter after the big bang.

Photograph of a protostar.

Figure 11.1
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A protostar in a stellar nursery.

A protostar rotates on its axis, and the rotational energy causes the rest of the cloud to flatten into a disc, known as a protoplanetary disc. The largest clumps in the protoplanetary disc become planets, and the smaller clumps become asteroids or comets.

Trace amounts of other elements, including oxygen, can be mixed with the hydrogen in the protoplanetary disc, and so water can form. On objects close to the protostar, all of the water boils away, and so they are rocky. On objects further away, all of the water freezes, and so they are icy. It is not yet known exactly how gaseous planets form.

11.3 Main sequence stars

As a protostar gets denser, gravitational potential energy is converted to kinetic energy. This causes the hydrogen nuclei to increase in velocity, and, if the protostar is massive enough, they eventually crash into each other with enough force for nuclear fusion to occur. This produces energy, in the form of photons - particles of light.

The force produced by nuclear fusion would blow the star apart if it weren’t held together by the force of gravity. When the two forces balance, the star becomes stable, and is said to be in hydrostatic equilibrium. It’s then known as a main sequence star. The main sequence period of a star’s life lasts as long as it’s fusing hydrogen to helium in its core.

Diagram showing that in a star, there is a balance between the outwards force due to fusion, and the inwards force due to gravity.

Figure 11.2
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In stars, the forces caused by nuclear fusion and gravity balance. This is known as hydrostatic equilibrium.

The proton-proton chain

Diagram of the proton-proton chain.

Figure 11.3
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The proton-proton chain.

In the proton-proton chain, two hydrogen nuclei (protons) collide, producing a deuterium nucleus (made of one proton and one neutron), a neutrino, and a positron. The positron can collide with an electron to produce a gamma ray.

When the deuterium nucleus collides with another hydrogen nucleus, it produces a helium nucleus (made of two protons and one neutron) and a gamma ray. When two helium nuclei collide, they produce two protons and a complete helium nucleus (made of two protons and two neutrons).

This process is extremely slow because the first and last stages occur very rarely.

Protostars with masses less than 8% the mass of the Sun (which is about 80 times the mass of Jupiter), never become stars, and are known as brown dwarfs. In stars about 1.3 times the mass of the Sun or less, hydrogen fusion occurs via the proton-proton chain reaction.

In stars that are more massive, and therefore hotter, the carbon-nitrogen-oxygen (CNO) cycle is more dominant. The CNO cycle produces more energy, but would not be possible in the first generation of stars, since there was no carbon, nitrogen, or oxygen in the early universe.

The CNO cycle

Diagram of the CNO cycle.

Figure 11.4
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The CNO cycle.

In the CNO cycle, a carbon nucleus (made of six protons and six neutrons - the equivalent of three helium nuclei) collides with a hydrogen nucleus (a proton), producing a gamma ray and a nitrogen nucleus (made of seven protons and six neutrons). This decays into a carbon nucleus (made of six protons and seven neutrons), a positron, and a neutrino.

The carbon nucleus collides with a hydrogen nucleus, producing a gamma ray and a nitrogen nucleus (made of seven protons and seven neutrons). This collides with another hydrogen nucleus, producing a gamma ray and an oxygen nucleus (made of eight protons and seven neutrons).

The oxygen nucleus decays into a positron, a neutrino, and a nitrogen nucleus (made of seven protons and eight neutrons). This collides with another hydrogen nucleus, to produce a helium nucleus (made of two protons and two neutrons), and a carbon nucleus. The cycle then begins again.

Despite its complexity, this process is much faster than the proton-proton chain reaction.

11.3.1 The H-R diagram

The term ‘main sequence’ refers to a star’s position on the H-R diagram. The H-R diagram is a scatter graph that plots the luminosity of stars, which is related to their mass, against their temperature, which is related to their colour. Danish astronomer Ejnar Hertzsprung[13] and American astronomer Henry Norris Russell[14] independently created the first H-R diagrams in 1911 and 1913.

The H-R diagram - a plot of colour against luminosity for stars. Colour is directly related to temperature and spectral type.

Figure 11.5
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The H-R diagram plots the luminosity of stars, which is related to their mass, against their temperature, which is related to their colour.

Diagram showing stars can be much smaller and larger than the Sun.

Figure 11.6
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The sizes of the Sun and other stars to scale.

Main sequence stars are divided into seven categories known as O, B, A, F, G, K, and M-type stars. This is known as the Harvard Classification Scheme, which was devised by American astronomer Annie Jump Cannon in the 1920s.[15]

O-type stars are the hottest, bluest, and most massive main sequence stars. They also have the shortest main sequence lifetimes, lasting just a few million years or so. M-type stars are the coolest, reddest, and least massive. They remain on the main sequence for hundreds of billions of years. The Sun, a G-type star, is somewhere in the middle.

The Sun is just over 100 times as wide as the Earth and over 300,000 times as massive, accounting for over 99% of the total mass of the Solar System and fuelling almost all life on Earth. It is about half way through its 10 billion year lifetime.

The final stages in a star’s life occur when it runs out of hydrogen to fuse in its core. Stars up to about 10 times the mass of the Sun will become red giants and then white dwarfs (discussed in Chapter 12). Stars that are more massive than this will become supergiants, and then undergo a supernova, becoming either a neutron star (discussed in Chapter 13) or a black hole (discussed in Chapter 14).

11.4 References

  1. Payne-Gaposchkin, C. H., Stellar atmospheres: a contribution to the observational study of high temperature in the reversing layers of stars, The Observatory, 1925.

  2. Atkinson, R. D. E., Houtermans, F. G., Zeitschrift für Physik 1929, 54, 656–665.

  3. Bethe, H. A., Physical Review 1939, 55, 434–456.

  4. Chandrasekhar, S., The Astrophysical Journal 1939, 90, 1–50.

  5. NASA, Understanding the Evolution of Life in the Universe, NASA Wilkinson Microwave Anisotropy Probe (WMAP).

  6. Hoyle, F., The Astrophysical Journal Supplement Series 1954, 1, 121–146.

  7. NASA, Cooking up the First Stars, NASA.

  8. NASA, Our Solar System: In Depth, NASA Solar System Exploration.

  9. Swedenborg, E., Principia: Philosophical and Mineralogical Works, translated by Clissold, A., Swedenborg Scientific Association, 1988 (1734).

  10. Kant, I., Universal Natural History and Theory of the Heavens, translated by Johnston, I., California State University, 2008 (1755).

  11. Laplace, P. S., The System of the World, R. Phillips, 1809 (1796).

  12. Safronov, V. S., Evolution of the protoplanetary cloud and formation of the earth and the planets, Israel Program for Scientific Translations, 1972.

  13. Hertzsprung, E., 1911, 63, 21.

  14. Russell, H. N., The Observatory 1913, 36, 324–329.

  15. Cannon, A. J., Pickering, E. C., Annals of Harvard College Observatory 1921, 91, 1–290.

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