The Hertzsprung-Russell (HR) diagram
1. General shape: main sequence, dwarfs and giants.
- In common with all stars, our Sun was formed from a giant cloud of gas.
- Figure 1 shows part of the Orion nebula, in which stars are formed.
- The nebula is made mostly of cold hydrogen gas. Over millions of years, gravity acts to coalesce the gas. This collapse warms the gas.
Figure 1 Part of Orion nebula- As the atoms fall towards each other, potential energy is transferred into kinetic energy, which is then transferred to heat energy as the atoms crash into each other.
- Because the mass of all the hydrogen atoms is so great, and the distances fallen by the atoms so enormous, the temperature in the middle of such a ball of gas rises to about 15000000 K. At this temperature, thermonuclear fusion takes place and hydrogen nuclei (protons) fuse together into helium nuclei, and a star is born.
- The energy released in the fusion process is emitted as electromagnetic radiation from the star’s surface.
Figure 2 A star is a battleground in which competing forces act - A star is a battleground in which competing forces act, as shown in Figure 2. The pull of gravity acting inwards is balanced by the outward pressure from the hot core.
- The pressure at the centre of a star can be billions of times larger than atmospheric pressure on the Earth.
- When a cloud of gas collapses, the stars that are formed may be of considerably different masses (Figure 3).
- Stars range in mass from about 100 times the Sun’s mass, down to about 01 of the Sun’s mass.
- Stars much above 100 solar masses are unstable, and stars below about 0.1 solar masses are too small to start the thermonuclear fusion of hydrogen nuclei.
- Most stars are main sequence stars, which means that the star is fueled by the fusion of hydrogen.
- The more massive stars are much more luminous than the smaller stars. This is because the gravitational forces that tend to collapse a star increase with mass.
Figure 3 a cloud of gas collapses, the stars that are formed may be of considerably different masses - So, for the star to be in equilibrium, it means that the outward pressure from the core must be larger.
- Therefore, the nuclear reactions must run at a higher rate generating more power, which leads to the star having a higher luminosity.
- Stars vary in luminosity from being about [math]10^6[/math] times more luminous than the Sun (absolute magnitude about -10) to being about [math] 10^4[/math] times less luminous than the Sun (absolute magnitude about +15).
- The variation in the luminosity of stars is displayed in the Hertzsprung-Russell diagram, as shown in Figure 4.
- The main sequence of stars runs in a diagonal line from the top left- hand corner.
- At the top left of the diagram are the bright O class stars with absolute magnitudes of -10 and surface temperatures of 50000 K; at the bottom right of the diagram, are dull M class stars with absolute magnitudes of +15 and surface temperatures of about 2500 K.
- Our Sun is a G class star with a surface temperature of about 5780 K and an absolute magnitude of +4.6.
- The Sun is a significant star in that it is more luminous than 95% of all stars.
- The best-known stars are the brightest ones, but there are billions of very small, dull stars that cannot be seen by the unaided eye.
Figure 4 The Hertzsprung-Russell (HR) diagram
2. The lifetimes of stars:
- The bright O class stars are very rare because they only live for a short time. Our Sun will exist for a total of about [math]10^{10}[/math] years.
- It is about 4.6 billion years old, so the Sun is about halfway through its life.
- A star that is about 100 times more massive than the Sun is about [math] 10^6[/math] times more luminous. So, although it has more nuclear fuel, it uses it very quickly.
- So, the brightest stars have lifetimes of the order of a few million years, whereas the dullest stars can live for [math] 10^{12} [/math] years or more (which is about 100 times longer than the Universe has been in existence).
3. The Sun’s evolutionary path:
- The red line ABCD in figure 4 shows the evolutionary path of a star, similar to the Sun, on the Hertzsprung-Russell diagram.
- As described earlier, the star collapses from a cold cloud of gas and reaches its position on the main sequence, where it remains for about 10 billion years, path A to B. After that time the star will have exhausted its supply of hydrogen, which will have been turned into helium.
- At that point the process of nuclear fusion stops, the pressure inside the core of the star reduces, and the gravitational forces begin to collapse the star.
- The collapse of the star causes the core to heat up even further, to temperatures in the region of 100 million kelvin (10K).
- At that temperature the helium nuclei have enough energy to overcome the repulsive electrostatic forces between them, and to come into contact.
- Once the helium nuclei get into contact, some of them will fuse into more massive nuclei such as beryllium, carbon and oxygen.
- This further nuclear reaction reignites the star.
- However, the massive temperature causes the star to expand into a red giant, which could be 100 times the current diameter of the Sun.
- Although the star’s surface temperature will be lower, at about 3000 K, the giant’s extreme surface area causes it to be much more luminous.
- The star moves along the path B to C into the giant branch of the stars.
- Further nuclear reactions can occur in stars much larger than the Sun, which takes them into the supergiant branch on the Hertzsprung-Russell diagram.
- However, the Sun is not massive enough to move into the supergiant branch.
- There comes a time when the supply of helium runs out in the star. At this point in a star of the Sun’s mass, nuclear fusion stops and the star collapses into a dwarf.
- Calculations suggest that white dwarfs of the Sun’s mass have about the same volume as the Earth.
- So, a white dwarf is extremely dense. The surface temperature of a white dwarf can be 10000K, which is much hotter than the Sun’s surface.
- However, because the dwarf star has such a small surface area, it has a low luminosity. The dwarf star is powered by the gravitational potential energy released as it slowly contracts.
- After a very long time, this energy will run out and the star will become a black dwarf. It is thought that no black dwarfs exist yet because the process takes a longer time than the current age of the Universe.