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Hertzsprung-Russel Diagram (HRD)

We could often see different kinds of stars. How can they be classified?

The Hertzsprung-Russel Diagram (HRD) is a scatter graph that is used to classify stars according to their luminosity, spectral type, colour, temperature and stellar evolutionary stage. It is not a map of locations of stars. A typical HRD looks like this:

The lower left corner is reserved for white dwarf stars, while red supergiants – the most massive stars – occupy the upper right corner. The red giants are a little below supergiants, while main sequence stars are located diagonally across the diagram. For instance, Betelgeuse, the eighth brightest star in the sky and the second brightest star in the constellation Orion is a red supergiant, and could be placed in the upper right corner of HRD. Our sun, on the other hand, is a main sequence star

The spectral class follows an arrangement of O, B, A, F, G, K, M. Stars can further be classified within each class into categories ranging from 0 to 9. In the Morgan-Keenan system, luminosity classes can be expressed by I, II, III, IV, V, which is a general representation of the size of the star. Roughly speaking, O stars are blue, B stars are blue-white, A stars are white, F stars are yellow-white, G stars are yellow, K stars are orange, and M stars are red. For instance, our Sun is a G2V star, meaning that it is a ‘yellow’ two tenths, main sequence star. Interestingly, people have invented phrases such as ‘Oh Be A Find Girl Kiss Me’ or ‘Oh Boy An F Grade Kills Me’ for easy memorization. This scale is located at the upper horizontal axis.

Why are there different types of stars? Before I proceed to explain that, I must first introduce the mass-luminosity relation. The Stefan-Boltzmann law, also known as Stefan’s law, states that total energy radiated per unit surface area of a black body across all wavelengths per unit of time is directly proportional to the fourth power of the black body’s temperature T. In this case, stars are considered as black bodies with a surface area of , while luminosity L refers to energy radiated per unit surface area and time. Thus, from Stefan’s law, the relationship between luminosity, radius of the star, and temperature is   , where σ is Stefan's constant, .

Stellar evolution
Stellar evolution refers to the process in which a star undergoes a sequence of transformations during its lifetime. There are many ways in which a star could undergo stellar evolution and it depends on the mass of the star. The following is mainly about how the Sun (or any solar mass stars) evolves.

A star radiates energy (in the form of heat or light or electromagnetic waves, for instance) constantly over its lifetime. For the majority of the star’s lifetime, the energy comes from the process of nuclear fusion, which takes place within the core of the star.

When no hydrogen is left in the core, nuclear fusion stops, and the helium core of the star starts to collapse. The thin layer of hydrogen surrounding the core will be heated up by the gravitational contraction. Fusion therefore begins in the layer and the star expands.

Although the surface temperature is low, the core temperature is extremely high. Since the size of the star (and thus the radius) increases, according to Stefan’s law, the total luminosity is also high. However, since the total surface area is extremely large, the average luminosity is low and the star appears to be red in colour. The star evolves from the main stage to the red giant stage.

In this stage, helium-burning takes place in the core and carbon will be formed, while hydrogen-burning continues to take place at the surface. At the same time, the shell and the outer layers are gradually expelled as planetary nebula. After this, the core is not hot enough for carbon-burning, such that it shrinks and collapses gradually. It grows fainter as well as hotter and becomes a white dwarf. A white dwarf is extremely dense. It is slightly smaller than the Earth, but it has as much matter as that of the Sun!

Theoretically, when a white dwarf has radiated all its remaining energy, it becomes a black dwarf. However, astronomers believe that a black dwarf does not exist currently because it takes a much longer time for a black dwarf to be formed compared to the age of the observable universe.

What about the stars which have masses that is distinctly different from the Sun? What happens to them? Simply put, a massive star (those larger than _ solar masses) becomes a red supergiant and undergoes heavy elements fusion (which is similar to helium burning, only that heavier elements are fused to synthesize even heavier elements because the temperature and pressure is high enough). Iron formation at the core of the star leads to a supernova explosion, where the outer layers of the star will be thrown off to space and the inner core collapses.

At this point, the mass of the collapsed core needs to be taken into account. If its mass is between 1.4 and 3 solar masses, a neutron star will be formed. It is an extremely compact ball of neutrons squeezed together, supported by neutron degenerate pressure. However, if its mass is more than 3 solar masses, it collapses into a black-hole. No one knows what happens within the event horizon of the black-hole. For more details, please refer to the previous articles in our blog!

This is basically a brief process of how stars of different masses evolve and change through time and it forms the framework of HR diagrams. For more information about stellar classification, stellar evolution, and H-R diagrams, please see