In the previous post, we saw that intensity of radiation emitted by a star is proportional to its temperature to the fourth power. Let’s now use that to find a formula for a star’s luminosity. In order to calculate luminosity, we multiply intensity by the surface area of the object. Since, we assume that all stars are perfect spheres, we can use the formula for sphere surface area.
Around 1900, Ejnar Hertzsprung and Henry Norris Russell independently derived a method for visually classifying stars. They plotted luminosity on the y-axis, and temperature on the x-axis. A very beautiful and clear pattern emerged. It must be noted that often the y-axis represents luminosity divided by the luminosity of our sun. This diagram is particularly useful in showing how a star ages and determining star types.
White dwarfs
White dwarfs are small old stars that were not massive enough to become a neutron star or a black hole. Their cores are made of electron-degenerate matter. Our Sun will become a white dwarf in about 10 billion years. These stars are very dense: they can have a mass of the Sun but the volume of the Earth. They are very hot, but have a low luminosity due to their small radius. Once formed, they continue to cool for a tremendously long time. Perhaps, until the heat death of the universe. They are in the bottom left corner of the HR diagram.
Red giants
Red giants have low temperatures, as seen on the x-axis (be careful as it goes from high to low). Their huge luminosities are due to their enormous radii. They are a step in the life cycle of stars, when a star has ran out of hydrogen in its core. They begin fusing hydrogen from the shell surrounding the core. The Sun will become a red giant in about 5 billion years, eating Mercury Venus and destroying Earth’s habitable zone. They are in the top right corner of the HR diagram.
Blue giants
These form analogously to red giants. When the hydrogen fuel in the core is exhausted, the star begins to expand. However, more massive stars become blue giants for a period of time before turning into red giants. Despite their huge temperatures, these stars have similar luminosities to red giants. This is because they are only about 5-10 times the radius of the Sun, while red giants can be up to 100 times larger.
Supergiants
These stars have tremendous diameters of over 300 times the size of the Sun. They are also very rare, as they constitute only about 1% of all stars. They have very short lifetimes of approximately a few million years, which is tiny on the cosmic scale. Some well known examples are Betelgeuse and UY Scuti, the largest known star in the universe. They form from huge stars exhausting the fuel in their cores.
References
Bowen-Jones, M., & Homer, D. (2014). Ib Physics. Oxford University Press.
Cain, F. (2015, December 25). Blue giant star. Universe Today. https://www.universetoday.com/24587/blue-giant-star/.
Hertzsprung-Russell diagram: Cosmos. Hertzsprung-Russell Diagram | COSMOS. (n.d.). https://astronomy.swin.edu.au/cosmos/h/hertzsprung-russell+diagram.
Redd, N. T. (2018, July 26). What is the Biggest Star? Space.com. https://www.space.com/41290-biggest-star.html.
Redd, N. T. (2018, March 28). Red giant stars: Facts, definition & the future of the sun. Space.com. https://www.space.com/22471-red-giant-stars.html#:~:text=In%20approximately%205%20billion%20years,and%20Venus%2C%20and%20reach%20Earth.