Introductory Astronomy: Stellar Radii

If we have found the luminosity of the star and its temperature, we can find its radius from the Mass - Luminosity - Temperature Relation. This relation tells us that the hotter an object is the more luminous it will be, and the larger an object is the more luminous it will be. It is easy to understand why hotter objects are more luminous. To understand why larger objects are more luminous, imagine a romantic candlelight dinner (with the person of your choice). Candlelight is romantic because it is not very bright. The flame of a candle has a small surface area and therefore a small luminosity. Now imagine that you are eating dinner with a 12 ft. candle flame. Instead of being romantic, it would be a "charring experience." Because the flame is so big, even though it is no hotter than a candle flame, it would have a very large luminosity.

The same thing happens with stars. Stars which are very hot but very small are not as bright as stars which are very large, even if the larger stars are at cooler temperatures. Think about the HR diagram shown below. Hotter objects are plotted on the left of the diagram and cooler on the right. Notice the white dwarfs in the lower left; they are very hot but almost too faint to see. On the other hand, there are very luminous giant stars which have lower temperatures. Based on the Mass - Luminosity - Temperature Relation, which object would you expect to be bigger???