What is the relationship between the temperature of a star and the spectrum of the star?

The relationship between the temperature of a star and its spectrum is described by a fundamental principle in physics called the Stefan-Boltzmann Law. This law states that the total energy radiated by a star is directly proportional to its surface temperature raised to the fourth power. In other words, as the temperature of a star increases, the total amount of energy it emits also increases drastically.

Now, when it comes to the spectrum of a star, temperature plays a crucial role in determining the types and intensities of the different wavelengths of light (or electromagnetic radiation) that a star emits. Hotter stars have higher energy levels, which cause them to emit more short-wavelength (high-frequency) light, such as ultraviolet or blue light. As the temperature gradually decreases, stars emit more long-wavelength (low-frequency) light, such as red or infrared light.

This relationship between temperature and the spectrum of a star can be observed using spectroscopy. Spectroscopy involves analyzing the light emitted by a star and breaking it down into its constituent wavelengths using a device called a spectroscope. By studying the intensity and distribution of these wavelengths, astronomers can determine the temperature of a star and identify its spectral type (e.g., O, B, A, F, G, K, M) which provides valuable information about its physical properties, composition, and evolutionary stage.