We determine the temperatures of stars from an analysis of their light (spectra). Spectral analysis is an important topic and so we will spend a fair amount of time on it. We will consider:

• how stellar spectra are formed
• how stellar spectra are used to infer the surface temperatures of stars
• how stellar spectra are used to give the chemical compositions of the atmospheres of stars

Both the continuous and absorption line spectra of stars can be used to infer the surface temperatures of stars. To understand continuous vs. line spectra, consider the spectrum of the Sun made using a prism:

If a more efficient tool is used to break up the Solar radiation into its constituent colors, we would, for example, see a continuous plus line spectrum:

The above plot shows how much energy is carried by photons of particular wavelengths (spectrum). The peak of the plot shows at which wavelength (color) the star appears the brightest.

Continuous Spectrum and Temperature

Blackbody Radiation

The continous part (the smooth part) of the spectrum of most stars resembles the spectrum of idealized radiators known as blackbodies. Blackbodies are idealized objects that are perfect absorbers of energy [and hence are perfectly black]. The emission spectrum of a blackbody radiator is easily calculated and is referred to as blackbody spectrum or a Planck curve. The spectra are exceedingly simple; emission from a blackbody is characterized by only its temperature T .^* Its shape, size, what it is made of, and so on, has no bearing on how the blackbody radiates!

The happy circumstance is that stars radiate in a manner that can be roughly described as blackbody.

We use this fact below and later.

(1) A simple measure of the temperature of a star is based on its color because we know from studies on studies in Terrestrial laboraties and theoretical musings, that the spectra of blackbody radiators of different temperatures look like;


The color of a star is determined by its temperature. Cooler stars produce relatively larger amounts of red light compared to blue light than do hotter stars.

(2) In addition to simply using the color of a star to infer its temperature, we can also use the information contained in Wien's law,

W(max) = 3x10⁷ Angstroms / T(K),

to infer temperatures of stars. Note -- 1 Angstrom = 10^-8 centimeters. Wien's law suggests that the wavelength at which is blackody radiator is the brightest is determined by its temperature.

Below, we show two representations of the Solar spectrum. The Sun is indeed fairly well-represented by a blackbody of temperature ~ 5,800 Kelvin:

Wien's law, W = 3x10⁷ A / T(K), tells you that because the strongest emission from the Sun falls at a wavelength of 5,200 A (see the above plot), that

T(K) = 3x10⁷ A / W = 3x10⁷ / 5.2x10³ K = (3/5.2) x 10^(7-3) K = 5.8x10³ K

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^*Another property of a blackbody radiator that we will use later is contained in the Stefan-Boltzmann law. The Stefan-Blotzmann law describes how much power a blackbody radiates per unit area of its surface. For a blackbody of temperature T, the power radiated per unit area is

P = constant x T⁴