Hydrogen Lines: The Balmer Thermometer

Often, instead of measuring the entire spectrum of a star, we can estimate its temperature by looking at only certain wavelengths of the spectrum. One of the best examples of this temperature sensitivity comes by comparing the Balmer lines, which are emission lines produced by neutral hydrogen atoms. The strength of these lines in the spectrum of a star is an excellent indication of the temperature of that star. This is why the Balmer lines are often called the Balmer Thermometer.

The Balmer thermometer works because the Balmer lines are produced only by hydrogen atoms whose electrons are in the second energy level. If the surface of a star is as cool as the surface of the Sun (about 5800 K) or cooler, most of the atoms are in the ground state. This means that, although stars like the Sun have a lot of hydrogen in their atmospheres, very little of their hydrogen atoms have electrons in the second energy level (most electrons are in the first energy level, which is called the ground state). Without electrons in the second level, very little Balmer radiation is produced. So, cool stars have very weak Balmer lines.

In very hot stars (like O stars which have surface temperatures of around 20,000 K), almost all of the hydrogen is either ionized (which means it has lost its electrons completely) or has electrons in only very high energy levels. Again, there are very few hydrogen atoms with electrons in the second energy level, so the Balmer lines of these stars are weak.

However, in A stars (surface temperature about 10,000 K), most of the hydrogen atoms have electrons in the second energy level. These stars therefore have very strong hydrogen lines.

The change in the strength of the hydrogen lines with the temperature can be easily seen if we graph the spectra of different classes of stars together and compare their hydrogen lines. Such a graph would like something like the one shown right.

Astronomers can calculate exactly how strong the Balmer lines should be as the surface temperature of the star increases. By looking at the hydrogen lines of any star, we can then compare their strength to the calculated strengths and find the temperature of the star. However, because the Balmer lines are weak in both very hot and very cool stars, we have to look at other spectral lines of other elements to distinguish between the two. The Balmer lines are fairly easy to observe, so they are a good way to determine the temperature of a star, at least as a first guess!