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# 12.11 Temperature and Spectral Class

Graphic representation of Wein's Law. Click here for original source URL.

Representative stellar spectra from a range of spectral classes. Click here for original source URL.

Spectroscopy is vital to understanding the temperatures of stars. We can study stellar spectra and measure which color is the most strongly radiated by a star. We can then use Wien’s law to calculate the temperature. There are other clear patterns in the spectral features of stars — this was the puzzle that Cannon and Payne-Gaposchkin had to solve. Initially they organized stars according to the strength of the hydrogen Balmer lines (with A being the strongest), but after a physical explanation was found for spectral lines, they rearranged the spectral classes according to temperature. The sequence that was finally adopted begins with the hottest stars, class O, which show ionized helium lines in their spectra, and proceeds from hot to cool in the order: O, B, A, F, G, K, and M. (The rearrangement of the letters and the omission of many of the original types make the sequence harder to remember — this is another example of the historical baggage that astronomers carry around.)

Generations of astronomy students have created phrases as an aid to remembering the sequence. Oven-Baked Ants: Fry Gently, Keep Moist is one. Overseas Broadcast: A Flash! Godzilla Kills Mothra is another. Some students prefer Oh Boy! Astronomy Final’s Gonna Kill Me! The somewhat tired classic is Oh Be A Fine Girl/Guy Kiss Me. (You can think of your own, maybe better than any of these!) Most stars can be classified into these groups. For finer discrimination each of the classes are subdivided from 0 to 9 (from hot to cool). The Sun, for example, is classified as a G2 star. Astronomers Morgan and Keenan added to the system a luminosity class using Roman numerals. This is useful because stars of very different luminosities can have the same temperature in their photosphere. These designations are 0 for hyper giants, I for super giants, II for bright giants, III for regular giants, IV for sub-giants, V for main sequence stars, VI for sub-dwarfs, and VII for white dwarfs. Since the Sun is a main sequence star fusing hydrogen into helium, its full designator is G2V.

Here is a summary of the features of the spectral classes. Ionized helium is only seen in the hottest stars, above 30,000K. Hydrogen absorption lines appear most strongly in stars of class A and B. At even lower temperatures, lines of ionized calcium, sodium and iron appear. By class M, at 3000K, the energies are so low that atoms can stick together into molecules, such as titanium oxide (TiO) and magnesium hydride (MgH). Even water molecules have been identified in the spectra of such cool stars, where of course they take the form of steam! The physical properties — in the order spectral class, temperature, mass range in solar masses, luminosity range in solar luminosity, fraction of main sequence stars in this class — of the stellar sequence are listed below:

• O: > 30,000 K, < 16, > 30,000, 0.00003%
• B: 10,000-30,000 K, 2.1-16, 25-30,000, 0.13%
• A: 7500-10,000 K, 1.4-2.1, 5-25, 0.6%
• F: 6000-7500 K, 1-1.4, 1.5-5, 3%
• G: 5200-6000, 0.8-1, 0.6-1.5, 7.5%
• K: 3700-5200 K, 0.45-0.8, 0.1-0.6, 12%
• M: 2400-3700 K, 0.08-0.45, < 0.1, 76%

Note in this list how the vast majority of main sequence stars are cool and dim. How can we understand the appearance of different spectral features in terms of microscopic physics? Each spectral class corresponds to a different temperature of the photosphere gas in the star. As a gas gets hotter, it emits bluer and larger amounts of radiation. At a certain temperature, the electrons get stripped from the atomic nuclei. This process is called ionization and the positively charged nuclei are called ions. Heavier elements require higher temperatures to be ionized. The different spectral features get stronger and weaker as the temperature varies. Physical conditions have to be just right to produce a particular type of electron transition. For example, molecules are only seen in the coolest M stars, because at higher temperatures most molecules are broken into their constituent atoms. Spectral lines of metals are seen in cool G and K stars, but hydrogen lines are not seen because the temperature is not high enough to excite electron transitions in hydrogen atoms. Stars as hot as A stars show strong hydrogen lines, but metal lines are not seen because the heavier atoms are mostly ionized. It takes a high temperature to ionize helium, so helium lines are only seen in O and B stars. Keep in mind that the absence of spectral lines of a given element in a stellar spectrum can mean different things – that the element is not present or that the physical conditions in the photosphere are not right to produce an electron transition.

Recently, infrared techniques have been used to study stars that are so cool that they were not known when the original spectral sequence was created. Stars cooler than M stars are extremely red and emit most of their energy at near infrared wavelengths. Surveys such as 2MASS (2 Micron All Sky Survey) have found substantial numbers of stars that are very dim in optical light. 2MASS was a facility consisting of infrared telescopes in Arizona and Chile that surveyed the sky at wavelengths 2-4 times longer than visible light. An even more sensitive facility is NASA's WISE (Wide-field Infrared Survey Explorer) satellite. Thanks to these inferred surveys, three new spectral classes have been defined. The L class has a typical temperature of 1200-2400 K. These objects represent the transition between the lowest mass star that can sustain fusion and a cooler object called a brown dwarf. The T class has a typical temperature of 500-1200 K. Most of the spectral features in stars this cool are due to molecules. Stars in classes L and T could be more numerous that all other spectral classes combined. Finally, WISE has identified a few dozen cool brown dwarfs with temperatures below 600 K. The coolest has an atmosphere cooler than boiling water! Such stars are transitional objects between stars and planets