Stellar Spectra and Quantum Mechanics

Much of Payne-Gaposchkin's work with stars involved studying their rainbows, which scientists call spectra. Astronomers obtained a star's spectrum by placing 1-3 prisms at the focus of a telescope, spreading the star light out. The resulting strip of light was focused onto a glass plate coated with photosensitive chemicals, which reacted by turning darker as each photon of starlight hit the plate. See the below spectra for two example images. These had to be analyzed using magnification; click on the image for an enlarged view. 

Early astronomers used black and white photography to look at star spectra, even though color photography was available at the time, because they could tell the wavelength, or color, of the light simply by measuring its location on the plate relative to a known line.

1-prism vs. 3-prism spectrum dispersion 

Continuous Visible Spectrum 

A glowing, hot emission source, like a star, emits a continuous spectrum that depends on its temperature. The colorful image shown above is a continuous (or "blackbody") visible spectrum. Observed astronomical objects' spectra are much more complicated because a star's radiation interacts with individual atoms and ions in its path before reaching a telescope on Earth. The star's blackbody radiation is especially affected by passing through the cooler gases in its atmosphere, or corona. It can also interact with gas or dust farther from the star - in a nebula, for instance. Each atom or ion can absorb and emit light only at specific wavelengths, or energies, because of the quantum mechanical properties of electrons.

If an atom, ion, or molecule is at the lowest possible energy level, it and its electrons are said to be in the ground state. Any electrons that have higher energy than the ground state are excited. If an excited electron emits a photon of light and moves to a lower energy level, it decays. If an electron is hit by a photon with exactly the energy needed to get to a higher level, it absorbs the energy and moves to the higher level. The amounts of energy for an electron to successfully transition between different levels are specific to the element, ion, or molecule the electron is part of and are the same whether emitting a photon or absorbing one. Because the particular pattern of spectral lines generated by a specific element, ion, or molecule is constant, it can be used as a "fingerprint" to recognize its presence. 

As an example, the visible spectrum of light from hydrogen (with one electron), displays four wavelengths, 410 nanometers (nm), 434 nm, 486 nm, and 656 nm. (See diagrams of hydrogen absorption and emission spectra below in Figures 5c and 5d, as well as the labeled red lines indicating lines in the photonegatives of actual spectra in Figure 5a above.) The dark lines in the spectra below are called absorption lines because the star's blackbody light at that wavelength has been absorbed, or partially absorbed, by an electron of hydrogen at a specific temperature (or ionization level). Emission lines occur when an energized electron falls to a lower level. They can happen together, as when high energy starlight excites an electron in a hydrogen atom in a dust cloud (creating an absorption line), and then it decays (creating an emission line). In stars, the hydrogen lines are usually seen in absorption.

Hydrogen spectral lines were very important to stellar classification because of the abundance of the element in the universe. These lines became especially interesting to astronomers in 1885, when Johann Balmer discovered an empirical equation to predict their exact wavelengths. As the first spectral lines associated with this series are located in the visible part of the electromagnetic spectrum, these lines are historically referred to as "H-alpha" (H-α), "H-beta" (H-β), "H-gamma" (H-γ) and so on, where H is the element hydrogen.

Visible Hydrogen Absorption Lines

Visible Emission Lines of Hydrogen

There are several prominent "near-ultraviolet" Balmer lines with wavelengths shorter than 400 nm which are not visible to the human eye. The total number of Balmer lines is an infinite continuum as it approaches a limit of 364.6 nm in the ultraviolet. Early astronomers often studied the spectral region between H-β and H-ε, since the photographic chemicals used were sensitive in this range.

Payne-Gaposchkin finished her thesis in 1925. Both she and the scientific community were using predictions from quantum theory (fully developed that year) and data from experiments on Earth, to identify these spectral "fingerprints" to understand what was being seen out in the universe. Her thesis used the magnitude of particular spectral lines from metal ions, combined with ionization theory equations, to determine not only how much of which elements were present in the stars, but also stars' temperatures. 

Classifying Star Spectra

As the number of electrons becomes larger, an element's "fingerprint" becomes much more complex because the number of possible spectral lines becomes much greater. Since there are many elements in stars, their spectra are very complex! Figure 5e shows a Modern spectrum of the sun taken by a high-resolution Echelle spectrograph. This rainbow is so long and detailed that they have "wrapped" it like text to fit in a square for this image.

Full Spectrum of the Sun 

Annie Jump Cannon developed a stellar classification system based on what lines were present in a star's spectrum. Figure 5f below is a chart of example spectra for the main categories of Cannon's stellar classification system, which used the letters OBAFGKM (famously learned with the mnemonic, "Oh, Be A Fine Girl/Guy/Goober/Goon, Kiss Me"). In this image, H-α is on the right and H-ε on the left. For example, notice that the green absorption line of H-γ only shows in O6.5 and M5, but is missing or extremely faint in the other classes.

Example Spectra for Cannon's Star Classification System

One fascinating implication of Payne-Gaposchkin's thesis on stellar makeups was the confirmation of Annie Cannon's stellar classiciation system. With the additional information of chemical composition, astronomers were able to show that class reflected star temperatures. Figure 6 (with the pink box) and the above spectra show how certain line patterns (evidence of specific elements) is an important feature for discriminating between the classes. 

CPG Stellar Temp vs. AJC Classification

Our sun is a G-type star. To show how complex the actual solar spectrum is, a detail (from 425-430 nm) of a partial solar spectrum has been overlaid (Fig. 8 within the below Fig. 7). The wide lines indicate the simplest level of classification, with these smaller lines giving nuance to the classification scheme.

Simplified Star Classification Spectra w/Partial Solar Spectrum

Continue on to read about Payne-Gaposchkin deloyed this scheme in her work process to determined the power output and constitution of the stars!

Image Sources

5. Payne, C. (1925). Stellar atmospheres; A contribution to the observational study of high temperature in the reversing layers of stars. (Doctoral dissertation), p. 188. Retrieved from SAO/NASA Astrophysics Data System. (1925PhDT.........1P)

6. Adapted from Figure 10 from Stellar atmospheres; A contribution to the observational study of high temperature in the reversing layers of stars. (Doctoral dissertation) by C. Payne, 1925, p. 196. Retrieved from SAO/NASA Astrophysics Data System. (1925PhDT.........1P)

7. Mikhailov, E. (2013). Spectrum chart [Image]. Retrieved from http://physics.wm.edu/~evmik/classes/2013_spring_Modern_Astrophysics_476/

8. Bernadelli, A. (2011). Energy levels and absorption spectra [PowerPoint Slides]. Retrieved from https://www.slideshare.net/asober/energy-levels-and-absorption-spectra