By Joshua N. Winn, Princeton University
The spectrum of a star is like a bar code that reveals its ingredients with each atom producing a whole bunch of lines, with a known pattern. So, how does this work? Read on more to find out.
Comparing a Star and Solar Spectrum
One can look at some stellar spectra in a different way: instead of rainbows, they can plot intensity versus wavelength, across the visible range of the spectrum. If the Sun were a perfect blackbody, the spectrum would be a smooth curve peaking at around half a micron, but a real spectrum has lots of divots: those are the absorption lines. One can clearly see that the star is not completely black at those wavelengths. There is some intensity, but it’s lower by as much as 30% than the surrounding spectrum. There’s a dip at 0.656 microns, from hydrogen, and there’s one at 0.589 microns from sodium, and lots of others.
Let’s compare the solar spectrum with the spectra of other stars. For that, we need to use a logarithmic intensity axis, to capture the wide range of intensities on a single chart. First let’s pick a bluish-white star, like mu Andromedae.
One can tell it’s bluer than the Sun because the intensity rises toward shorter wavelengths, the blue end of the spectrum. And the pattern of absorption lines is different, too. We hardly see the sodium line, and the hydrogen line is deeper. The deep lines at shorter wavelengths are also from hydrogen; they represent jumps from n equals 2 to 4, 5, and 6. Does that mean mu Andromedae has more hydrogen than the Sun, and the Sun has more sodium? That’s what some astronomers used to think, but the truth is more subtle.
A big clue came when the pioneers of astronomical spectroscopy discovered that stellar spectra can be sorted into a single sequence.
Titanium Oxide: The Unexpected Molecule
This pattern can be clearly seen in a chart, in which the x-axis is the position of a star in this sequence, and the y-axis is the strength of various absorption lines, how dark they are in the spectrum. It was observed that at one end, some helium lines were strongest. When we move down the spectrum sequence, the hydrogen lines take over, and then later, the lines of sodium and calcium rise and fall in strength. At the very end, there are lines from a molecule one might not have expected: titanium oxide; it’s closely related to the active ingredient in some sunscreen lotions. So, what does that mean? Are the stars at this end of the sequence made out of sunscreen lotion?
No. It turns out all the stars are made of basically the same ingredients in the same proportions. What’s changing, as we move along the sequence, is the temperature of the star’s outer layers. The thing is that to produce an absorption line, not only do we need photons with the right energy, we also need a supply of atoms with electrons sitting in the lower energy level, ready to absorb those photons. And the supply of such atoms will depend on temperature.
This article comes directly from content in the video series Introduction to Astrophysics. Watch it now, on Wondrium.
Atom Loses an Electron
Consider the hydrogen line at 0.656 microns. It’s often called the H-alpha line, and it’s from electrons hopping between the n equals 2 and 3 energy levels. For that to happen, we need lots of hydrogen atoms with electrons sitting in that second level. And that only happens over a restricted range of temperatures. This is because temperature is a measure of the kinetic energy per atom. If the temperature is too low, the electrons will all be stuck in the lowest-energy state: n equals 1, not 2. If we raise the temperature, the atoms collide at higher speeds, exciting more of their electrons up to n equals 2. But if we make it too hot, the electron will hop even higher, or we get ripped off the atom completely.
When an atom loses an electron, we say it’s been ionized. For hydrogen, that takes 13.6 eV of energy. So, if the kinetic energy of a hydrogen atom approaches 13.6 eV, it’s in danger of getting ionized when it collides with another atom. Putting it all together, the number of electrons in the n equals 2 state will be the product of two opposing factors. The first factor is the fraction of neutral atoms whose electrons are in the n equals 2 state, as opposed to some other energy level. That’s a rising function of temperature. In fact, it’s our friend the Boltzmann factor, e to the −E2 over kT.
The Pattern of Lines Encodes the Temperature
The second factor is the probability that the hydrogen avoids ionization, and that’s a falling function of temperature. The relevant equation to understand this better would be the Saha equation.
The product of those two factors, rising and falling functions of temperature, has a peak somewhere in the middle. For our hydrogen example, it comes out to be about 10,000° Kelvin. For helium, the absorption lines are maximized at a higher temperature, because the relevant electron is more tightly bound to the nucleus. Sodium and calcium have weakly bound outermost electrons that produce lines that are strongest for Sun-like stars, at 5 or 6000°. So, the pattern of lines encodes the temperature.
Cecilia Payne
The first person to crack this code was Cecilia Payne, later Payne-Gaposchkin, in 1925. By interpreting stellar spectra with the newly discovered laws of quantum theory, she could deduce the temperature and the composition of a star based on its spectrum.
She was the first person to figure out what the stars are made of. In general, they’re about 75% hydrogen, by mass, and 24% helium, with the remaining percent or so from heavier elements, especially carbon, nitrogen, and oxygen. Sodium, calcium, and titanium oxide are only present in minute quantities, but they happen to have electron energy levels in the right places to produce strong lines, when the temperature is right.
Common Questions about the Spectrum of a Star
If the Sun were a perfect blackbody, the spectrum would be a smooth curve peaking at around half a micron, but a real spectrum has lots of divots: those are the absorption lines.
To produce an absorption line, not only do we need photons with the right energy, we also need a supply of atoms with electrons sitting in the lower energy level, ready to absorb those photons.
By interpreting stellar spectra with the newly discovered laws of quantum theory, Cecilia Payne could deduce the temperature and the composition of a star based on its spectrum.
