Kirchhoff's Laws and Spectral Analysis

Gustav Kirchhoff (1824-1887) formulated empirical rules for spectroscopic analysis. We can place these in a physical context:

1. A hot dense gas or solid object produces a continuous spectrum with no dark spectral lines.

It radiates as a black body of temperature T, according to the Planck function.

2. A hot diffuse gas produces bright emission lines.

Emission lines occur when electrons move from a higher orbit to a lower orbit in the atoms, emitting a photon of exactly the right wavelength that corresponds to the energy difference in the orbits.
Example: A star-forming gas cloud in a distant galaxy (courtesy Stacy McGaugh)

3. A cool diffuse gas in front of a continuous source produces dark lines in the continuous spectrum.

Light of a wavelength that corresponds to energy differences in atomic orbits will be absorbed, boosting the electrons to a higher orbit.

The properties of spectral lines

True: I see lines of element X in a star. Therefore it must have X in it.
False: I don't see X lines in a star. Therefore it has no X in it.

Things which affect spectral lines:

Chemical abundance

If a star doesn't have element X, you won't see lines from element X.

Temperature

A star's temperature determines the number of electrons which normally live in each of the energy levels. If no electrons live in a given level, you won't see lines from that level.

The population of energy levels depends on temperature, given by the Boltzmann distribution:

Also, if an atom is ionized, the spectral lines change (or are non-existant). The fractional ionization is given by the Saha equation:

Example: Balmer absorption lines

Balmer lines come from n=2 (first excited) level of hydrogen. If very few electrons live in that level, there will be little Balmer absorption even if there is lots of hydrogen. Therefore, cool stars have weak hydrogen lines.

On the other hand, very hot stars also have weak hydrogen lines, since they are hot enough to completely ionize hydrogen.

Similar things happen for all atoms and molecules, depending on their ionization and excitation energies.

So we see different lines in stars of different temperatures, even if they have the same chemical composition.

Atomic Structure

Some lines are favored on quantum mechanical grounds. Think about an electron in an excited state. It wants to fall back down to the ground state. How does it do this?

It could go any of these paths. The one it is most likely to go depends on the details of the structure of the atom and the ionization state, and the spectral lines you would get are different in each case.

Density

If an electron "hangs up" in an excited state, the atom may collide with another atom and collisionally de-excite so that the energy is lost through the motion of atoms, not through the emission of a spectral line.