Hi Ken,
Interesting that you worked at Philips Research. Our paths may well have crossed in the early 2000s, when I did three summer internships at PRL. At the time I was torn between a career in astronomy versus joining Philips, but the decision was made for me when PRL closed down. Just in case the world wasn’t already small enough – I’m guessing you worked in Alan Knapp’s group? His wife taught me chemistry at school…
As you say – you can get a long way by assuming local thermal equilibrium. How far is an interestingly controversial question. Without any independent way of measuring the physical conditions and composition of a star, it’s hard to verify exactly how accurate models are.
It’s a very long time since I’ve looked at these kinds of calculation, but I think the jigsaw piece you’re missing is Kirchoff’s Law. From memory, this has the consequence that any plasma that is in equilibrium for the polychromatic case is also in equilibrium with regard to emission and absorption at every monochromatic wavelength of light. The result is that you never need to solve the polychromatic case. You solve the equilibrium equations monochromatically for every wavelength you’re interested in. As I recall, if you’re interested in solving for the equilibrium occupation probabilities of the quantum states, your monochromatic equations give you a bunch of (thousands of) simultaneous equations that you can solve with a big (sparse) matrix inversion operation. You should end up with something resembling a Boltzmann distribution.
The oscillator strengths reflect the fact that transitions are more likely between quantum mechanical states with similar wavefunctions – which give rise to strong lines – versus those with very dissimilar wavefunctions – which give rise to weak “forbidden” lines. But calculating wavefunctions is somewhere between difficult and impossible, and numerical approximation often don’t seem to resemble reality particularly well. Hence the tendency to use empirical lab measurements.
Best wishes,
Dominic