One possible explanation I thought of (which I'm surprised the paper doesn't consider) is whether this is just showing the distribution of wavelength ranges of spectrometers that researchers are using. I tried to find some examples online, but I guess you'd need to be involved in the field to know what exactly to search for.
Me neither, but admittedly mainly because I've never even considered the question.
Some reflection gives me the expectation that there should be fewer high frequency lines due to conservation of energy, and very many low frequency lines.
Then I imagine experimental limitations mean it's very hard to see all the low frequency transitions, but honestly I have no idea how the cross sections of the transitions go with energy so I should stop speculating.
True, but I'm not that convinced the Boltzmann really is the most natural distribution to claim fits. Especially on the blue side it looks like the residuals could be pretty atrocious. Why didn't they try to some other right-skewed distributions? You could try a log-normal for instance, that would have a much simpler interpretation.
I think this crazy thermodynamic idea is really the entire motivation for the paper, and explains why they didn't really spend any effort exploring it.