I guess my point is that I wouldn't necessarily expect there to be any clear trend to the set of all spectral lines. The Boltzmann fit looks fairly iffy to me as well -- it seems like they just picked an arbitrary distribution (which had a cute pseudo-explanation) that was unimodal with a log tail.
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.
> I wouldn't necessarily expect there to be any clear trend to the set of all spectral lines
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.
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.