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In the first version of my answer to Are sunspots vertically displaced from the surrounding photospheric plasma?, I naively used Kramer's law to attempt to show an inverse relationship between opacity $\kappa$ and temperature $T$ due to bound-free or free-free absorption in a region with density $\rho$: $$\kappa\propto\rho T^{-7/2}$$ Rob Jeffries pointed out that this might not be accurate in the photosphere, even though it works well deeper inside most stars (though for high-mass stars, Thomson scattering dominates and $\kappa$ is approximately constant). After some more reading, I concluded that this was right. At lower temperatures, interactions with ionized hydrogen mean that $H^-$ is the major contributor to opacity, and it follows a law $$\kappa\propto\rho^{1/2}T^9$$ I believe the transition of dominance happens around $\sim10^4\text{ K}$, meaning that $H^-$ opacity should be the major contribution in the stellar photosphere.

At even lower temperatures, however ($\sim4000\text{ K}$), molecular scattering can be important (see Tennyson et al. (2007)). While this is not necessarily important at all points in the stellar photosphere, I think that it should be important in sunspots, which can have temperatures in this range.

What is/are the major source(s) of opacity in sunspots? Does molecular scattering dominate, or is $H^-$ still important? If both are important, to varying degrees, how can the mean opacity be calculated?

My knowledge of stellar atmospheres and atmospheric models is limited, so I apologize if this comes down to being a basic question.

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  • $\begingroup$ did you see the research papers about different wavelength opacities of sunspots? $\endgroup$ – aliential Nov 11 '16 at 22:23
  • $\begingroup$ @comprehensible I don't know what you're referring to. $\endgroup$ – HDE 226868 Nov 11 '16 at 22:24
  • $\begingroup$ some studies of IR opacity and highly confusing research papers: google.fr/… $\endgroup$ – aliential Nov 11 '16 at 22:34
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    $\begingroup$ @comprehensible Indeed, I searched Google and read some of those very papers. $\endgroup$ – HDE 226868 Nov 12 '16 at 0:33
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In Ignjatovi´c et al. (2014), ion-atom absorption processes are discussed. They suggest that these processes are of equal, if not greater, influence on the observed sunspot opacity as absorption processes in $\mathrm{H}(1s)+\mathrm{H}^+$ and $\mathrm{H}(1s)+\mathrm{X}^+$ collisions (where $\mathrm{X}$ is one of the metal atoms $\mathrm{X} = \mathrm{Na, Ca, Mg, Si, Al}$). The main scattering processes discussed within the paper follow the photo-dissociation of $\mathrm{H}_2^+$ and $\mathrm{HX}^+$ by UV photons in the spectral region ($110$ $\mathrm{nm}$ $\lesssim \lambda \lesssim 230$ $\mathrm{nm}$).

I highly recommend reading through the paper—it is very interesting.

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  • $\begingroup$ Awesome, thanks. I'll read through that when I have a solid chunk of free time. $\endgroup$ – HDE 226868 Nov 12 '16 at 0:33

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