<p>In the first version of my answer to <a href="https://astronomy.stackexchange.com/q/19001/2153">Are sunspots vertically displaced from the surrounding photospheric plasma?</a>, I naively used <a href="https://en.wikipedia.org/wiki/Kramers%27_opacity_law" rel="nofollow noreferrer">Kramer's law</a> 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.</p>

<p>At even lower temperatures, however ($\sim4000\text{ K}$), molecular scattering can be important (see <a href="http://www.ucl.ac.uk/phys/amopp/people/jonathan_tennyson/papers/407.pdf" rel="nofollow noreferrer">Tennyson et al. (2007)</a>). 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.</p>

<p>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?</p>

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

CC BY-SA 3.0
2016-11-11T22:23:11.773Z
did you see the research papers about different wavelength opacities of sunspots?
bandybabboon
CC BY-SA 3.0
2016-11-11T22:24:18.200Z
@comprehensible I don't know what you're referring to.
HDE 226868
CC BY-SA 3.0
2016-11-11T22:34:48.993Z
some studies of IR opacity and highly confusing research papers: https://www.google.fr/search?sourceid=chrome-psyapi2&ion=1&espv=2&ie=UTF-8&q=opacity%20of%20sunspots&oq=opacity%20of%20sunspots&aqs=chrome.0.69i59j69i60l2j69i61.5816j0j4
bandybabboon
CC BY-SA 3.0
2016-11-12T00:33:28.573Z
@comprehensible Indeed, I searched Google and read some of those very papers.
HDE 226868
<the-sun><opacity>
What is the main source of opacity in sunspots?
HDE 226868
# What is the main source of opacity in sunspots?

(Asked by: username_0 on 2016-11-11)

In the first version of my answer to [Are sunspots vertically displaced from the surrounding photospheric plasma?](https://astronomy.stackexchange.com/q/19001/2153), I naively used [Kramer's law](https://en.wikipedia.org/wiki/Kramers%27_opacity_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)](http://www.ucl.ac.uk/phys/amopp/people/jonathan_tennyson/papers/407.pdf)). 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.

**Tags:** the-sun, opacity

> **Comments:**
> **username_1**: did you see the research papers about different wavelength opacities of sunspots?  
> **username_0**: @comprehensible I don't know what you're referring to.  
> **username_1**: some studies of IR opacity and highly confusing research papers: https://www.google.fr/search?sourceid=chrome-psyapi2&ion=1&espv=2&ie=UTF-8&q=opacity%20of%20sunspots&oq=opacity%20of%20sunspots&aqs=chrome.0.69i59j69i60l2j69i61.5816j0j4  
> **username_0**: @comprehensible Indeed, I searched Google and read some of those very papers.  

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## 0 answers

