How far can you see in solar plasma at just under 1 solar radius?

Question

I was trying to compose an answer to this question here, about touching the surface of a star, and I was going to mention that the popular depiction of the sun's surface as 'basically lava' (as depicted in Sunshine, for example) is wrong.

The usual definition of a star's radius is where the optical depth is 2/3. At this radius, the density of the sun is about 1/10th of air at sea level and can hardly be described as solid or liquid.

I wanted to get a sense of what this diffuse plasma would look like if you were in it and somehow impervious to the heat and radiation. Would it appear as a thin, glowing fog, through which you could still discern distant objects? Or would it appear as opaque as, say, a bonfire?

Rephrasing in a little more technical way, What is the extinction coefficient of solar plasma at ~1 Solar radius in the visible spectrum? What is the path length at which all light is effectively attenuated?

(Since it varies by wavelength, I mean specifically the region of the visible spectrum where the plasma is at its most transparent).

Answer 1

If you have a look at the top-left panel of Fig.11 in these lecture notes by Rob Rutten, you will see that the continuum opacity at optical wavelengths at the photosphere is about $10^{-6.7}$ cm$^{-1}$.

The inverse of this is the optical depth. You can see stuff through about 2-3 optical depths, so your "horizon", looking horizontally in the solar atmosphere is about 100 km.

However, the same plot shows that, because of the temperature and density variations with height, the photosphere becomes an order of magnitude more or less opaque at only 50km below or above the "photosphere" respectively.

What this means is that you can see about 100 km horizontally, but less than this (guesstimate 30km) looking downwards and more than this (guesstimate infinity - that is how the photosphere is defined!) looking upwards.

These numbers would all be revised downwards at the wavelengths of prominent absorption lines.

If you could look all around you, you would see a very asymmetric brightness/colour distribution. Overhead would be dimmer and cooler (redder); underneath, much brighter and hotter (more or less the same colour we see the photosphere).

Answer 2

I suspect part of the problem here is that cosmological optical depth is defined vertically (so far as I can discern from the wikipedia article), while you seem to be asking for the extinction coefficient for a horizontal path at the specified star-radius. So you'll need to find out what the $\alpha(z)$ is at that radius, play some games with integrated radiance due to the plasma in the horizontal line of site to estimate the noise factor, and compare that with the putative radiance from the distant object you wish to see.