Visual characteristics of planetary gas torus

In the universe I'm currently developing, humans stumble upon a magical alien construction: a small star surrounded by a gaseous torus of mostly molecular nitrogen & oxygen and atomic hydrogen & helium. The torus is 4 AU in radius and has a mean, constant density of around $$5.8*10^{-7} kg/m^3$$ and pressure $$3.2*10^{-2} Pa$$. The "small star" (not a natural star, but a luminous alien object about 10x dimmer than the sun) sits at the vacant center of the torus. The hole of the torus points perpendicular to the orbital plane of the system so that many planets orbit inside the torus.

For the benefit of the Q, let's ignore: how the gas torus maintains its structure, orbital velocity, temperature/pressure, etc.; and how the planets continue to orbit unperturbed despite drag & close proximity. The explanation is all just maaagic magic ma agic ma a.

The central hole of the torus has a radius of around 20 million kilometers and a new planetary orbit can be found every few hundred thousand kilometers outward from there. The orbits become elliptical and misaligned from the ecliptic out past the 4 AU mark, where the torus abruptly ends. My question is how will the presence of this torus affect the visibility or appearance of the celestial environment? The gas density is comparable to the Karman line here on Earth, but we've got a lot less than 100 km of it, let alone millions. Would our human explorers see the planets inside, or would they be looking at a great big white haze? If the humans set down and camped out on one of the planets, say, on one orbiting at the halfway 2 AU mark, would their view of the planets (assume a high, icy albedo) near or far be obstructed by all the intervening gases?

• Larry Niven: Integral Trees, Smoke ring. Novels set in a gaseous torus. I would suggest you try to find these books and read them. Since the world that the books are set in are mostly or completely what you are trying to build. Larry Niven tends towards harder science so it would be at least a good starting point for your own design. I don't recall how clear the ring was as described in the books, other then there was cloud and general haze, some layers more opaque then others. The inhabitants could not see the stars from inside, the star lit it up the gasses too much to allow the stars to be Mar 31 at 0:07

This is a really interesting question. If we take the parameters given, we can calculate the optical depth of the torus. Assuming an opacity of $$\kappa=0.001\;\text{cm}^2\text{g}^{-1}$$, I found an optical depth of $$\tau\approx3.47$$ for an observer at the outer edge looking inward. It's actually significantly lower than I expected, but it's still large (well in the optically thick regime). A source at the center would have only roughly 3.1% of its light reach the outer edge, making it very difficult to see anything at all.

That's assuming we have an observer in the orbital plane. It might be possible to observe some of the planets with larger orbits from within the plane, and all might be visible outside the plane. If the torus has a thickness of, say, 1 AU, then an observer could look down on it and see an optical depth of $$\tau\approx0.434$$ for a source in the orbital plane (i.e. a planet!). From this vantage point, 65% of the light would be transmitted.

The gist here is that most of the inner planets would be enshrouded if you looked through the disk, but if it's thin enough (and, frankly, even reasonably thick), you could see them without too much difficult if you exit the plane of the system.

• Thank you for your answer! It looks like finding out how hundreds of millions of kilometers of gas affect traversing light is only a couple of simple calculations away. Of course it's the astronomers that figured that one out lol
– BMF
Apr 1 at 13:59
• Hello HDE, me again. Your answer helps me find how much of an object's light an observer outside would see, but I wonder, how can I predict how bright the gas torus itself would be due to diffusion and scattering? I wonder if it might resemble something like the zodiacal light but on steroids.
– BMF
Jun 22 at 2:28
• @BMF That's a good question! I honestly don't know. Jun 23 at 13:52
• Ah, I see. I can't figure it out myself, but a possible approximation might be to find the percentage of light from the source that isn't reaching the observer from the direction of the source and spread that light over the visible area of the gas torus, finding its visible magnitude. (Assuming the gas doesn't reradiate the light at other wavelengths.) That would change as your angle above the ecliptic changes, though.
– BMF
Jun 23 at 14:36