Atmospheric composition/segregation across the gradient on an Alderson Disc

Question

The original design for the Alderson Disc has a huge, but very gradual, pressure gradient across the surfaces of the disc. The atmospheric pressure starts with near vacuum somewhere near where the orbit of Jupiter would be and very slowly building pressure as one gets closer to the sun.

What I am interested in is whether this pressure gradient may also represent changes in the primary chemical make up of the atmosphere?

Obviously some of the sorting this implies may not be immediately apparent, it may take large chunks of geological time for the atmosphere of an Alderson Disc to shake down. I'm interested in the long term dynamic equilibrium in this unusual environment.

Assume that the object has a large and powerful enough magnetosphere and gravity well that gas escape velocity is effectively infinite. Further assume that the object has an Earthlike rock cycle, i.e. reactive gases are not being permanently leeched from the atmosphere by the geology.

Answer 1

What I am interested in is whether this pressure gradient may also represent changes in the primary chemical make up of the atmosphere?

Given enough time there will be some stratification, with the less dense materials floating up and the denser ones sinking down, where with "up" I mean "against the positive gravity gradient" and with "down" I mean "with the positive gravity gradient", which translate in "in the outer of the disc" and "in the inner of the disc" respectively.

Answer 2

Air is subject to the tidal stresses on the disk, but wherever desired, these can be compensated for.

First, let's look at why the air might move. Kepler's third law says that the orbital period is proportional to the 1.5th power of the semimajor axis of the orbit (in this case, simply the distance out). But this platter rotates like a galaxy, with an orbital period proportional to the 1st power of the semimajor axis (directly proportional, in other words). In the absence of dark matter, we'll suppose there are tough structural elements provided the needed difference in acceleration.

Let's suppose Earth orbit is perfect: it is 1 AU out, it takes a year to orbit, the atmosphere is 1 atm, the gravity is 1 gee, which is close enough to directly inward at the not-quite-infinite flat plane of the platter for worldbuilding work. The actual gravity of the Sun at our orbit is 333,000 times stronger than Earth's due to the Sun's mass, but 23481 times weaker, squared, because that is how many Earth radii we are from the Sun, giving us just 0.604 milligee of solar gravity. This is exactly compensated by the orbital velocity when we are on the part of the Earth rotating through its orbital position. However, even when we rotate just 6 Mm off that position, the Sun contributes a noticeable difference between spring and neap tides.

At half the Earth's radius out on the disk, the solar gravity is 4x stronger, but the centrifugal acceleration ($\omega^2 r$) is 2x weaker. We could fix that by increasing the orbital speed by the 3/2 power to change omega (Kepler's square-cube law), but the landlord doesn't allow it. So we've got 2.416 - 0.302 = 2.114 milligee of uncompensated solar gravity pulling the air down toward the Sun (inward on the disk). By contrast, if we go out to 2 AU, the solar gravity is 1/4 as strong, and the centrifugal force is twice as strong, giving us 0.151 - 1.208 = -1.057 milligee of uncompensated centrifugal force pushing the air there out toward deep space. While that may not sound like a terrible amount of force, we should bear in mind it adds up over (in the outer limit I just gave) 150 million km, with an average value of 0.529 milligee, which is like 1 gee over a little more than 70,000 km (if gravity didn't decrease over that distance). Compare that to Everest and we see we have a potential problem.

The notion that the air might take a while to move seems excessively optimistic to me. Atmospheric tides create detectable daily changes of pressure on Earth, which is shall we say a very small round piece of platter indeed. Once the air starts moving, on a disk like yours, it would need something to stop it, but instead it has more force pulling it onward, so we're talking about what the Ringworld crew might describe as "an air flow".

A way to fix this is with walls at the edge - Wikipedia describes one 1000 km high at the inner limit, but according to the math I just described, that's not nearly high enough, even assuming the gravity doesn't decrease much with height because it's a bit like an infinite plane, but on the other hand, gravity near the center hole should point outward from the Sun (because there's many planets worth of mass only outward there) creating something of a natural wall anyway. What I don't like about this is that it assumes most of the disk is made up of gas giant biomes due to the truly immense amount of atmosphere being stored there just so Earth has 1 atm.

Another way is to simply make a 70000 km deep hole at the Earth position for the air to dip down into. Problem: the construct is only 6000 km thick. But this isn't that much of a problem, because we make the "hole" by adding material and making gravity (and hence deeper hole). A thickened ridge along the disk pulls the air toward it. But... that increases the gravity. Well, not so fast --- Earth and Saturn both have 1 gee gravity, but Saturn's gravity drops off far more slowly than Earth's. We could build in a big speedbump of heavy material on the platter plane to lure air back to Earth orbit, then have Earth's own landscape pushed outward from it, held up on a thinner (maybe 2000 km) membrane of material, so the gravity feels like 1 gee, yet the bump is providing a pull back to Earth. Making a suspension bridge to hold the whole Earth (plus) thousands of km up in the air is actually much easier than holding this absurd platter thingy together in the first place. The nature of these speedbumps would be such that you could have different atmospheric compositions, dictated by local 'geology', with gaps of low air pressure that reduce the intermixing between them. You could also have a non-equilibrium air pressure that really wouldn't decay over any short interval because the bulge makes it too hard for the air to reach an 'escape velocity' to get to the next speedbump.

Two more thoughts:

• the differences in composition wouldn't always have to be baked into the geology at different radii. You could have a weak speedbump that holds much of the air, but plenty of particles still escape, like a small planet. These are usually hydrogen, so the atmosphere at that region becomes very dry, and presumably wherever the hydrogen ends up becomes more wet, or conceivably even a reducing atmosphere with formaldehyde, methane, even ammonia at high levels.

• I was thinking the disk might be easier around a small dim star (red dwarf). The semi-major axis of the most distant TRAPPIST-1 planet is only 9 million km, and the innermost a bit under two. Unfortunately (as suggested by the fast orbit of those planets) the trappistar gravity will be 25 times stronger, so the atmosphere situation isn't that different. The star is much closer to the landscape, but now 1/8 as wide (just 13 times the radius of the Earth), meaning its edges rear up only two or three times higher over the landscape than in the sun-sized disk. But at least the delivery costs for construction materials should be less! :)

Answer 3

"Frame Challenge": Let's fix the disc.

The standard design is pretty absurd - rounding up what from this compendium sounds like about 3000 solar masses worth of planet-building material, in order to make a flat disk that can't hold together without some kind of active stabilization. Before we try to put an atmosphere on it, let's replace this with something that seems somewhat more plausible.

• Cosmic strings are hypothetical topological defects in space. Typically they are proposed to have considerable gravity, to bend light passing by them so that there appears to be less than 360 degrees in a circle around them, to be associated with domain walls or higher dimensions. There's a ton of stuff on Arxiv and it is virtually all above my pay grade.

• For our purposes, we'll suppose the Disc formed naturally from a tiny cosmic string that remained within our observable universe. It forms a closed loop in space. Possibly it may be rotating - I don't know if you could tell - but the material that is drawn toward it should be rotating to some extent because everything in space does. Because the string is massive, I'm going to go out on a limb here and suggest it takes a lot of energy to bend it, which is why it doesn't fold itself up into a black hole. Maybe if you ram a star into it, it bends enough to make gravitational waves.

• The bulk of the ordinary matter associated with this object dates to its collision with a white dwarf. The abrupt change in topology when the star struck the defect in space destabilized it enough to spray a substantial cloud of hydrogen, carbon, nitrogen and hydrogen throughout the area, which subsequently condensed at the Disc. The Disc itself would tend to draw this matter into a cylinder with a moderate tidal flattening in the direction of the center.

• The Disc is flattened for one of two reasons. The traditional reason is that somebody put (and actively maintains the position of) a star at the center of the Disc, which pulls the material inward to a greater degree than it would otherwise go....

• I'd prefer something weirder, so I'm going to suggest instead that the looped cosmic string actually has 720 degrees around it - meaning it connects two distinct, roughly-Euclidean spacetime regions together, like a Star Gate. For some reason space is contracting at the plane of intersection, creating an effective gravity toward the entire plane of the Disc. If this gravity is stronger than the string's gravity, the object can have a habitable 1-gee surface similar to that of a 3000-solar-mass construct, but be made out of a much smaller amount of material. The gravity of the string and any spin of the Disc still tends to keep a hole in the middle.

• Instead of having a sun in the middle, I think about this effectively very massive object and picture it having an accretion disc around it generating light. Especially if there is still debris from the white dwarf in the area. This would be twilight in the plane of the Disc, except -- I'm going to suppose a major collision, such as with a returning chunk of the white dwarf, knocked the Disc off its original axis. Like many star systems, it is now misaligned with its original rotational plane, and light is visible from both sides of the Disc at all times. Since this isn't actually a black hole I'm going to hope it doesn't have to go too far into UV.

Once we have these preliminaries out of the way, we can handwave the atmosphere. We've given the Disc a chance to settle down so that it is roughly flat - the air is at equal pressure everywhere. We blow away enough atmosphere with mishaps that people can breathe. Now we just need to look at ongoing geological cycles. These cycles are not coming from a deep core and mantle like Earth's, but a far thinner layer of material exposed to continuing disruptions from space; nonetheless, the atmosphere is directly replenished by warm, active underlying materials.

Some parts of the Disc are mostly CHON from dispersed white dwarf material. Different parts of the white dwarf would have more hydrogen or more oxygen, leading to reducing versus oxidizing regions along the ring as they accreted. Some super-Earths might have gotten in it at some point though, giving it a more diverse mix of minerals and some other exotic volatiles like sulfur compounds. At this point you have fairly broad latitude to suppose that different regions of the Disc will be producing their own atmosphere, which slowly migrates into other areas, which should allow any particular biomes required by the plot.