Various questions about atmospheres

[Evil Dr Ganymede]

Sorry, yet another bunch of random generic planet building questions from me... this one's about atmospheres . Stop me if this is all getting too incomprehensible for people, it's just that this is the only discussion board I know that actually has people willing to help on random planet building topics .


1) Greenhouse gas question

I can't for the life of me find any info on the net describing what actually makes a gas a 'greenhouse gas' (though I now know that CO2, CH4, N2O, CFCs, PFCs, and SF6 are all very good ones). I know it's because of their infrared opacity, but I don't know what makes a gas opaque to IR radition - is it just down to being a molecule of several atoms (something to do with molcular bonds vibrating)?

The reason I'm asking is that I want to know whether helium is ag reenhouse gas. I know that hydrogen at high pressures has increased infrared opacity that can allow it to trap heat (see DJ Stevenson's paper on interstellar planets for details) - but what about helium? Or does Helium not trap IR radiation because it's a noble gas and its molecules only consist of single He atoms?

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2) Helium worlds

There seems to be a range of large planets with about 2 earth masses that can hold onto helium but not hydrogen in their atmospheres. Therefore I'd imagine these would have retain a lot of their primordial helium in the air as a buffer gas.

For a large world I designed, I gave it an atmosphere with 2.4 times the surface pressure as Earth, consisting of about 40% He, 50% N2, and 6% O2 and the rest being Ozone and Argon. The helium was retained from formation, the rest of it was pumped out by volcanoes/metabolised by life. The molecular weight (MW) of the atmosphere is about 19, compared to Earth's 29. The structure of the atmosphere is likely to be a bit odd, since all the Helium ought to all rise up and stay at the top of the atmosphere since it's so much lighter than the rest (so I don't think the surface inhabitants would have very squeaky voices!).

Does that sound vaguely possible? Can anyone see any problems with toxicities or pressure effects? This is supposed to be breathable by people without technical assistance (masks, etc).

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3) Atmospheric pressures

I'm wondering if there is a way to figure out what the atmospheric pressure at the surface should be if you know the average molecular weight of the atmosphere... All I know is the P = (rho) * g * h equation (and the one to figure out scale heights - I know the scale height for this planet is about 9 km, if you take the temperature as being the surface average temperature of the planet). I gather that at standard temperature and pressure (STP), a gas with an MW of 19 weighs 19 g, and fills a volume of 22.414 litres. From that I reckon that the density of the atmosphere should be 0.835 kg/m3 (which is pretty much the same as 19/29ths the density of our own atmosphere, so that's promising). The surface gravity for this planet is 14.82 m/s2, the surface pressure is 2.4 atmospheres (240,000 Pa), so the thickness of the atmosphere using the rho.g.h. equation should be... 19.4 km?!

That sounds rather thin to me... especially since the scale height is about 8 or 9 km. I guess one place where I could be going wrong is that I'm not dealing with 'standard temperature and pressure' here, since the surface pressure is 2.4 atms. How do I take that into account - would 1 mole of this atmosphere (with a mass of 19 g) fills a volume of (22.414/2.4=) 9.34 m3? Do I just multiply the 0.835 kg/m3 density by 2.4? If I do that, I get an atmospheric thickness of only 8.08 km, which sounds even more wacky. Isn't Earth's atmosphere supposed to be something like 100 km high?

Ideally I'd like to be able to figure out the pressure from the molecular weight, gravity and some assumed atmosphere height, rather than just use a randomly determined atmospheric pressure and work out the atmospheric height from that. But I guess I'd have to know what a reasonable atmosphere height would be in the first case...

So, for anyone in the know - am I on the right track here?

[granthutchison]

1) Greenhouse gases absorb longer IR wavelengths in a way that dominates the black body radiation emitted by the Earth, but not by the Sun - so sunlight can get to the Earth relatively unobstructed, but when the Earth reradiates the energy at lower wavelengths, the radiation is impeded. IR absorption is, as you say, due to chemical bonds - vibration and rotation modes. Electron transitions in individual atoms occur at higher energies, and absorb photons in the UV, visible and high IR bands, so individual atoms like He won't produce significant greenhouse effects.

2) The only flaw I can see is the idea of He metabolism - it's an exceedingly inert gas that should pass through an organism unchanged. Or are you deploying some hideous flourine-based metabolism?

3) I think the flaw is the whole notion of "atmospheric height", since a real atmosphere doesn't really have a height. Your formula simply calculates the height of a column of uniform density and under uniform gravity which would generate a given pressure - completely different from the real world. If you want to calculate surface pressure from first principles, you need to plug in the mean molecular mass, the gravity of your planet and the total mass of gas sitting above its surface. Then you'd use the principles of hydrostatic equilibrium to find the pressure at the base of the atmosphere. So you could achieve the same atmospheric pressure with many different gas mixes - it would depend on how much you added to the planet.
To convert from STP to some other condition, you can use the gas law relationship PV = RT for a good approximation except at very high density.
Double the pressure, halve the volume. Double the temperature, double the volume.

Grant

[Evil Dr Ganymede]

1) IR absorption is, as you say, due to chemical bonds - vibration and rotation modes. Electron transitions in individual atoms occur at higher energies, and absorb photons in the UV, visible and high IR bands, so individual atoms like He won't produce significant greenhouse effects.

I suspected as much. Thanks! At least I know not to add a greenhouse effect for all that He now

2) The only flaw I can see is the idea of He metabolism - it's an exceedingly inert gas that should pass through an organism unchanged. Or are you deploying some hideous flourine-based metabolism?

Nonono. I said 'the rest was pumped out by volcanoes/metabolised by life'. The Helium is entirely primordial (well, a bit might be from decay of Uranium and Thorium in the crust) - the N2 and the O2 was what was from volcanoes or produced by life. That's why Helium makes such a good buffer gas for an atmosphere, because it isn't used by life at all.

3) I think the flaw is the whole notion of "atmospheric height", since a real atmosphere doesn't really have a height. Your formula simply calculates the height of a column of uniform density and under uniform gravity which would generate a given pressure - completely different from the real world. If you want to calculate surface pressure from first principles, you need to plug in the mean molecular mass, the gravity of your planet and the total mass of gas sitting above its surface. Then you'd use the principles of hydrostatic equilibrium to find the pressure at the base of the atmosphere. So you could achieve the same atmospheric pressure with many different gas mixes - it would depend on how much you added to the planet.

Don't suppose you could give an example of how to work this out, could you? I mean, to know the total mass of gas, don't you have to know the atmospheric thickness? By 'principles of hydrostatic equilibrium' do you mean (rho*g*h)? That's what I was using anyway. The only other possibly relevant equation I know is the scale height equation, and that demands that you already know the base pressure so that doesn't help here.

Thanks for the help!

[granthutchison]

Nonono. I said 'the rest was pumped out by volcanoes/metabolised by life'.

Ah, sorry. I misread "the rest of it ..." as meaning "the rest of the helium ..." Wouldn't have made sense, on re-reading.

Don't suppose you could give an example of how to work this out, could you?

I think we're coming at things from two slightly different directions, but with the same result. The points I was trying to make were: a) there isn't a way to work out the atmospheric pressure based purely on molecular weight - you need to know the total mass of gas, too; b) "atmospheric height" doesn't seem like a useful number to me - it's neither a fundamental variable you can manipulate independently, or a number that says anything particularly informative about the atmosphere that you can't get better from the scale height.

Here's what I was thinking. Suppose you have a planet of the same density as Earth, but eight times the mass. So that's twice the radius, four times the surface area, and twice the surface gravity. Suppose you decide that such a planet might also retain eight times the gas that Earth ended up with. Hydrostatic equilibrium says that the pressure on any given square metre in the atmosphere must equal the total mass of gas above it times the force of gravity on that mass (from that you can integrate your way to a scale height). So eight times the gas spread over four times the area gives twice the areal mass; times twice the gravity gives four times the surface pressure, whatever gases are involved. Base pressure, four atmospheres. Now plug in the mean molecular weight to the scale height formula, and find out how pressure falls with altitude. Now, what pressure do you consider to be "the edge of the atmosphere"? Plug that in once you know the scale height, and you have a real measure of atmospheric height that you can compare across planets.

I don't see any way to find the surface pressure from first principles without passing though the total mass of gas. You might use a figure for "atmospheric height" as a way to calculate it, but the number just seems extraneous to the logic, to me.

Grant

[Evil Dr Ganymede]

I'll start at the end...

Now plug in the mean molecular weight to the scale height formula, and find out how pressure falls with altitude. Now, what pressure do you consider to be "the edge of the atmosphere"? Plug that in once you know the scale height, and you have a real measure of atmospheric height that you can compare across planets.

OK. This bit I follow.

Here's what I was thinking. Suppose you have a planet of the same density as Earth, but eight times the mass. So that's twice the radius, four times the surface area, and twice the surface gravity. Suppose you decide that such a planet might also retain eight times the gas that Earth ended up with. Hydrostatic equilibrium says that the pressure on any given square metre in the atmosphere must equal the total mass of gas above it times the force of gravity on that mass (from that you can integrate your way to a scale height). So eight times the gas spread over four times the area gives twice the areal mass; times twice the gravity gives four times the surface pressure, whatever gases are involved. Base pressure, four atmospheres.

It's this bit I have problems with... . How would one determine how much mass of gas a planet holds onto? I mean, Earth and Venus have practically the same masses, but Venus's atmosphere must surely have a MUCH greater mass than the Earth's. Would that essentially be arbitrary? Right now, the system I'm using (from the Traveller RPG, if anyone's interested) randomly determines the atmospheric pressure - roll dice, check appropriate table. It's vaguely related to size, but not particularly strongly. So would the method you propose here replace that with a table of atmosphere masses instead?

I'm starting to think I may be running in circles here. I was hoping for a way to determine the surface pressure knowing just the surface gravity, the height of the atmosphere (which I'll say would be the distance between the surface and wherever the pressure drops to 1% of the surface value). But of course you can't figure the latter bit out unless you know the scale height, and for that you need to know what the base pressure is...

I think the problem with starting from atmosphere mass is that it seems to be entirely arbitrary. As I said earlier, Venus and Earth have pretty much identical masses and radii, but the Cytherean atmosphere must be a hell of a lot more massive than the Earth's - it's made almost entirely of heavier CO2. and there must be about 90 times as much gas there as on Earth. So while you can determine what the lightest gas a planet can hold onto is, that doesn't tell you anything about how much gas the planet can hold.

I now suspect it might just be a lot easier to start off with getting the atmospheric pressure from a table and work backwards from that, figuring out the mass of the atmosphere from the pressure and molecular mass of the gas. Hrm.

[selden]

Oh Evil One,

It seems to me that a contributing factor would be the initial chemical composition of the planet: the availability of oxygen and carbon would tend to determine how much CO2 is generated, for example. The amount of techtonic activity would be another -- although I really don't know what factors would contribute to that activity.

Have you investigated any of the accretion programs available? Although most of them are based on older theories of planetary formation, they might produce more satisfying results than simple random numbers.

[granthutchison]

I think the problem with starting from atmosphere mass is that it seems to be entirely arbitrary.

I agree. I wasn't really commending it as an approach, just responding to your request for a top-down way of deriving atmospheric pressure. Like you, I don't see a way round making a pretty arbitrary decision about gas mass. Other considerations include the level of outgassing, the level of chemical fixing of atmospheric gas (based on from the presence/absence of tectonics, oceans and life), and whether the planet has effectively lost and rebuilt its atmosphere, as Earth must have done after the Orpheus impact. (I do wonder if any giant terrestrial planet with a relatively small atmospheric pressure might not need a major impact factored into its history in order to get rid of some atmosphere - you might give your large helium world a giant moon or a slow/tilted/retrograde rotation to imply this sort of history.)

I now suspect it might just be a lot easier to start off with getting the atmospheric pressure from a table and work backwards from that, figuring out the mass of the atmosphere from the pressure and molecular mass of the gas.

I think so. In fact, knowing the mass of atmosphere is probably irrelevant for your purposes, if you go that way. You just need to factor in the molecular mass and temperature and cut straight to the scale height.

[Evil Dr Ganymede]

Thanks for the help folks. You've given me much to ponder over, I'm sure I'll be back with yet more odd world building questions