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Toxicity means that the certain concentration of a substance is going to have destructive effect on some cells of your body, and there is nothing short of wearing environmental suit which might possibly mitigate that. Narc effect could be mitigated to some extent, but prolonged exposure to such "mitigation" is probably not very healthy. Studies show that human body cannot adapt to inert gas narcosis beyond its initial biological tolerance limits - not in the short term, at least. Walking on a world with excessive narc factor would be like being perpetually drunk.

karov, chemical composition is very important for both human survivability and greenhouse effect. It is not the sheer pressure of density of the atmosphere that would matter for the latter, but partial pressures of the relevant greenhouse gases - most potent ones (among those that would be breathable for humans to greater or lesser extent) being SF₆, CF₄, H₂O and various hydrocarbons - see GWP values in the table I've posted here for reference (GWP index for H₂O has never been calculated, but it's greenhouse effect is estimated to be, at least, by several orders of magnitude higher than that of CH₄). You get very little greenhouse effect (by several orders of magnitude less then CO₂) from diatomic gases (i.e. O₂, N₂, H₂) and no greenhouse effect to speak of from monoatomic noble gases (i.e. He, Ne, Ar, Kr, Xe). So, if you're looking for greenhouse effect, you would be better of pumping some potent greenhouse gases into your atmosphere rather then increasing sheer pressure of diatomic gases (of which you cannot have too much without bumping narc factor or ppO2 beyond limits that are safe for humans anyway).

However, when speculating about various greenhouse gases, you should also keep in mind their narc factors, toxicity and flammability (the latter two may be estimated from NFPA 704 index values in "H" and "F" columns of my table). CO₂ is a very bad choice since it only has very moderate greenhouse effect, but is extremely narcotic and mildly toxic. CH₄ has better greenhouse effect and is non-toxic - but it is still relatively narcotic and highly flammable (which means, you wouldn't want to mix it with oxygen at any great ratios). N₂O (nitrous oxide, aka "laughing gas") is actually quite a bit better then CO₂ - despite its notorious reputation as potent drug (which it certainly is, but much less so than our good old carbon dioxide) it is much more effective as GHG. CF₄ is an even more potent GHG and has narc factor almost as low as N₂ - but it is mildly toxic, so you wouldn't want too much of that stuff in the air you breath either. SF₆ is about as narcotic as CH₄, but it is completely inert and non-toxic - and it has greenhouse potency by several orders of magnitude greater then anything else that may be safely inhaled by humans in more then trace amounts. Downside - SF₆ is quite a bit harder to come by then CH₄, CO₂ or N₂O.

EDIT: According to my simulations, the most effective greenhouse atmosphere that would be still safely breathable for humans would consist of 64% SF₆ and 36% O₂ pumped under 0.5 bar pressure. You might also want to add about 1-2% of N₂ and about 0.02% CO₂ to that in order to have a self-sustaining Earth-like biosphere.

Your second best option would be 68% O₂, 28% N₂O, 3.97% N₂ and 0.03% CO₂ under 0.3 bar. You would only have a fraction of the greenhouse effect you'd get out of the previous option, but this much nitrous oxide would be much easier to obtain. Do not mind the high NFPA "health hazard" index - it is greatly overrated mainly because of its reputedly high narcotic potency and its oxidizing qualities. In fact, N₂O is no more toxic than O₂ and not really that narcotic compared to CO₂ or Xenon, for instance.

Finally, your third best option is probably hydrox (H₂/O₂) pumped under 8 bar pressure. You would have about 1% O₂ in that mix and some trace amounts of N₂ and CO₂ - the rest being H₂. While hydrogen is not a very potent greenhouse gas, this much of it would probably still have considerable effect and it won't be any fire hazard with so small O₂ fraction (you cannot increase pressure above 8 bar, because H₂ would start having narc effect at point). Advantage - plenty of H₂ on Jupiter!

Not so. Atomic neon has mole mass of 20.18 g/mol. Molecular nitrogen - 28.01 g/mol. Neon, as "noble gas", does not form diatomic molecules as nitrogen does.

Ok, I'm more of a sci-fi writer then an actual scientists - though I do like to write hard sci-fi rather then rely on suspension of disbelief For me, "not impossible" means "possible". And since Ne/SF₆ atmosphere certainly makes a more interesting setting then N₂, I assume it is possible until I have a conclusive prove of the opposite.

Argon won't work as dill under 7 bars since it has two times greater narc factor then N₂. You'd want to use Ne or He (Ne would be better, but He is easier to come by). H₂ would work too under 7 bars since you've got lots of it on Jupiter - hydrox is perfectly safe and breathable for humans as long as your O₂/H₂ ratio does not exceed 4:96 and as long as ppH₂ stays below 8 bars. Methane is a good greenhouse gas and it would not be a fire hazard as long as you keep ppO₂ low enough. SF₆ is the best greenhouse gas you can think of and it is completely inert (almost as inert as noble gases) - but it might be bit harder to come by here in Sol System.

Josh, abundance of elements other then H, He, C and O (which are, by far, more abundant then anything else) in the Sol System is a purely circumstantial. For instance, we have anomalously high abundance of N and anomalously low abundance of Fe here judging by the estimated relative abundance of those elements in the Milky Way. There is nothing to say that there would be no similar anomalies in other places - thus there could be unusually high abundance of F and S, which would readily react with each other and produce SF₆ (which is one of the most stable compounds of F). Again, especially if we consider nomad planets, they would not be subject to stellar winds as much as planets closer to a star, so they would be able to better hold on to lighter inert elements and chances are, there would be much more Ne in the atmosphere then N₂ (since as Ne is estimated to be nearly twice more abundant in this galaxy). There could also be other factors that would allow rocky planets to hold on noble gases better then Earth, Mars, Venus and Titan managed. Again, as I said, there seems to be anomalously high abundance of N in the Sol System - but, even then, Earth and Titan seem to have gotten the most of it since you haven't got much of it on Mars and Venus (not to mention other rocky bodies). I really do not think we should regard all patterns we observe in a single stellar system as universally applicable.

Terraformer-

Well, aerostats based on "light gas balloon" principle have their merits since they require no power input for lift... How about you replace part of N₂ in the atmosphere with, say, SF₆ (sulfur hexafluoride) - which has more then 5 times the mole mass of nitrogen and lots of greenhouse effect, but is still completely inert and much less narcotic than CO₂ (it is still about 6 times more narcotic then N₂, but you could have up to 25% of it under 1 atm without getting narced - even more, if you replace the rest of N₂ with non-narcotic neon). An atmosphere consisting of 44% Ne, 33% SF₆, 21% O₂, 2% N₂ and some trace amounts of CO₂ would still be perfectly breathable for humans and capable of sustaining Earth-like biosphere under 1 atm pressure, but you would have 64.36 g/mol mole mass (which would give you more then twice the density of Earth atmosphere under the same pressure and temperature) and lots of greenhouse effect.

Don't forget that the substance phase is a function of both temperature and pressure. A substance can exist in a true liquid phase only if both temperature and pressure are between triple point and critical point values (though it could also exist in solid and gaseous phases depending on particular temperature/pressure values). If pressure is below triple point, the substance will transition directly between structured solid to gaseous phases and vice versa with temperature variations. At pressures above critical point, there will be no clear boundary between supercritical "gas" (which still behaves very much like any normal gas), "compressible fluid" (which would be as dense as liquid but retain some properties of gas) and amorphous (unstructured) "solid" - but there would still be a distinct boundary between compressible "liquid" / amorphous "solid" ans crystalline/metallic solid at some point of pressure/temperature curve. Helium, technically, becomes supercritical at pressure above 227 kPa (≈ 2.3 ATA), though we would never be able to tell it from a "normal" gas at temperatures compatible with human survival.

Yes, it would be very difficult (see impossible) to build an aerostat based on "light gas balloon" principle that would work in hydrogen atmosphere, though "hot air balloon" and "low pressure balloon" principles would work just as fine in hydrogen, given sufficiently high pressure and sufficiently low temperature. But true, "light gas balloon" principle is usually the most efficient, since lighter-then-air lifting gas maintains its volume and density by itself under ambient atmospheric conditions and neither any power input (as with "hot air balloon") nor any particularly strong and heavy support structure (as with "low pressure balloon") is required in order to achieve buoyancy buoyancy. 

Lifting efficiency of a wing, on the other hand, has no immediate relation to the mole mass of the environment - it is mainly a function of the global value of density, airspeed, wing area, wing aspect ratio, angle of attack and gravity (since g has no effect on the lifting force, but lifting force needs to offset weight which is a function of g). The global value of density for gases is pressure * mole mass / (R * temperature) but, as far as dynamic lift is concerned, you do not particularly care how much of that density comes from pressure, mole mass or temperature as long as your density/g ratio is high enough. Efficiency of winged aircraft is also directly related to the speed of sound (which is a function of temperature, mole mass and specific heat capacity) - the higher this value is, the more airspeed (and thus lift) you can achieve without hitting the critical Mach and being subjected to negative effects of reduced lift, wave drag and amplified skin friction (this is also a limiting factor or propeller/rotor blade lengths and RPM rates). In this respect low mole mass is a good thing since it usually results in higher speed of sound under the same temperature (e.g. the sound travels about 4 times faster in hydrogen then in nitrogen at 20 °C). 

Relying on extreme pressure difference between inside and outside environment might not be a very viable concept, as that would either entail super-strong (and thus super-heavy support structure) or reliance on some dynamic forces (which could lead to a disaster in case of power failure). We are talking more about temperature difference here, which has nothing to do with pressure. Neutral buoyancy equation for gaseous environments looks like this:

m₀ = p[env]·M[env]·V[disp]/R·T[env] - p[L]·M[L]·V[L]/R·T[L]

where m₀ is the mass of your aerostat (without mass of the lifting gas), p[env], T[env] and M[env] are pressure, temperature and mole mass of the environment (atmosphere), p[L], T[L], M[L], V[L] are pressure, temperature, mole mass and volume of the lifting gas, V[disp] is total volume of the environment gas displaced by the aerostat and R is the ideal gas constant (8.3144621 J/mol·K). This comes from the fact that, under constant gravity, total mass of your aerostat must be equal to the total mass of the displaced environment gas and terms on the right side of the equation are merely masses of the displaced environment gas and the lifting gas expressed in terms of their volumes and densities using the ideal gas law.

For all practical purposes, you can consider that the any useful volume of displaced environment gas the same as the volume of your lifting gas, since you do not normally get much useful buoyancy from the volume of gas displaced by solid/liquid substances. Which gives you this:

m₀ = (p[env]·M[env]/T[env] - p[L]·M[L]/T[L])·V[L]/R

Basically, in order to maximize the useful mass of your aerostat (m₀) you would want the mole mass of the lifting gas to be as low as possible and its temperature as high as possible. You do not really want to mess with pressure too much, however - although decreasing pressure of the lifting gas could potentially increase your buoyancy, in practice, it would also oblige you to reinforce the structure and, usually, lead to increase of mass by greater magnitude (and thus nullify any theoretical buoyancy advantage you might have gained).

Now, if your environment gas is mostly H₂/He you haven't got much room to play with mole mass of the lifting gas, though you'd still want to keep it as low as possible - so, you would likely want to use heliox, hydrox or hydreliox as breathing gas inside your habitat. Humans can safely breath heliox under pressures up to about 14 ATA - above that pressure, helium causes HPNS which is likely not healthy in the long-term. Under high pressure, you can also add some hydrogen into the mixture (hydrox or hydreliox) but, for obvious reasons, you do not normally want to mix H₂ with O₂ at ratios greater then 4:96. Hydrox (H₂/O₂) with 1-4% oxygen mole fractions is perfectly safe and breathable and for pressures between 5 and 8 ATA (lower pressure would force you to increase O₂ content above safe ratio and higher partial pressure of H₂ could cause narcotic effect).

Trimix (He/N₂/O₂) would have no real merit for your floating habitats - humans do not really need any nitrogen and it will only unnecessarily increase mole mass of your "lifting gas" (they use trimix on deep dives because N₂ narcosis somewhat compensates for HPNS effects of He, but that's probably not very good health in the long run). If you want pressure above 14 ATA, H₂ and Ne would be much better options for diluting heliox.

Since hydrox atmosphere inside the habitat would give you best aerostatic efficiency, and pressure amplifies lifting effects you get out of mole mass or temperature difference, 8 ATA outside pressure would probably be ideal. So, let's see how heavy you can make hemi-sphere habitat of 1 km diameter filled with 1/99 hydox at 20 °C (293.15 K) in 20/80 helium-hydrogen atmosphere at 8 ATA (≈ 8×10⁵ Pa) pressure and 50 K temperature.

Volume of the lifting gas would be approximately equal to 2/3·π·500³ m³. Mole mass of 1/99 hydrox is 0.00232 kg/mol while mole mass of 20/80 He/H₂ mixture is 0.00241 kg/mol. Thus:

m₀ = (0.00241 kg/mol / 50 K - 0.00232 kg/mol / 293.15 K) × 2/3π × 500³ m³ × 8×10⁵ Pa / 8.3144621 J/mol·K = 1014794730 kg

That's about 1 million metric ton - not bad!

Now let's see how well 10/90 heliox (M = 0.00681 kg/mol) at 2 ATA pressure would perform (we cannot drop the partial pressure of O₂ much below 0.16 ATA if we want humans to live there and even 8/92 hydrox would be already be a major fire hazard). 

m₀ = (0.00241 kg/mol / 50 K - 0.00681 kg/mol / 293.15 K) × 2/3π × 500³ m³ × 2×10⁵ Pa / 8.3144621 J/mol·K = 157244535 kg

About 150,000 metric ton. Still impressive, but would that be enough for a structure of 1 km diameter?