Could a far-out dwarf planet have a thick hydrogen atmosphere?

[SmartS=true]

The solar wind is nonexistent beyond ~100 AU, so could a dwarf planet that far out capture and retain a fairly thick hydrogen atmosphere?

[More Boosters]

I wouldn't give anything out there a high chance of having a thick hydrogen atmosphere as most hydrogen in the system is likely to have collapsed into the accretion disk when our sun first formed, and those planets probably didn't form out there to begin with. You could argue that there's less challenge in holding on to hydrogen but then the thing itself is that much sparser.

[SmartS=true]

[quote name='More Boosters']I wouldn't give anything out there a high chance of having a thick hydrogen atmosphere as most hydrogen in the system is likely to have collapsed into the accretion disk when our sun first formed, and those planets probably didn't form out there to begin with. You could argue that there's less challenge in holding on to hydrogen but then the thing itself is that much sparser.[/QUOTE]

By thick I didn't mean a hydrogen envelope such as what the gas giants have, but an atmosphere of anywhere between a dozen and a few hundred bars.

[Kryten]

No, not enough gravity.

[prophet_01]

Hydrogen is very tricky to begin with... The gravity to hold on to it and to actually hold onto enough of it to get that kind of pressure would be massive. We're talking about an object much bigger than earth here. So a dwarf planet isn't exactly what you're looking for.
It's very unlikely at best that such a heavy object could form out there. There's not enough mass at that distance as far as I know

[More Boosters]

[quote name='SmartS=true']By thick I didn't mean a hydrogen envelope such as what the gas giants have, but an atmosphere of anywhere between a dozen and a few hundred bars.[/QUOTE]

There is one way actually, but not like you would think.

They wouldn't be dwarf planets, but they could be [URL="https://en.wikipedia.org/wiki/Gas_dwarf"]gas dwarfs. They probably wouldn't form all the way out there however.

[/URL][HR][/HR]
Sorry for hijacking the thread OP but you'd probably find this interesting and I didn't want to create another thread, is there any chance that Mercury is a [URL="https://en.wikipedia.org/wiki/Chthonian_planet"]Chthonian[/URL] planet,that is, a planet that used to be a gas giant but lost all its stuff to the sun? Edited November 23, 2015 by More Boosters

[fredinno]

[quote name='prophet_01']Hydrogen is very tricky to begin with... The gravity to hold on to it and to actually hold onto enough of it to get that kind of pressure would be massive. We're talking about an object much bigger than earth here. So a dwarf planet isn't exactly what you're looking for.
It's very unlikely at best that such a heavy object could form out there. There's not enough mass at that distance as far as I know[/QUOTE]

It could have been slung out of the early solar system by gravitational interactions, and is the reason objects like Sedna exist.
But that's a full-fledged planet, not a dwarf planet.

[MaxL_1023]

That far out, hydrogen would condense to a liquid if it had that kind of density. Hydrogen boils at 20k (13.8k triple point), so outside of 100AU it would liquefy as long as the pressure is more than 7.04 kpa. Unless the body was big enough to have significant internal heat, you would not see a hydrogen atmosphere at that distance.

Most likely, any object that formed in the dwarf planet (say < 0.1 Earth Mass) range would be too close in to capture any hydrogen, then ejected to a distant orbit where the gas density is basically zero. I don't think the universe is old enough for liquid hydrogen planets - you would need a gas giant to eventually cool completely and have it in interstellar space or around a black dwarf.

[SmartS=true]

[quote name='MaxL_1023']That far out, hydrogen would condense to a liquid if it had that kind of density. Hydrogen boils at 20k (13.8k triple point), so outside of 100AU it would liquefy as long as the pressure is more than 7.04 kpa. Unless the body was big enough to have significant internal heat, you would not see a hydrogen atmosphere at that distance.

Most likely, any object that formed in the dwarf planet (say < 0.1 Earth Mass) range would be too close in to capture any hydrogen, then ejected to a distant orbit where the gas density is basically zero. I don't think the universe is old enough for liquid hydrogen planets - you would need a gas giant to eventually cool completely and have it in interstellar space or around a black dwarf.[/QUOTE]

Could a large satellite cause enough tidal heating to keep the hydrogen gaseous?

[Kryten]

Then it'd just escape.

[kerbiloid]

The main question: where would it get a sufficient amount of that hydrogen to be gorgeously called "atmosphere".

Dwarf planets have appeared near a Sun, so you would use the near-Sun temperature to calculate, not the far-from-Sun frost.
So, any free hydrogen would dissipate from them before they have been composed.

***

Escape velocity = sqrt(2 * GM / r) = sqrt(2 * G * density * 4/3 * pi * r^3 / r) = sqrt(2 * G * density * 4/3 * pi * r^2) = sqrt(2 * G * density * 4/3 * pi) * r ~= sqrt(2 * 6.67e-11 * 5500 * 4/3 * pi) * r ~= 0.00175 * r.

I.e for a planet with an earth-like density:
Escape velocity, m/s ~= 1.75 * r,
where r = planet radius, km

For example Earth = 1.75 * 6371 ~= 11150 m/s

***

Mean-square velocity of a gas molecule, m/s = sqrt(3RT/m),
where m - molar mass, kg/mol

***

Temperature equilibrium equation:
L = 4 pi R^2 * 5.67e-8 T^4

Equilibrium temperature at R radius from star:
T = [L / (4 pi R^2 * 5.67e-8)]^0.25
Sun luminosity L = 3.83e26 W

T = (3.83e26 / (4 * pi * R^2 * 5.67e-8))^0.25 = (3.83e26 / (4 * pi * 5.67e-8))^0.25 / sqrt(R),
where R in m.
or
T = (3.83e26 / (4 * pi * 5.67e-8))^0.25 / 1.5e11^0.5 / R^0.5 ~= 393/sqrt(R),
where R in AU.

Cosmic background temperature ~= 2.7 K

I.e.
T = 393/sqrt(R), where R in AU.
but never less than 2.7 K.

***

Escape velocity, m/s ~= 1.75 * r,

To avoid fast atmosphere dissipation, escape velocity must be ~5 times greater than a molecular speed


Cosmic background hydrogen speed = sqrt(3 * 8.3144 * 2.7 / 0.002) = 183 m/s

Minimal planet radius far from stars to keep hydrogen near cosmic background temperature ~= 183 * 5 / 1.75 ~= 500 km.


Mean-square velocity of a gas molecule near a Sun, m/s = sqrt(3 * 8.31 * 393/(sqrt(R) * m)) ~= 100 / (m^0.5 * R^0.25),
where m in kg/mol, R in AU.

So, minimal radius to keep hydrogen molecules near a planet ~= 100 / (0.002^0.5 * R^0.25) * 5 / 1.75 ~= 6388 / R^0.25, km.
(but not less than 500 km).

***

R, AU → min radius, km

1 AU → 6388 km
100 AU → 2000 km
1000 AU → 1100 km
> 20000 AU → 500 km

[PB666]

you have put alot of thought into this.

Hydrogen has a molecukar weight of 2.0394 and it does have a boiling point close to absolute zero at sp. The criteria are then its molecular weight and propensity to boil. So if the planet has sufficient enough gravity to keep hydrogen close to the surface and increase surface pressure that hydrogen is at the transition point it will keep hydrogen longer. If not vaporization pressure and ambient velocity, remember as a gas hydrogen moves the fastest, hydrogen escapes. Because of the dwarf planets are not a good choice, and solar winds suffice to blow hydrogen off the planet just as has happened to atmosphere of mars.

That is the second solution, to have a strong magnetic field of that deflects these winds. This means that the planet has a molten core to complete a dynamo. THis means the planet is large enough to have a molten core. Therefore the second solution requires a large central body.

[kerbiloid]

Boiling point does not really rule here because of sublimation. Especially for bare protons (which the hydrogen is).
Any time some portion of atoms would leave the surface of a planet and when they do this, they speed is about 200 m/s, enough to escape from a little planette.
Like a piece of dry ice left outside of refrigerator.
Magnetic field would only make them fly away not strictly, but along tricky curve trajectories, because somewhere it will stop them, while somewhere - boost.