# Heavy gas artificial atmosphere on Ceres?

Is there any heavy enough gas that could be used to make an artificial atmosphere around Ceres without it escaping into space?

• What research have you done? For example what is the surface temperature and escape velocity of Ceres, what elements or compounds are gaseous at that temperature, what atmosphere does Ceres already have? – user8406 Apr 27 '15 at 11:30

Jeans escape is one of the principal mechanisms via which planets and moons loses their lighter atmospheric gases. Jeans escape would be a viable escape mechanism even for xenon on Ceres.

Molecules of gas have a random velocity described by the Maxwell distribution. The most probable velocity is a function of temperature and atomic weight: $v_p = \sqrt{2kT/m}$. Escape velocity is independent of mass. The velocity distribution of a component of a celestial object's atmosphere needs to be well below escape velocity in order for a celestial object to hold on to that component of the atmosphere.

I'll assume a modest atmosphere on Ceres of some high molecular mass gas. The Earth's exobase is about 600 km. I'll assume a much smaller value of 20 km for Ceres. The temperature in the Earth's atmosphere is complex. It drops linearly in the troposphere, rises in the stratosphere, falls again in the mesosphere, and rises in the thermosphere. It's the temperature at the top of the thermosphere that drives thermal escape. In the Earth's atmosphere, this can be well over 1000 kelvin. Ceres is further from the Sun; I'll assume a smaller value of 400 kelvin.

Escape velocity from an altitude of 20 km on Ceres is about 500 m/s. The most probable velocity of xenon at 400 kelvin is about 225 m/s. This is far too large. The Maxwell distribution has a long tail. The loss rate is proportional to $v_\text{p} (\lambda+1) e^{-\lambda}$, where $\lambda = {v_\text{esc}}^2/{v_\text{p}}^2$. In the case of xenon at 400 kelvin and an escape velocity of 500 m/s, $\lambda$ is about 5. (Compare to helium escaping from the Earth's atmosphere, where $\lambda$ is almost 14.) Ceres wouldn't be able to hold on to a xenon atmosphere. It would escape thermally.

What about a complex molecule whose molecular mass is greater than that of xenon? There are two problems here. One is that Ceres is rather cold. Most large complex molecules aren't gases at 168 to 235 kelvin, Ceres' surface temperature. Uranium hexafluoride (molecular weight = 352) would be a nice candidate if Ceres was hot. Sulfur hexafluoride is close with a triple point of 223.5 kelvin at 2.3 bar, but its molecular mass of 146 is only slightly larger than that of xenon. Another problem is that the high energy radiation from the Sun would dissociate those complex molecules, and then it's game over because the products have smaller molecular masses and hence higher thermal velocities.

• Excellent answer to a weak question! – user8406 Apr 27 '15 at 11:50
• This is nice, but you're not considering temperature change with increased pressure and thermal absorption of various gases. – TildalWave Apr 27 '15 at 11:53
• @TildalWave - One common attribute of celestial objects with an atmosphere is that they have a thermosphere. It's the temperature at the top of the thermosphere that drives thermal escape. I assumed 400 kelvin. A value of 200 kelvin seems non-physical to me, but even with that low of a temperature, $\lambda$ is still around 10 for xenon, which is too low. Ceres couldn't hold on to a xenon atmosphere, at least not for long. – David Hammen Apr 27 '15 at 11:57
• Why do u assume 400 K for the atmosphere temperature on Ceres? – Anixx Apr 27 '15 at 12:25
• What about higher molecular compounds (like polymerized perfluorocarbons) at further away celestial bodies (such as, say Rhea) so that they not to dissociate? – Anixx Apr 27 '15 at 12:29