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The setting is a moon-sized body with solid surface, thick (but mostly transparent) atmosphere and magnetosphere. But most heat from the space is supplied with relativistic charged particles impacting the atmosphere in some regions. And only minute quantities – via (solar radiation)-like transport; about 1/30 the Earth’s solar light energy flux. The body would be an artificial construct, but unnatural features shouldn’t be very prominent. We need the surface to be inhabited, so, it may not be very cold.

The problem: how to transport heat from the atmosphere to the surface? The surface will inevitably lose heat to the outer space via thermal radiation, whereas hot air won’t go down easily to compensate for it.

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  • $\begingroup$ A blast of relativistic particles will rapidly erode the atmosphere away from the planet, which is perhaps more of a complication than worrying about when the planet gets to thermal equilibrium. $\endgroup$ – Thucydides May 14 '16 at 2:26
  • $\begingroup$ @Thucydides: Really much of the atmosphere will escape as neutral atoms? Ions (produced by collisions) will be retained by the magnetic field. $\endgroup$ – Incnis Mrsi May 14 '16 at 18:48
  • $\begingroup$ A magnetic field would require a molten rotating core, and moon-sized bodies typically don't have that. How massive is your planet? That should limit the amount of atmospheric escape. $\endgroup$ – Akshat Mahajan May 18 '16 at 15:22
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If the flux of particles is constant and you wait "sufficiently long", the system (planet+atmosphere) will get into thermal equilibrium and the equations will be simple, incoming energy equals heat loss, which can be approximated by blackbody radiation.

Note that the atmosphere also loses heat via thermal radiation, but this radiation goes not only to the outer space, but approximately at the same rate to the surface as well, so once the atmosphere reaches thermal equilibrium with the energy influx, it will continue heating the surface (in addition to the convection).

Of course, "relativistic charged particles" and "human life" do not coexist easily.

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  • $\begingroup$ This can make sense, especially if the hot stratosphere has some opacity in the near infrared band. $\endgroup$ – Incnis Mrsi May 17 '16 at 9:34
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If the atmosphere is hotter than the surface, heat will naturally conduct to surface. Of course there will be many loss to outer space.

There could be some kind of insulated big balloon that keep the heat from escaping. Of course it would make space travel very complicated (you would have to go through a sas). The balloon would be less insulated on the points where the particles are impacting.

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  • $\begingroup$ Which law will cause hotter atmosphere to convect to the surface? Ah, Ī̲ possibly forgot to specify: my body has the standard direction of gravity: the outer space is at the top and the surface is the bottom ☺ $\endgroup$ – Incnis Mrsi May 14 '16 at 18:44
  • $\begingroup$ Do you really need the hottest atmosphere to be near the surface ? If all the atmosphere is hot, then the surface can be hot enough, outer atmosphere being hotter. $\endgroup$ – Anne Aunyme May 17 '16 at 8:11
  • $\begingroup$ Ī̲ don’t object to anything but “heat will naturally convect to surface”. You may not be an engineer while ignoring established terminology on different modes of heat transfer. $\endgroup$ – Incnis Mrsi May 17 '16 at 8:47
  • $\begingroup$ I was actually thinking about conduction, not convection. I am an engineer, just not an engineer in thermodynamics, so I don't use this vocabulary very often. There is no need to pedantically insult me. $\endgroup$ – Anne Aunyme May 17 '16 at 9:06
  • $\begingroup$ No, Ī̲ obviously don’t want the air near the surface to be 500 K hot, but thermal conduction in hot and sparse stratosphere could unlikely be able to supply the surface with enough heat. Some kind of radiative transfer (see Radovan Garabík’s answer and comments) seems to be more viable option. $\endgroup$ – Incnis Mrsi May 17 '16 at 9:35

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