If a planet is always directed with the same side to the sun, does a the thermal equilibrium develop, and how does it look like?

If a planet with an atmosphere and a flat surface is always directed with the same side to the sun (or star), how does the (nonstatic) thermodynamic equilibrium look like?

Has eventually an equilibrium developed in which there is a constant heat transfer through the planet from the sunlit side to the dark side?

And besides that, a constant heat transfer from the sunlit side to the dark side develops by means of heat transfer by wind fields in the atmosphere?

An equilibrium will certainly develop while the incoming energy on the sunlit side will be the same as the outgoing energy on the dark side.

How does this wind field look like in the (non-static) equilibrium? Will there develop a constant high pressure on the sunlit side and a constant low pressure on the dark side, balancing each other, causing heat only to be transferred by heat conduction, or will winds develop, causing heat to be transferred by convection?

• I don't think it reaches any kind of very steady state in any plausible scenario because there is turbulence. People run simulations of exoplanet atmospheres including those of tidally-locked planets: it's reasonably easy to find pointers I think. – tfb Feb 13 '17 at 20:57

Has eventually an equilibrium developed in which there is a constant heat transfer through the planet from the sunlit side to the dark side?

Each individual area will be in equilibrium, but that is true regardless of how much heat transfer is done through the planet or via the atmosphere. Once you involve an atmosphere, the modelling would become quite complex.

An equilibrium will certainly develop while the incoming energy on the sunlit side will be the same as the outgoing energy on the dark side.

Not necessarily. If you imagine a body without an atmosphere, it's likely there will be very little heat transfer from one side to the other. The sunlit side will increase temperature until the radiation from that side removes almost all of the incoming radiation. It would have incoming energy orders of magnitude greater than the dark side radiated energy.

Any atmosphere would reduce this temperature difference, but be unlikely to reduce the difference to zero.

The winds might be different based on density, depth, rotation speed (even when tidally locked) and landforms. There's no simple solution. The larger the temperature difference, the greater the energy that convection can exploit, so the greater the likelihood that convection patterns will dominate.

• I guess I'd rather use 'steady-state' to describe the overall situation. I don't think it reaches equilibrium unless the planet reaches the same temperature as the star. – Jon Custer Feb 13 '17 at 20:47
• Not true. The star does not encompass the entire field of view. Other angles are looking at (very cold) space. – BowlOfRed Feb 13 '17 at 20:50
• But that is kind of the point - the planet does not come in to equilibrium - heat is flowing through it from one side to the other, then being radiated out in to space. That is steady-state, not equilibrium. – Jon Custer Feb 13 '17 at 20:52
• I don't understand what you mean. Are you asking if all portions of the planet will have equal temperature? Thermal equilibrium is when the heat flow in equals the heat flow out. And that will certainly happen. – BowlOfRed Feb 13 '17 at 23:09
• @BowlOfRed-You're right by saying the incoming energy on the sunlit aide doesn't equal the outgoing energy on the dark side! Of course, I had to say that the incoming minus the outgoing energy on the sunlit site is equal to the energy outgoing energy on the dark side. – descheleschilder Feb 14 '17 at 4:15

This is a very interesting question. For sure, the planet will reach steady state. If the planet has a significant atmosphere, I don't think that conduction through the planet will be the major contributor to the heat transfer. I think it will be natural convection. In my judgment, there will be a convective circulation pattern, with upflow near the center of the sunlit side, and downflow near the center of the dark side. So heat will flow from from the sunlit side to the dark side. At high altitude on the sunlit side there will be flow toward the dark side, and at low altitude, there will be flow from the dark side. Vice-versa for the dark side. In addition to the convective heat transfer, there will be radiation emitted to space (cooling) and radiation received on the sunlit side from the sun. So the balance between radiation and convection will determine the time average temperature distribution with altitude and solar angle.