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The thing with global warming is that it absorbs infrared (IR) radiation from the planet and reradiates much of it back to the planet (whereas the Sun's peak flux is in the visible region, that is unaffected by CO2).

But with red dwarfs - it's different. The CO2 is going to reradiate back much of that incoming IR radiation from the Sun (in fact, this is why the upper atmosphere of Venus is so cold).

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Ah, but there are different kinds of infrared, it's a very wide spectrum of electromagnetic energy after all. It ranges from about 700 nanometers (0.7 microns) at the visible end to about 1 mm (1000 microns) at the microwave end. Wien's law states that the energy peak of blackbody radiation is at a wavelength in microns given by lambda(max) = 2900/T where T is the absolute temperature of the radiator in kelvins. So your M dwarf at 3000 K is going to radiate most strongly at around one micron, and CO2 is still quite transparent to that (see http://en.wikipedia.org/wiki/File:Atmospheric_Transmission.png for the CO2 absorption spectrum). CO2 is most absorbing in a wide band at around 17 microns, corresponding to a temperature of about 170 K.

Note that this is a better match for temperatures in the Arctic and Antarctic, where average temperature is around 240 K, compared to the tropics where average temperature is around 300 K, and global warming is definitely stronger in the arctic than in the tropics. But at some point, you can't describe such complicated physics in general terms like we are doing here, you need to do the detailed computer modelling.

On Venus, the atmosphere is so thick with CO2 that it is essentially opaque at all long infrared wavelengths and Venus has had to keep warming up until it could radiate out at shorter wavelengths and temperatures near 700 K.

At high altitudes on Venus, the CO2 becomes a much more efficient radiator than absorber, so it gets very cold. Again, the physics is complicated since the atmosphere is rarified enough to be in a state of non-thermodynamic equilibrium.

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The planetary radiation temperature (what you would measure if you pointed a bolometer from space at the planet) is lower, often much lower than the surface temperature. The amount of IR radiation escaping to space from the earth is near your 240K, than the surace average (285K), because much of the radiation to space is from high in the atmosphere where the temperature is much colder than the surface temperature. So the lower wavelengths of the IR are more important than a naive Weins argument would imply. –  Omega Centauri Aug 3 '11 at 18:21
    
more important for what? –  Pete Jackson Aug 3 '11 at 18:54
    
I'm just suggesting that high in the planets atmosphere the thermal radiation peak will be at a longer wavelength than you would expect if you used the surface temperature. This is especially true for very IR opaque atmospheres such as Venus. In any case for an earthlike planet, the basic argument, that thermal reradiation is at at least an order of magnitude longer wavelength than the stellar shortwave heating is still correct. –  Omega Centauri Aug 4 '11 at 17:59

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