Why might a thick atmosphere prevent the dark side of a tidally locked planet from freezing?

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On a tidally locked planet, one hemisphere perpetually faces its star while the other remains in darkness. Without a sufficiently thick atmosphere, the lack of a day-night cycle would cause the atmosphere on the cold, dark side to freeze and deposit onto the surface.1

However, if a planet possesses a sufficiently massive atmosphere, global wind patterns can effectively redistribute heat from the sunlit hemisphere to the dark side. This atmospheric circulation prevents the temperature from dropping to the point where the gases would freeze out, thereby maintaining a more stable climate across the planet's surface.1