  Several clues indicate that Titan's atmosphere has been depleted in methane
during some period of its history, possibly as recently as 0.5-1 billion years
ago. It could also happen in the future. Under these conditions, the atmosphere
becomes only composed of nitrogen with a range of temperature and pressure
allowing liquid or solid nitrogen to condense. Here, we explore these exotic
climates throughout Titan's history with a 3D Global Climate Model (GCM)
including the nitrogen cycle and the radiative effect of nitrogen clouds. We
show that for the last billion years, only small polar nitrogen lakes should
have formed. Yet, before 1 Ga, a significant part of the atmosphere could have
condensed, forming deep nitrogen polar seas, which could have flowed and
flooded the equatorial regions. Alternatively, nitrogen could be frozen on the
surface like on Triton, but this would require an initial surface albedo higher
than 0.65 at 4 Ga. Such a state could be stable even today if nitrogen ice
albedo is higher than this value. According to our model, nitrogen flows and
rain may have been efficient to erode the surface. Thus, we can speculate that
a paleo-nitrogen cycle may explain the erosion and the age of Titan's surface,
and may have produced some of the present valley networks and shorelines.
Moreover, by diffusion of liquid nitrogen in the crust, a paleo-nitrogen cycle
could be responsible of the flattening of the polar regions and be at the
origin of the methane outgassing on Titan.
