CO2 condensation is a serious limit to the deglaciation of Earth-like planets

It is widely believed that the carbonate-silicate cycle is the main agent to trigger deglaciations by CO$_2$ greenhouse warming on Earth and on Earth-like planets when they get in frozen state. Here we use a 3D Global Climate Model to simulate the ability of frozen planets to escape from glaciation by accumulating enough gaseous CO$_2$. We find that Earth-like planets orbiting a Sun-like star may never be able to escape from glaciation if their orbital distance is greater than $\sim$ 1.27 AU (Flux $<$ 847 W m$^{-2}$ or 62$\%$ of the Solar constant), because CO$_2$ would condense at the poles forming permanent CO$_2$ ice caps. This limits the amount of CO$_2$ in the atmosphere and thus its greenhouse effect. The amount of CO$_2$ that can be trapped in the polar caps depends on the efficiency of CO$_2$ ice to flow laterally as well as its graviational stability relative to subsurface water ice. The flow of CO$_2$ ice from poles to equator is mostly controlled by the bottom temperature, and hence by the internal heat flux. We find that a frozen Earth-like planet located at 1.30 AU of a Sun-like star could store as much as 1.5/4.5/15 bars of dry ice at the poles, for internal heat fluxes of 100/30/10 mW m$^{-2}$. But these amounts are lower limits. For planets with a significant water ice cover, we show that CO$_2$ ice deposits should be gravitationnally unstable. They get buried beneath the water ice cover in geologically short timescales of $\sim$~10$^4$ yrs, mainly controlled by the viscosity of water ice. CO$_2$ would be permanently sequestered underneath the water ice cover, in the form of CO$_2$ liquids, CO$_2$ clathrate hydrates and/or dissolved in subglacial water reservoirs (if any). This would considerably increase the amount of CO$_2$ trapped and further reduce the probability of deglaciation.