  The habitable zone is the region around a star where standing bodies of
liquid water can be stable on a planetary surface. Its width is often assumed
to be dictated by the efficiency of the carbonate-silicate cycle, which has
maintained habitable surface conditions on our planet for billions of years.
This cycle may be inhibited by surface condensation of significant amounts of
$CO_{\mathrm{2}}$ ice, which is likely to occur on distant planets containing
high enough levels of atmospheric $CO_{\mathrm{2}}$. Such a process could
permanently trap $CO_{\mathrm{2}}$ ice within the planet, threatening its
long-term habitability. Recent work has modeled this scenario for initially
cold and icy planetary bodies orbiting the Sun. Here, we use an advanced energy
balance model to consider both initially warm and cold rapidly-rotating planets
orbiting F - K stars. We show that the range of orbital distances where
significant surface $CO_{\mathrm{2}}$ ice condensation occurs is significantly
reduced for warm start planets. Star type does not affect this conclusion,
although surface $CO_{\mathrm{2}}$ ice condenses over a larger fraction of the
habitable zone around hotter stars. The warm start simulations are thus
consistent with 1-D model predictions, suggesting that the classical habitable
zone limits in those earlier models are still valid. We also find that the cold
start simulations exhibit trends that are consistent with those of previous
work for the Sun although we now extend the analysis to other star types.
