  Water-rich planets such as Earth are expected to become eventually
uninhabitable, because liquid water does not remain stable at the surface as
surface temperatures increase with the solar luminosity over time. Whether a
large increase of atmospheric concentrations of greenhouse gases such as CO$_2$
could also destroy the habitability of water-rich planets has remained unclear.
We show with three-dimensional aqua-planet numerical experiments that
CO$_2$-induced forcing as readily destabilizes the climate as does solar
forcing. The climate instability is caused by a positive cloud feedback. The
climate does not run away, but instead attains a new steady state with
global-mean sea-surface temperatures above 330 K. The upper atmosphere is
considerably moister in this warm steady state than in the reference climate,
implying that the planet would be subject to substantial loss of water to
space. For either a certain range of elevated CO$_2$ concentrations or solar
irradiation, we find both cold and warm equilibrium states, implying that the
transition to the warm state may not simply be reversed by removing the
additional forcing.
