  Implicit in the definition of the classical circumstellar habitable zone (HZ)
is the hypothesis that the carbonate-silicate cycle can maintain clement
climates on exoplanets with land and surface water across a range of
instellations by adjusting atmospheric $\mathrm{CO_2}$ partial pressure
($p\mathrm{CO_2}$). This hypothesis is made by analogy to the Earth system, but
it is an open question whether silicate weathering can stabilize climate on
planets in the outer reaches of the HZ, where instellations are lower than
those received by even the Archean Earth and $\mathrm{CO_2}$ is thought likely
to dominate atmospheres. Since weathering products are carried from land to
ocean by the action of water, silicate weathering is intimately coupled to the
hydrologic cycle, which intensifies with hotter temperatures under Earth-like
conditions. Here, we use global climate model (GCM) simulations to demonstrate
that the hydrologic cycle responds counterintuitively to changes in climate on
planets with $\mathrm{CO_2}$-$\mathrm{H_2O}$ atmospheres at low instellations
and high $p\mathrm{CO_2}$, with global evaporation and precipitation decreasing
as $p\mathrm{CO_2}$ and temperatures increase at a given instellation. Within
the MAC weathering formulation, weathering then decreases with increasing
$p\mathrm{CO_2}$ for a range of instellations and $p\mathrm{CO_2}$ typical of
the outer reaches of the HZ, resulting in an unstable carbon cycle that may
lead to either runaway $\mathrm{CO_2}$ accumulation or depletion of
$\mathrm{CO_2}$ to colder (possibly Snowball) conditions. While the behavior of
the system has not been completely mapped out, the results suggest that
silicate weathering could fail to maintain habitable conditions in the outer
reaches of the nominal HZ.
