  Conventional definitions of habitability require abundant liquid surface
water to exist continuously over geologic timescales. Water in each of its
thermodynamic phases interacts with solar and thermal radiation and is the
cause for strong climatic feedbacks. Thus, assessments of the habitable zone
require models to include a complete treatment of the hydrological cycle over
geologic time. Here, we use the Community Atmosphere Model from the National
Center for Atmospheric Research to study the evolution of climate for an
Earth-like planet at constant CO2, under a wide range of stellar fluxes from
F-, G-, and K-dwarf main sequence stars. Around each star we find four stable
climate states defined by mutually exclusive global mean surface temperatures
(Ts); snowball (Ts < 235 K), waterbelt (235 K < Ts < 250 K), temperate (275 K <
Ts < 315 K), and moist greenhouse (Ts > 330 K). Each is separated by abrupt
climatic transitions. Waterbelt, temperate, and cooler moist greenhouse
climates can maintain open-ocean against both sea-ice albedo and hydrogen
escape processes respectively, and thus constitute habitable worlds. We
consider the warmest possible habitable planet as having Ts ~ 355 K, at which
point diffusion limited water-loss could remove an Earth ocean in ~1 Gyr.
Without long timescale regulation of non-condensable greenhouse species at
Earth-like temperatures and pressures, such as CO2, habitability can be
maintained for an upper limit of ~2.2, ~2.4 and ~4.7 Gyr around F-, G- and
K-dwarf stars respectively due to main sequence brightening.
