  A planet's climate can be strongly affected by its orbital eccentricity and
obliquity. Here we use a 1-dimensional energy balance model modified to include
a simple runaway greenhouse (RGH) parameterization to explore the effects of
these two parameters on the climate of Earth-like aqua planets - completely
ocean-covered planets - orbiting F-, G-, K-, and M-dwarf stars. We find that
the range of instellations for which planets exhibit habitable surface
conditions throughout an orbit decreases with increasing eccentricity. However,
the appearance of temporarily habitable conditions during an orbit creates an
eccentric habitable zone (EHZ) that is sensitive to orbital eccentricity and
obliquity, planetary latitude, and host star spectral type. We find that the
fraction of a planet's orbit over which it exhibits habitable surface
conditions is larger on eccentric planets orbiting M-dwarf stars, due to the
lower broadband planetary albedos of these planets. Planets with larger
obliquities have smaller EHZs, but exhibit warmer climates if they do not enter
a snowball state during their orbits. We also find no transient runaway
greenhouse state on planets at all eccentricities. Rather, planets spend their
entire orbits either in a RGH or not. For G-dwarf planets receiving 100% of the
modern solar constant and with eccentricities above 0.55, an entire Earth ocean
inventory can be lost in 3.6 Gyr. M-dwarf planets, due to their larger incident
XUV flux, can become desiccated in only 690 Myr with eccentricities above 0.38.
This work has important implications for eccentric planets that may exhibit
surface habitability despite technically departing from the traditional
habitable zone as they orbit their host stars.
