  Eccentricity is an important orbital parameter. Understanding its effect on
planetary climate and habitability is critical for us to search for a habitable
world beyond our solar system. The orbital configurations of M-dwarf planets
are always tidally-locked at resonance states, which are quite different from
those around Sun-like stars. M-dwarf planets need to be investigated
separately. Here we use a comprehensive three-dimensional atmospheric general
circulation model to systematically investigate how eccentricity influences
climate and habitability of M-dwarf exoplanets. The simulation results show
that (1) the seasonal climatic cycles of such planets are very weak even for e
= 0.4. It is unlikely that an aqua planet falls out of a habitable zone during
its orbit. (2) The annual global mean surface temperature significantly
increases with increased eccentricity, due to the decrease of the cloud albedo.
Both the runaway greenhouse inner edge and moist greenhouse inner edge shift
outward. (3) Planets in an eccentric orbit can be captured in other spin-orbit
resonance states which lead to different climate patterns, namely eyeball
pattern and striped-ball pattern.The striped-ball pattern has evidently higher
surface temperatures due to the reduced planetary albedo. Near the outer edge,
planets with p = 1.0 and 2.0 are more resistant to the snowball state due to
more locally-concentrated stellar fluxes. Thus, planets with integer spin-orbit
resonance numbers have wider habitable zones than those with half-integer
spin-orbit resonance states. Above all, as a comparison to circular orbit,
eccentricity shrinks the width of the habitable zone.
