  e Eridani, the fifth-closest Sun-like star, hosts at least three planets and
could possibly harbor more. However, the veracity of the planet candidates in
the system and its full planetary architecture remain unknown. Here we analyze
the planetary architecture of e Eridani via DYNAMITE, a method providing an
integrative assessment of the system architecture (and possibly yet-undetected
planets) by combining statistical, exoplanet-population level knowledge with
incomplete but specific information available on the system. DYNAMITE predicts
the most likely location of an additional planet in the system based on the
Kepler population demographic information from more than 2000 planets.
Additionally, we analyze the dynamical stability of e Eridani system via N-body
simulations. Our DYNAMITE and dynamical stability analyses provide support for
planet candidates g, c, and f, and also predict one additional planet candidate
with an orbital period between 549 -- 733 days, in the habitable zone of the
system. We find that planet candidate f, if it exists, would also lie in the
habitable zone. Our dynamical stability analysis also shows that the e Eridani
planetary eccentricities, as reported, do not allow for a stable system,
suggesting that they are lower. We introduce a new statistical approach for
estimating the equilibrium and surface temperatures of exoplanets, based on a
prior on the planetary albedo distribution. e Eridani is a rich planetary
system with a possibility of containing two potentially habitable planets, and
its vicinity to our Solar System makes it an important target for future
imaging studies and biosignature searches.
