  One of the most remarkable properties of extrasolar planets is their high
orbital eccentricities. Observations have shown that at least 20% of these
planets, including some with particularly high eccentricities, are orbiting a
component of a wide binary star system. The presence of a distant binary
companion can cause significant secular perturbations to the orbit of a planet.
In particular, at high relative inclinations, a planet can undergo a
large-amplitude eccentricity oscillation. This so-called "Kozai mechanism" is
effective at a very long range, and its amplitude is purely dependent on the
relative orbital inclination. In this paper, we address the following simple
question: assuming that every host star with a detected giant planet also has a
(possibly unseen, e.g., substellar) distant companion, with reasonable
distributions of orbital parameters and masses, how well could secular
perturbations reproduce the observed eccentricity distribution of planets? Our
calculations show that the Kozai mechanism consistently produces an excess of
planets with very high (e >0.6) and very low (e < 0.1) eccentricities. The
paucity of near-circular orbits in the observed sample cannot be explained
solely by the Kozai mechanism, because, even with high enough inclinations, the
Kozai mechanism often fails to produce significant eccentricity perturbations
when there are other competing sources of orbital perturbations on secular
timescales, such as general relativity. On the other hand, the Kozai mechanism
can produce many highly eccentric orbits. Indeed the overproduction of high
eccentricities observed in our models could be combined with plausible
circularizing mechanisms (e.g., friction from residual gas) to create more
intermediate eccentricities (e=0.1-0.6).
