  Of the fourteen transiting extrasolar planetary systems for which radii have
been measured, at least three appear to be considerably larger than theoretical
estimates suggest. It has been proposed by Bodenheimer, Lin & Mardling that
undetected companions acting to excite the orbital eccentricity are responsible
for these oversized planets, as they find new equilibrium radii in response to
being tidally heated. In the case of HD 209458, this hypothesis has been
rejected by some authors because there is no sign of such a companion at the 5
m/s level, and because it is difficult to say conclusively that the
eccentricity is non-zero. Transit timing analysis [...]. Whether or not a
companion is responsible for the large radius of HD 209458b, almost certainly
some short-period systems have companions which force their eccentricities to
nonzero values. This paper is dedicated to quantifying this effect.
  The eccentricity of a short-period planet will only be excited as long as its
(non-resonant) companion's eccentricity is non-zero. Here we show that the
latter decays on a timescale which depends on the structure of the interior
planet, a timescale which is often shorter than the lifetime of the system.
This includes Earth-mass planets in the habitable zones of some stars. We
determine which configurations are capable of sustaining significant
eccentricity for at least the age of the system, and show that these include
systems with companion masses as low as a fraction of an Earth mass. The
orbital parameters of such companions are consistent with recent calculations
which show that the migration process can induce the formation of low mass
planets external to the orbits of hot Jupiters. Systems with inflated planets
are therefore good targets in the search for terrestrial planets.
