  The NASA Kepler and K2 Missions have recently revealed a population of
transiting giant planets orbiting moderately evolved, low-luminosity red giant
branch stars. Here, we present radial velocity measurements of three of these
systems, revealing significantly non-zero orbital eccentricities in each case.
Comparing these systems with the known planet population suggests that close-in
giant planets around evolved stars tend to have more eccentric orbits than
those around main-sequence stars. We interpret this as tentative evidence that
the orbits of these planets pass through a transient, moderately eccentric
phase where they shrink faster than they circularize due to tides raised on
evolved host stars. Additional radial velocity measurements of currently known
systems, along with new systems discovered by the recently launched NASA TESS
mission, may constrain the timescale and mass dependence of this process.
