  We conducted a Doppler survey at Keck combined with NIRC2 K-band AO imaging
to search for massive, long-period companions to 123 known exoplanet systems
with one or two planets detected using the radial velocity (RV) method. Our
survey is sensitive to Jupiter mass planets out to 20 AU for a majority of
stars in our sample, and we report the discovery of eight new long-period
planets, in addition to 20 systems with statistically significant RV trends
indicating the presence of an outer companion beyond 5 AU. We combine our RV
observations with AO imaging to determine the range of allowed masses and
orbital separations for these companions, and account for variations in our
sensitivity to companions among stars in our sample. We estimate the total
occurrence rate of companions in our sample to be 52 +/- 5% over the range 1 -
20 M_Jup and 5 - 20 AU. Our data also suggest a declining frequency for gas
giant planets in these systems beyond 3-10 AU, in contrast to earlier studies
that found a rising frequency for giant planets in the range 0.01-3 AU. This
suggests either that the frequency of gas giant planets peaks between 3-10 AU,
or that outer companions in these systems have a different semi-major axis
distribution than the overall gas giant planet population. Our results also
suggest that hot gas giants may be more likely to have an outer companion than
cold gas giants. We find that planets with an outer companion have higher
average eccentricities than their single counterparts, suggesting that
dynamical interactions between planets may play an important role in these
systems.
