  Nearby stars are prime targets for exoplanet searches and characterization
using a variety of detection techniques. Combining constraints from the
complementary detection methods of high contrast imaging (HCI) and radial
velocity (RV) can further constrain the planetary architectures of these
systems because these methods place limits at different regions of the
companion mass and semi-major axis parameter space. We aim to constrain the
planetary architectures from the combination of HCI and RV data for 6 nearby
stars within 6 pc: $\tau$ Ceti, Kapteyn's star, AX Mic, 40 Eri, HD 36395, and
HD 42581. We compiled the sample from stars with available archival VLT/NACO
HCI data at L$^{\prime}$ band (3.8 $\mu$m). The NACO data were fully reanalyzed
using the state-of-the-art direct imaging pipeline PynPoint and combined with
RV data from HARPS, Keck/HIRES, and CORALIE. A Monte Carlo approach was used to
assess the completeness in the companion mass/semi-major axis parameter space
from the combination of the HCI and RV data sets. We find that the HCI data add
significant information to the RV constraints, increasing the completeness for
certain companions masses/semi-major axes by up to 68 - 99% for 4 of the 6
stars in our sample, and by up to 1 - 13% for the remaining stars. The
improvements are strongest for intermediate semi-major axes (15 - 40 AU),
corresponding to the semi-major axes of the ice giants in our own solar system.
The HCI mass limits reach 5 - 20 $M_{\textrm{Jup}}$ in the background-limited
regime, depending on the age of the star. Through the combination of HCI and RV
data, we find that stringent constraints can be placed on the possible
substellar companions in these systems. Applying these methods systematically
to nearby stars will quantify our current knowledge of the planet population in
the solar neighborhood and inform future observations.
