  We report results from 2 1/2 yr of high precision radial velocity (RV)
monitoring of Barnard's star. The high RV measurement precision of the
VLT-UT2+UVES of 2.65 m/s made the following findings possible. (1) The first
detection of the change in the RV of a star caused by its space motion (RV
secular acceleration). (2) An anti-correlation of the measured RV with the
strength of the filling-in of the Halpha line by emission. (3) Very stringent
mass upper limits to planetary companions. Using only data from the first 2
years, we obtain a best-fit value for the RV secular acceleration of
5.15+/-0.89 m/s/yr. This agrees with the predicted value of 4.50 m/s/yr based
on the Hipparcos proper motion and parallax combined with the known absolute
radial velocity of the star. When the RV data of the last half-year are added
the best-fit slope is strongly reduced to 2.97+/-0.51 m/s/yr suggesting the
presence of additional RV variability in the star. Part of it can be attributed
to stellar activity as we demonstrate by correlating the residual RVs with an
index that describes the filling-in of the Halpha line by emission. A
correlation coefficient of -0.50 indicates that the appearance of active
regions causes a blueshift of photospheric absorption lines. Assuming that
active regions basically inhibit convection we discuss the possibility that the
fundamental (inactive) convection pattern in this M4V star produces a
convective redshift. We also determine upper limits to the projected mass msini
and to the true mass m of hypothetical planetary companions in circular orbits.
For the separation range 0.017-0.98 AU we exclude any planet with msini>0.12
Mjupiter and m>0.86 Mjupiter. Throughout the habitable zone, i.e. 0.034-0.082
AU, we exclude planets with msini>7.5 Mearth and m>3.1 Mneptune.
