The low-level radial velocity variability in Barnards star (= GJ 699) - Secular acceleration, indications for convective redshift, and planet mass limits

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 which would indicate that the majority of the absorption lines relevant for our RV measurements is formed in a region of convective overshoot. This interpretation could possibly extend a trend indicated in the behaviour of earlier spectral types that exhibit convective blueshift, but with decreasing line asymmetries and blueshifts as one goes from G to K dwarfs. Based on this assumption, we estimate that the variation of the visible plage coverage is about 20%. We also determine upper limits to the projected mass m\sin i and to the true mass m of hypothetical planetary companions in circular orbits.