Astrometric measurements are presented for seven nearby stars with previously detected planets: six M dwarfs (GJ 317, GJ 667C, GJ 581, GJ 849, GJ 876, and GJ 1214) and one K dwarf (BD-10 -3166). Measurements are also presented for six additional nearby M dwarfs without known planets, but which are more favorable to astrometric detections of low mass companions, as well as three binary systems for which we provide astrometric orbit solutions. Observations have baselines of 3 to 13 years, and were made as part of the RECONS long-term astrometry and photometry program at the CTIO/SMARTS 0.9 m telescope. We provide trigonometric parallaxes and proper motions for all 16 systems, and perform an extensive analysis of the astrometric residuals to determine the minimum detectable companion mass for the 12 M dwarfs not having close stellar secondaries. For the six M dwarfs with known planets, we are not sensitive to planets, but can rule out the presence of all but the least massive brown dwarfs at periods of 2–12 years. For the six more astrometrically favorable M dwarfs, we conclude that none have brown dwarf companions, and are sensitive to companions with masses as low as 1 for periods longer than two years. In particular, we conclude that Proxima Centauri has no Jovian companions at orbital periods of 2–12 years. These results complement previously published M dwarf planet occurrence rates by providing astrometrically determined upper mass limits on potential super-Jupiter companions at orbits of two years and longer. As part of a continuing survey, these results are consistent with the paucity of super-Jupiter and brown dwarf companions we find among the over 250 red dwarfs within 25 pc observed longer than five years in our astrometric program.
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