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We conducted multi-epoch VLBI observations to search for astrometric reflexmotion caused by a sub-stellar companion of the M8.5 dwarf TVLM 513-46546. Theobservations yield an absolute parallax corresponding to a distance of10.762+/-0.027 pc and a proper motion of 78.09+/-0.17 mas/yr. From the absenceof significant residual motion, we place an upper limit to any reflex motioncaused by a companion, extending the parameter space covered by previousnear-infrared direct-imaging searches. By covering different orbital periods,the data exclude a phase-space of companion masses and orbital periods rangingfrom 3.8 Mjup with an orbital radius of ~0.05 AU (orbital period of 16 days) to0.3 Mjup with an orbital radius of ~0.7 AU (orbital period of 710 days).

An Astrometric Search for a Sub-stellar Companion of the M8.5 Dwarf TVLM 513-46546 Using Very Long Baseline Interferometry