VLBA determination of the distance to nearby star-forming regions.: I.: The distance to T Tauri with 0.4% accuracy

In this article, we present the results of a series of 12 3.6 cm radio continuum observations of T Tau Sb, one of the companions of the famous young stellar object T Tauri. The data were collected roughly every 2 months between 2003 September and 2005 July with the Very Long Baseline Array (VLBA). Thanks to the remarkably accurate astrometry delivered by the VLBA, the absolute position of T Tau Sb could be measured with a precision typically better than about 100 mu as at each of the 12 observed epochs. The trajectory of T Tau Sb on the plane of the sky could therefore be traced very precisely and was modeled as the superposition of the trigonometric parallax of the source and an accelerated proper motion. The best fit yields a distance to T Tau Sb of 147.6 +/- 0.6 pc. The observed positions of T Tau Sb are in good agreement with recent infrared measurements, but they seem to favor a somewhat longer orbital period than that recently reported by Duchene and coworkers for the T Tau Sa/T Tau Sb system.