The Parallax of the Red Hypergiant VX Sgr with Accurate Tropospheric Delay Calibration

We report astrometric results of VLBI phase-referencing observations of 22 GHz \hho\ masers emission toward the red hypergiant \vxsgr, one of most massive and luminous red hypergiant stars in our Galaxy, using the Very Long Baseline Array. A background source, \Jtwoze, projected 4\d4 from the target \vxsgr, was used as the phase reference. For the low declinations of these sources, such a large separation normally would seriously degrade the relative astrometry. We use a two-step method of tropospheric delay calibration, which combines the VLBI geodetic-block (or GPS) calibration with an image-optimization calibration, to obtain a trigonometric parallax of $0.64\pm 0.04$ mas, corresponding to a distance of 1.56${}_{-0.10}^{+0.11}$ kpc. The measured proper motion of \vxsgr\ is $0.36\pm 0.76$ and $-2.92\pm 0.78$ \masy\ in the eastward and northward directions. The parallax and proper motion confirms that \vxsgr
belong to the Sgr OB1 association. Rescaling bolometric luminosities in the literature to our parallax distance, we find the luminosity of \vxsgr~is $(1.95 \pm 0.62) \times 10^5$ \Lsun, where the uncertainty is dominated by differing photometry measurements.