We report astrometric results of VLBI phase-referencing observations of 22 GHz H _ { 2 } O masers emission toward the red hypergiant VX Sgr , one of most massive and luminous red hypergiant stars in our Galaxy , using the Very Long Baseline Array .
A background source , J1820 - 2528 , projected 4 { \hbox to 0.0 pt { . } } ^ { \circ } 4 from the target VX Sgr , 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 ^ { +0.11 } _ { -0.10 } kpc .
The measured proper motion of VX Sgr is 0.36 \pm 0.76 and -2.92 \pm 0.78 mas yr ^ { -1 } in the eastward and northward directions .
The parallax and proper motion confirms that VX Sgr belong to the Sgr OB1 association .
Rescaling bolometric luminosities in the literature to our parallax distance , we find the luminosity of VX Sgr is ( 1.95 \pm 0.62 ) \times 10 ^ { 5 } L _ { \odot } , where the uncertainty is dominated by differing photometry measurements .