Astrometry of OH/IR stars using 1612 MHz hydroxyl masers. I. Annual parallaxes of WX Psc and OH138.0+7.2

We report on the measurement of the trigonometric parallaxes of 1612 MHz hydroxyl masers around two asymptotic giant branch stars, WX Psc and OH138.0+7.2, using the NRAO Very Long Baseline Array with in-beam phase referencing calibration. We obtained a 3-sigma upper limit of <=5.3 mas on the parallax of WX Psc, corresponding to a lower limit distance estimate of >~190 pc. The obtained parallax of OH138.0+7.2 is 0.52+/-0.09 mas (+/-18%), corresponding to a distance of 1.9(+0.4,-0.3) kpc, making this the first hydroxyl maser parallax below one milliarcsecond. We also introduce a new method of error analysis for detecting systematic errors in the astrometry. Finally, we compare our trigonometric distances to published phase-lag distances toward these stars and find a good agreement between the two methods.