Possible fluctuation of the position of Sagittarius A* relative to extragalactic radio sources

When we measure the position of an extragalactic radio source through the Galaxy, apparent position wander will be induced because of the gravitational deflection by intervening stars in the Galaxy. When measuring the annual parallax of a radio source with respect to the nearby extragalactic radio sources, such position wander should be taken into account. This effect is especially serious in the case of the trigonometric measurement of Sgr A*, located in the Galactic center. We estimated the optical depth and the event rate of the position wander of the extragalactic radio sources near Sgr A* and found that such position wander degrades the measurement of trigonometric parallax of Sgr A* significantly. For observations with an accuracy of 10 muas, the probability of degradation is a few tens of percent. Several years of continuous observation are needed for the separation of this gravitational position wander from the annual parallactic motion. Even for observations with an accuracy of 25 muas, a few years of continuous observation are needed to eliminate the effect of position wander.