Influence of the Galactic gravitational field on the positional accuracy of extragalactic sources

We investigate the influence of random variations of the Galactic gravitational field on the apparent celestial positions of extragalactic sources. The basic statistical characteristics of a stochastic process (first-order moments, an autocorrelation function and a power spectral density) are used to describe a light ray deflection in a gravitational field of randomly moving point masses as a function of the source coordinates. We map a 2D distribution of the standard deviation of the angular shifts in positions of distant sources (including reference sources of the International Celestial Reference Frame) with respect to their true positions. For different Galactic matter distributions the standard deviation of the offset angle can reach several tens of $\mu as$ (microarcsecond) toward the Galactic center, decreasing down to 4-6 $\mu as$ at high galactic latitudes. The conditional standard deviation (`jitter') of 2.5 $\mu as$ is reached within 10 years at high galactic latitudes and within a few months toward the inner part of the Galaxy. The photometric microlensing events are not expected to be disturbed by astrometric random variations anywhere except the inner part of the Galaxy as the Einstein--Chvolson times are typically much shorter than the jittering timescale. While a jitter of a single reference source can be up to dozens of $\mu as$ over some reasonable observational time, using a sample of reference sources would reduce the error in relative astrometry. The obtained results can be used for estimating the physical upper limits on the time-dependent accuracy of astrometric measurements.