  Accelerations of both the solar system barycenter (SSB) and stars in the
Milky Way cause a systematic observational effect on the stellar proper
motions, which was first studied in the early 1990s and developed by J.
Kovalevsky (aberration in proper motions, 2003, A&A, 404, 743). This paper
intends to extend that work and aims to estimate the magnitude and significance
of the aberration in proper motions of stars, especially in the region near the
Galactic center. We adopt two models for the Galactic rotation curve to
evaluate the aberrational effect on the Galactic plane. Based on the
theoretical developments, we show that the effect of aberration in proper
motions depends on the galactocentric distance of stars; it is dominated by the
acceleration of stars in the central region of the Galaxy. Within 200 pc from
the Galactic center, the systematic proper motion can reach an amplitude larger
than 1000 uas/yr by applying a flat rotation curve. With a more realistic
rotation curve which is linearly rising in the core region of the Galaxy, the
aberrational proper motions are limited up to about 150 uas/yr. Then we
investigate the applicability of the theoretical expressions concerning the
aberrational proper motions, especially for those stars with short period
orbits. If the orbital period of stars is only a fraction of the light time
from the star to the SSB, the expression proposed by Kovalevsky is not
appropriate. With a more suitable formulation, we found that the aberration has
no effect on the determination of the stellar orbits on the celestial sphere.
The aberrational effect under consideration is small but not negligible with
high-accurate astrometry in the future, particularly in constructing the Gaia
celestial reference system realized by Galactic stars.
