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.
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