Mitigating astrometric bias in barycentric correction with PEXO

Extremely precise radial velocity is essential for the detection of sub-m/s radial velocity of stars induced by Earth-like planets. Although modeling of the barycentric correction of radial velocity could achieve 1 mm/s precision, the input astrometry could be biased due to nonlinear motions of stars caused by companions. To account for astrometry-induced bias in barycentric correction, we correct for astrometric bias by minimizing the scatter of reduced RV data with PEXO. In particular, we apply this method to the barycentric correction for 266 stars from HARPS data archive. We find that the RV scatter for 8 targets are significantly reduced due to correction of astrometric bias. Among these targets, 2 targets exhibit bias caused by known massive companions, while for the remaining 6 targets, the bias could be attributed to unknown companions or Gaia systematics. Furthermore, 14 targets have an astrometry-induced annual RV variation higher than 0.05 m/s, and 10 of them are closer than 10 pc. We show the results of Barnard's star as an example, and find that an annual RV bias of 10 cm/s is mitigated by replacing BarCor by PEXO as the barycentric correction code. Our work demonstrates the necessity of astrometric bias correction and the utilization of barycentric correction code within a relativistic framework in high-precision RV for the detection of Earth-like planets.