Astrometric Radial Velocities from the Hipparcos-Gaia Catalog of Accelerations and Implications for Astrometric Acceleration Measurements

Abstract

Astrometry from the Gaia satellite and from the long-term combination of Hipparcos and Gaia are now sensitive to sky-plane accelerations as low as $\approx$1 m/s/yr. This paper quantifies and explores an important caveat: apparent nonlinear motion due to a star's nonzero radial velocity can be indistinguishable from real astrometric acceleration. This nonlinear motion is parallel to the proper motion, so it can be both quantified and avoided by projecting apparent astrometric accelerations into components parallel and perpendicular to the proper motion. We illustrate this distinction for a sample of very nearby, fast-moving stars from the Hipparcos-Gaia Catalog of Accelerations (HGCA). We then generalize the effect of stellar radial velocity and projections of the astrometric acceleration to binary stars in which we observe the acceleration of both components. Finally, we demonstrate that the proper motion differences in the HGCA are statistically well-behaved even for the nearest and fastest-moving stars, at least in the component perpendicular to the proper motion. This distinction -- between astrometric acceleration parallel and perpendicular to proper motion -- could have important consequences for future missions reaching extreme astrometric sensitivities around nearby stars.