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

TL;DR

This work addresses how nonzero stellar radial velocities can produce apparent astrometric accelerations that mimic real sky-plane accelerations in HGCA/Gaia analyses. By decomposing the astrometric acceleration into parallel and perpendicular components relative to the proper motion and modeling the dependence on the radial velocity, the authors quantify how RV uncertainty bias the inferred accelerations and extend the framework to binary systems where both components are accelerated. The key finding is that the acceleration component parallel to the proper motion is sensitive to the RV, while the perpendicular component remains robust, enabling RV inference and more reliable constraints in binaries; for very nearby, fast-moving stars the RV effect can be significant and must be accounted for in high-precision astrometry. These results have practical implications for upcoming missions (e.g., TOLIMAN, LIFE) by informing observing strategies and analysis pipelines to mitigate perspective acceleration and maximize sensitivity to true accelerations around nearby stars.

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.

Figures (7)

• Figure 1: Difference between the long-term and Gaia EDR3 proper motions in the HGCA for HIP 114046 (=HD 217987), scaled by their time difference and interpreted as an acceleration. The error ellipse is computed from the sum of the covariance matrices for the two proper motions. HIP 114046 appears to show astrometric acceleration---a nonzero difference in proper motion---at about $2.6\sigma$ significance.
• Figure 2: Same as Figure \ref{['fig:firstexample']}, but with an error ellipse in orange that minimizes the HGCA $\chi^2$ by changing the assumed stellar RV. This minimum $\chi^2$ is $\approx$2.4, or $\approx$1.5$\sigma$ given the single remaining degree of freedom. The direction of proper motion is shown with the black arrow and thick blue line.
• Figure 3: Similar to Figure \ref{['fig:firstexample_withRV']} but for a selection of nearby stars showing different behaviors. Clockwise from top left: Proxima Centauri has an astrometric acceleration consistent with zero in the HGCA. Barnard's Star is a highly significant accelerator in the HGCA, but for a slightly different RV, the significance of this acceleration drops below 1$\sigma$. Kapteyn's Star, an exceptionally fast mover, remains $\approx$4$\sigma$ inconsistent with constant proper motion even after optimizing the assumed RV. HIP 21088 (=Stein 2051) remains inconsistent with constant proper motion, but the direction of the measured acceleration matches the orientation of the known white dwarf companion Giammichele+Bergeron+Dufour+2012Sahu+Anderson+Casertano+etal_2017.
• Figure 4: Left to right: $\chi^2$ for the binaries Gl 725 AB, 61 Cyg AB, and Gl 338 AB computed using Equations \ref{['eq:chisq_binary']} (top) and \ref{['eq:chisq_binary_full']} (bottom). Equation \ref{['eq:chisq_binary_full']} can achieve tighter constraints on RV at the partial expense of precision on mass ratio thanks to its separate constraints that the two acceleration vectors in a binary each point to the other star; this is most apparent for the 61 Cyg AB system (middle panels). The inner and outer black contours on each panel enclose 68.3% and 95.4% of the numerically integrated probability, respectively. The cyan stars indicate the RVs in the HGCA and the mass ratios inferred from photometry Kervella+Merand+Pichon+etal_2008Mann+Feiden+Gaidos+etal_2015Kervella+Arenou+Mignard+etal_2019, while the blue circle indicates the dynamical mass measurement of 61 Cyg AB by Giovinazzi+Blake+Robertson+etal_2025.
• Figure 5: Left: histogram of $\chi^2$ values from the HGCA Brandt_2021 for stars within 30 pc, compared with the $\chi^2$ distribution with two degrees of freedom. There is a small excess of stars showing apparently real accelerations. Right: the same $\chi^2$ values, but for a sample of nearby, high proper motion stars whose astrometric corrections are especially sensitive to the assumed RV as described in Section \ref{['sec:RVimpact']}. A larger fraction of these appear to be accelerating. The orange histogram indicates those stars with known companions that are expected to induce significant astrometric accelerations, as indicated by 'y' in Table \ref{['tab:nearbystars']}. The $\chi^2$ distribution on the right is normalized to the number of stars in the blue histogram, i.e., those without known and astrometrically significant companions.