Differential proper motion spin of the Hipparcos and Gaia celestial reference frames

Abstract: The Hipparcos catalog provides the first epoch of the celestial reference frame (CRF) in the optical domain and serves as an indispensable tool to verify and improve the Gaia CRF for the brighter stars ($V<11$ mag) and to identify the elusive astrometric binary stars with dim or invisible companions, including long-period exoplanets. The systems of positions in Hipparcos and Gaia cannot be directly compared, because they refer to two different mean epochs. It is shown that the proper motion systems for carefully filtered common stars are not statistically consistent within the given formal errors. The vector field of proper motion differences is fitted with 126 vector spherical harmonics up to degree 7 revealing a global pattern at high signal-to-noise ratios, including the three terms of rigid rotation. The origin of the differential spin and other large harmonic terms is investigated by producing a similar decomposition of the Gaia$-$HG proper motion field, where HG stands for the long-term proper motions derived from the Hipparcos and Gaia DR3 positions, for the same sample of stars. Hipparcos proper motions emerge as the largest source of sky-correlated distortions of the multi-epoch optical CRF with a median value of $\sim 190$ $\mu$as yr$^{-1}$ and a global spin of $\sim 226$ $\mu$as yr$^{-1}$, while the Hipparcos positions and Gaia EDR3 proper motions are explicitly consistent by construction at a level of $\sim 10$ $\mu$as yr$^{-1}$. The latter, however, include multiple distortions of higher degree, which should be taken into account in astrometric applications using the HG field.