From Images to Orbits: A Hubble 2030s Astrometric Legacy for the M31-M33 Star Cluster Systems

Abstract: The most irreplaceable capability of HST in the 2030s is not only its angular resolution or its UV--optical sensitivity, but its accumulated time baseline. We recommend a Hubble Local Group Astrometric Legacy that would obtain matched 2030s ACS/WFC and WFC3/UVIS imaging of selected M31 and M33 star cluster fields, combine those observations with a careful astrometric audit of the existing archive, and deliver public transverse velocity products through MAST. PHAT and PHATTER already provide exceptional first epochs across the nearest large external spirals, resolving tens to hundreds of millions of stars and identifying thousands of star clusters and compact background reference objects. Earlier targeted HST programs, dating back to the mid 90's, can extend the temporal baseline in selected cases, but only after camera, chip, filter, dithering, crowding, and reference-frame triage. A coherent 2030s repeat campaign would turn the best of this archive into bulk cluster motions, enabling the first systematic orbital mapping of star cluster populations beyond the Milky Way. These measurements would constrain disk heating, cluster disruption, accretion histories, stream associations, the M31--M33 interaction, and the mass distributions of Local Group spirals. The same program would also preserve and stress-test the calibration infrastructure needed for high-stability optical/UV astrophysics in the HWO era: geometric-distortion solutions, PSF and CTE modeling, matched-epoch observing strategies, long-term reference frames, and durable public high-level products.