The $sim500$, Myr A2IV star HR 1645 has one of the most significant low-amplitude accelerations of nearby early-type stars measured from a comparison of the {it Hipparcos} and {it Gaia} astrometric catalogues. This signal is consistent with either a stellar companion with a moderate mass ratio ($qsim0.5$) on a short period ($P<1$,yr), or a substellar companion at a separation wide enough to be resolved with ground-based high contrast imaging instruments; long-period equal mass ratio stellar companions that are also consistent with the measured acceleration are excluded with previous imaging observations. The small but significant amplitude of the acceleration made HR 1645 a promising candidate for targeted searches for brown dwarf and planetary-mass companions around nearby, young stars. In this paper we explore the origin of the astrometric acceleration by modelling the signal induced by a wide-orbit M8 companion discovered with the Gemini Planet Imager, as well as the effects of an inner short-period spectroscopic companion discovered a century ago but not since followed-up. We present the first constraints on the orbit of the inner companion, and demonstrate that it is a plausible cause of the astrometric acceleration. This result demonstrates the importance of vetting of targets with measured astrometric acceleration for short-period stellar companions prior to conducting targeted direct imaging surveys for wide-orbit substellar companions.
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