Joint constraints on the mass and projected separation of a companion to 12 Psc based only on the measured RV trend (left) and using both the RV trend and the astrometric acceleration (right). The hydrogen-burning limit (HBL; ≈75 M_Jup) and deuterium-burning limit (≈13 M_Jup) are labeled. Based on the strength of the radial acceleration, the companion would be a brown dwarf or giant planet at close separations of ≲20 au; more massive stellar or white dwarf companions are required on wider orbits. When the HGCA acceleration is included, the range of possible masses and separations is more limited. The measured separation and dynamical mass of 12 Psc B (from Section 4.5) are shown with the star.