Updated Mutual Inclination Measurement for 14 Her b and c

Abstract

The mutual inclination $\psi$ between orbits within multi-planetary systems is difficult to measure directly. Through a joint analysis of RVs, Hipparcos-Gaia absolute astrometry and relative astrometry of JWST, \citet{Bardalez2025} recently found two possible values of $\psi_{bc}={32_{-15.1}^{+13.6}}^{\circ}$ and $\psi_{bc}={145.0_{-11.1}^{+15.8}}^{\circ}$ for the nearby, non-transit planet system, 14\,Her. By incorporating additional astrometry from Gaia second data release (DR2), we have further constrained the orbital orientation of 14\,Her\,b, resulting in a definitive and unambiguous mutual inclination of $\psi_{bc}={35.3_{-7.3}^{+6.8}}^{\circ}$. The unusual misaligned orbital architecture of 14\,Her system may serve as a benchmark for dynamical studies.