Updated Mutual Inclination Measurement for 14 Her b and c

TL;DR

This study refines the measurement of the mutual inclination between planets in the 14 Her system using combined astrometric data, revealing a definitive orbital configuration that informs dynamical theories.

Contribution

It provides the first unambiguous measurement of the mutual inclination in the 14 Her system by incorporating Gaia DR2 data, improving previous estimates.

Findings

Mutual inclination of 14 Her b and c is approximately 35.3 degrees.

The orbital architecture of 14 Her is confirmed as significantly misaligned.

Results serve as a benchmark for dynamical studies of planetary systems.

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.