Transiting Planetary Systems with Distant Giant Companions Remain Moderately Coplanar

Abstract: The mutual inclination between inner planets and distant giant companions provides an important probe of planetary system formation and dynamical evolution, yet direct measurements of this quantity remain scarce. We combine radial velocity (RV) observations with Hipparcos--Gaia astrometry to constrain the orbital architecture of 19 planetary systems hosting at least one transiting inner planet and one outer giant companion. Using a hierarchical Bayesian framework, we infer the population-level distribution of the minimum mutual inclination, $ΔI$, between the inner and outer planetary orbits. We find that the $ΔI$ distribution is well described by a Rayleigh model with a scale parameter of $σ= 15.8<sup>{+2.8}_{-2.6}°$, which is strongly preferred over an isotropic distribution ($Δ\log Z=5.45$). This result suggests that transiting systems hosting distant giant companions remain substantially more coplanar than expected for an isotropic population, consistent with the partial preservation of primordial coplanarity. A division by the mass ($0.3\,M_{\rm Jup}$) of the inner transiting planet suggests that giant-inner-planet systems may have lower $ΔI$ than small-inner-planet systems, with $P(σ<em>{\rm giant}&lt;σ</em>{\rm small})=0.952$; however, the current data do not significantly favor a model allowing different $σ$ values for the two subsamples over one in which they share a common $σ$. Future Gaia DR4 astrometry will enable more robust population-level studies of the three-dimensional architectures of systems with distant giant companions.