Misaligned Disk and Stellar Oblateness Driven Sculpting of Exoplanetary Systems: Origin of Perpendicular Orbits in HD 3167

A significant proportion of exoplanets have been detected with highly tilted or even polar orbits relative to their host stars' equatorial planes. These unusual orbital configurations are often linked to post-disk secular interactions among multiple bodies. However, many aspects remain elusive. In this study, we investigate the role of disk-induced spin-orbit misalignments in shaping architecture of multi-planet systems, taking into account the combined effect of the host star's oblateness and the full-space disk potential. We demonstrate that large mutual planetary inclinations can arise from a saddle-center bifurcation occurring during the photoevaporation of the disk. This bifurcation triggers an instant, non-adiabatic transition in the planet's libration. Following this process, the orbital evolution diverges into several distinct patterns. Notably, in scenarios involving a near-polar primordial misalignment, the orbit, consistently librating about a coplanar equilibrium axis, can be captured by an orthogonal equilibrium during the decay of the stellar oblateness. However, the orbit will be eventually recaptured by the coplanar equilibrium, aligned or anti-aligned with the orientation of the outer orbit, resulting in either a prograde or retrograde inner-outer orbit configuration. Additionally, general relativity contributes to maintaining eccentricity stability within these dynamic scenarios. Through the proposed mechanism, we can provide a plausible explanation for the unique, near-perpendicular and likely retrograde orbit architecture observed in the HD 3167 system, enhancing our understanding of exoplanetary system dynamics.