Tidal coplanarization of circumbinary planetary systems through stellar Cassini states

Circumbinary planets (CBPs) currently identified are in nearly coplanar configurations relative to their host binaries, yet the dynamical origin of this preference remains unclear. We investigate this question by simulating the secular spin-orbit evolution of CBP systems with tidal decay. A representative case shows that the system evolves through three stages (coplanarization, spin-orbit synchronization, and spin-orbit alignment) through the angular momentum exchange between stellar spin and orbital motion. The evolution of mutual inclination is strongly coupled to stellar obliquity. Phase-space analysis and examination of stellar Cassini states reveal that arbitrary initial inclinations are gradually damped to coplanarity by tides, while stellar obliquity is adiabatically captured into Cassini states with diminishing oscillation amplitudes. This study provides a self-consistent analytical and numerical framework for determining stellar Cassini states and understanding coupled spin-orbit evolution in CBP systems. It shows that tidal dissipation, combined with adiabatic capture into Cassini states, drives the observed dynamical behavior.