Tidal evolution of the spin-orbit angle in exoplanetary systems

The angle between the stellar spin and the planetary orbit axes (spin-orbit angle) is supposed to carry valuable information on the initial condition of the planet formation and the subsequent migration history. Indeed current observations of the Rossiter- McLaughlin effect have revealed a wide range of spin-orbit misalignments for transiting exoplanets. We examine in detail the tidal evolution of a simple system comprising a Sun-like star and a hot Jupiter adopting the equilibrium tide and the inertial wave dissipation effects simultaneously. We find that the combined tidal model works as a very efficient realignment mechanism; it predicts three distinct states of the spin-orbit angle (i.e., parallel, polar, and anti-parallel orbits) for a while, but the latter two states eventually approach the parallel spin-orbit configuration. The intermediate spin-orbit angles as measured in recent observations are difficult to be achieved. Therefore the current model cannot reproduce the observed broad distribution of the spin-orbit angles, at least in its simple form. This indicates that the observed diversity of the spin-orbit angles may emerge from more complicated interactions with outer planets and/or may be the consequence of the primordial misalignment between the proto-planetary disk and the stellar spin, which requires future detailed studies.