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On the tidal origin of hot Jupiter stellar obliquity trends

It is debated whether the two hot Jupiter populations --- those on orbits misaligned from their host star's spin axis and those well-aligned --- result from two migration channels or from two tidal realignment regimes. Here I demonstrate that equilibrium tides raised by a planet on its star can account for three observed spin-orbit alignment trends: the aligned orbits of hot Jupiters orbiting cool stars, the planetary mass cut-off for retrograde planets, and the stratification by planet mass of cool host stars' rotation frequencies. The first trend can be caused by strong versus weak magnetic braking (the Kraft break), rather than realignment of the star's convective envelope versus the entire star. The second trend can result from a small effective stellar moment of inertia participating in the tidal realignment in hot stars, enabling massive retrograde planets to partially realign to become prograde. The third trend is attributable to higher mass planets more effectively counteracting braking to spin up their stars. Both hot and cool star require a small effective stellar moment of inertia participating in the tidal realignment, e.g., an outer layer weakly coupled to the interior. I demonstrate via Monte Carlo that this model can match the observed trends and distributions of sky-projected misalignments and stellar rotation frequencies. I discuss implications for inferring hot Jupiter migration mechanisms from obliquities, emphasizing that even hot stars do not constitute a pristine sample.