Tidal Erasure of Stellar Obliquities Constrains the Timing of Hot Jupiter Formation

Stars with hot Jupiters sometimes have high obliquities, which are possible relics of hot Jupiter formation. Based on the characteristics of systems with and without high obliquities, it is suspected that obliquities are tidally damped when the star has a thick convective envelope, as is the case for main-sequence stars cooler than ∼6100 K, and the orbit is within ∼8 stellar radii. A promising theory for tidal obliquity damping is the dissipation of inertial waves within the star's convective envelope. Here, we consider the implications of this theory for the timing of hot Jupiter formation. Specifically, hot stars that currently lack a convective envelope possess one during their pre-main sequence. We find that hot Jupiters orbiting within a critical distance of ∼0.02 au from a misaligned main-sequence star lacking a thick convective envelope must have acquired their tight orbits after a few tens of millions of years in order to have retained their obliquities throughout the pre-main sequence. There are four known systems for which this argument applies-XO-3b, Corot-3b, WASP-14b, and WASP-121b-subject to uncertainties surrounding inertial wave dissipation. Moreover, we conclude that a recently identified overabundance of near-polar hot Jupiters is unlikely sculpted by tides, instead reflecting their primordial configuration. Finally, hot Jupiters arriving around cool stars after a few hundreds of millions of years likely find the host star rotating too slowly for efficient obliquity damping. We predict that the critical effective temperature separating aligned and misaligned stars should vary with metallicity, from 6300 to 6000 K as [Fe/H] varies from -0.3 to +0.3.