On a Possible Solution to the Tidal Realignment Problem for Hot Jupiters

Hot stars with hot Jupiters have a wide range of obliquities, while cool stars with hot Jupiters tend to have low obliquities. An enticing explanation for this pattern is tidal realignment of the cool host stars, although this explanation assumes that obliquity damping occurs faster than orbital decay, an assumption that needs further exploration. Here we revisit this tidal realignment problem, building on previous work identifying a low-frequency component of the time-variable tidal potential that affects the obliquity but not the orbital separation. We adopt a recent empirically-based model for the stellar tidal quality factor and its sharp increase with forcing frequency. This leads to enhanced dissipation at low frequencies, and efficient obliquity damping. We model the tidal evolution of 46 observed hot Jupiters orbiting cool stars. A key parameter is the stellar age, which we determine in a homogeneous manner for the sample, taking advantage of Gaia DR2 data. We explore a variety of tidal histories and futures for each system, finding in most cases that the stellar obliquity is successfully damped before the planet is destroyed. A testable prediction of our model is that hot-Jupiter hosts with orbital periods shorter than 2--3 days should have obliquities much smaller than $1^\circ$. With the possible exception of WASP-19b, the predicted future lifetimes of the planets range from $10^8$\,yr to more than $10^{10}$\,yr. Thus, our model implies that these hot Jupiters are probably not in immediate danger of being devoured by their host stars while they are on the main sequence.