Constraining stellar tidal quality factors from planet-induced stellar spin-up

The dynamical evolution of tight star-planet systems is influenced by tidal interactions between the star and the planet, as was shown recently. The rate at which spins and orbits in such a system evolve depends on the stellar and planetary tidal dissipation efficiency. Here, we present a method to constrain the modified tidal quality factor $Q'_*$ of a planet-hosting star whose rotational evolution has been altered by its planet through angular momentum transfer from the planetary orbital motion to the rotation of the stellar convective zone. The altered rotation is estimated from an observed discrepancy of magnetic activity of the planet-hosting star and a coeval companion star, i.e. this method is applicable to star-planet systems with wide stellar companions. We give an example of the planet-hosting wide binary system HD189733 and find that the planet host's modified tidal quality factor is constrained to be $Q'_* \leq 2.33 \times 10^7$.