Empirical Constraints on Tidal Dissipation in Exoplanet Host Stars

Abstract

The orbits of short-period exoplanets are sculpted by tidal dissipation. However, the mechanisms and associated efficiencies of these tidal interactions are poorly constrained. We present robust constraints on the tidal quality factors of short-period exoplanetary host stars through the usage of a novel empirical technique. The method is based on analyzing structures in the population-level distribution of tidal decay times, defined as the time remaining before a planet spirals into its host star due to stellar tides. Using simple synthetic planet population simulations and analytic theory, we show that there exists a steady-state portion of the decay time distribution with an approximately power-law form. This steady-state feature is clearly evident in the decay time distribution of the observed short-period planet population. We use this to constrain both the magnitude and frequency dependence of the stellar tidal quality factor and show that it must decrease sharply with planetary orbital period. Specifically, with $Q_{\star}' = Q_0 (P/2 \ \mathrm{days})^{\alpha}$, we find $10^{5.5} \lesssim Q_0 \lesssim 10^7$ and $-4.33 \lesssim \alpha \lesssim -2$. Our results are most consistent with predictions from tidal resonance locking, in which the planets are locked into resonance with a tidally excited gravity mode in their host stars.