Tidal Circularization of Binaries by Resonance Locking I: The Importance of the Pre-Main-Sequence.

Although tidal dissipation in binary stars has been studied for over a century, theoretical predictions have yet to match the observed properties of binary populations. This work quantitatively examines the recent proposal of tidal circularization by resonance locking, where tidal dissipation arises from resonances between the star's natural oscillation frequencies and harmonics of the orbital frequency, and where resonances are `locked' for an extended period of time due to concurrent stellar evolution. We focus on tidal resonances with axi-symmetric gravity-modes, and examine binaries with primary masses from one to two solar masses. We find that orbital evolution via resonance locking occurs primarily during the star's pre-main-sequence phase, with the main-sequence phase contributing negligibly. Resonance locking, ignoring non-linearity, can circularize binaries with peri-centre distances out to $\sim 10$ stellar radii, corresponding to circular periods of $\sim 4-6$ days. However, we find resonantly excited gravity-modes will become nonlinear in stellar cores, which prevents them from reaching their full, linear amplitudes. We estimate that such a `saturated resonance lock' reduces the circularization period by about a third, but resonance locking remains much more effective than the cumulative actions of equilibrium tides. In a companion paper, we examine recent binary data to compare against theory.