Rotation Period Evolution in Low-mass Binary Stars: The Impact of Tidal Torques and Magnetic Braking

We examine how tides, stellar evolution, and magnetic braking shape the rotation period (P rot) evolution of low-mass stellar binaries up to orbital periods (P orb) of 100 days across a wide range of tidal dissipation parameters using two common equilibrium tidal models. We find that many binaries with P orb ≲ 20 days tidally lock, and most with P orb ≲ 4 days tidally lock into synchronous rotation on circularized orbits. At short P orb, tidal torques produce a population of fast rotators that single-star-only models of magnetic braking fail to produce. In many cases, we show that the competition between magnetic braking and tides produces a population of subsynchronous rotators that persists for 1 Gyr, even in short-P orb binaries, qualitatively reproducing the subsynchronous eclipsing binaries discovered in the Kepler field by Lurie et al. Both equilibrium tidal models predict that binaries can tidally interact out to P orb ≈ 80 days, while the constant phase lag tidal model predicts that binaries can tidally lock out to P orb ≈ 100 days. Tidal torques often force the P rot evolution of stellar binaries to depart from the long-term magnetic-braking-driven spin-down experienced by single stars, revealing that P rot is not a valid proxy for age in all cases, i.e., gyrochronology can underpredict ages by up to 300% unless one accounts for binarity. We suggest that accurate determinations of orbital eccentricties and P rot can be used to discriminate between which equilibrium tidal models best describe tidal interactions in low-mass binary stars.