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Tides in Close Binary Systems

Abstract

We consider three aspects of tidal interactions in close binary systems. 1) We first develop a framework for predicting and interpreting photometric observations of eccentric binaries, which we term tidal asteroseismology. In such systems, the Fourier transform of the observed lightcurve is expected to consist of pulsations at harmonics of the orbital frequency. We use linear stellar perturbation theory to predict the expected pulsation amplitude spectra. Our numerical model does not assume adiabaticity, and accounts for stellar rotation in the traditional approximation. We apply our model to the recently discovered Kepler system KOI-54, a 42-day face-on stellar binary with e=0.83. Our modeling yields pulsation spectra that are semi-quantitatively consistent with observations of KOI-54. KOI-54's spectrum also contains several nonharmonic pulsations, which can be explained by nonlinear three-mode coupling. 2) We next consider the situation of a white dwarf (WD) binary inspiraling due to the emission of gravitational waves. We show that resonance locks, previously considered in binaries with an early-type star, occur universally in WD binaries. In a resonance lock, the orbital and spin frequencies evolve in lockstep, so that the tidal forcing frequency is approximately constant and a particular normal mode remains resonant, producing efficient tidal dissipation and nearly synchronous rotation. We derive analytic formulas for the tidal quality factor and tidal heating rate during a g-mode resonance lock, and verify our results numerically. We apply our analysis to the 13-minute double-WD binary J0651, and show that our predictions are roughly consistent with observations. 3) Lastly, we examine the general dynamics of resonance locking in more detail. Previous analyses of resonance locking, including my own earlier work, invoke the adiabatic (a.k.a. Lorentzian) approximation for the mode amplitude, valid only in the limit of relatively strong mode damping. We relax this approximation, analytically derive conditions under which the fixed point associated with resonance locking is stable, and further check our analytic results with numerical integration of the coupled mode, spin, and orbital evolution equations. These show that resonance locking can sometimes take the form of complex limit cycles or even chaotic trajectories. We also show that resonance locks can accelerate the course of tidal evolution in eccentric systems.

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