2011A&A...528A..48M

A number of binary systems present evidence of enhanced activity around periastron passage, suggesting a connection between tidal interactions and these periastron effects. The aim of this investigation is to study the time-dependent response of a star's surface as it is perturbed by a binary companion. Here we focus on the tidal shear energy dissipation. We derive a mathematical expression for computing the rate of dissipation, {dot}(E), of the kinetic energy by the viscous flows that are driven by tidal interactions on the surface layer of a binary star. The method is tested by comparing the results from a grid of model calculations with the analytical predictions of Hut (1981A&A....99..126H) and the synchronization timescales of Zahn (1977A&A....57..383Z; 2008, EAS Pub. Ser., 29, 67). Our results for the dependence of the average (over orbital cycle) energy dissipation, {dot}(E)_ave, on orbital separation are consistent with those of Hut (1981) for model binaries with an orbital separation at periastron r_per/R₁>8, where R₁ is the stellar radius. The model also reproduces the predicted pseudo-synchronization angular velocity for moderate eccentricities (e≤0.3). In addition, for circular orbits our approach yields the same scaling of synchronization timescales with orbital separation as given by Zahn (1977, 2008) for convective envelopes. The computations give the distribution of {dot}(E) over the stellar surface, and show that it is generally concentrated at the equatorial latitude, with maxima generally located around four clearly defined longitudes, corresponding to the fastest azimuthal velocity perturbations. Maximum amplitudes occur around periastron passage or slightly thereafter for supersynchronously rotating stars. In very eccentric binaries, the distribution of {dot}(E) over the surface changes significantly as a function of orbital phase, with small spatial structures appearing after periastron. An exploratory calculation for a highly eccentric binary system with parameters similar to those of δ Sco (e=0.94, P=3944.7d) indicates that {dot}(E)_ave changes by ∼5 orders of magnitude over the 82 days before periastron, suggesting that the sudden and large amplitude variations in surface properties around periastron may, indeed, contribute toward the activity observed around this orbital phase.