Eccentric binaries: Periastron events and tidal heating

Periastron brightening events, also known as the heartbeat phenomenon, are a clear manifestation of interaction effects in binary systems. We explore the role of tidal shear energy dissipation in stars undergoing periastron brightening events by performing a computation from first principles that uses a quasi-hydrodynamic Lagrangian scheme to simultaneously solve the orbital motion and the equations of motion of a 3D grid of volume elements covering the inner, rigidly rotating region of a tidally perturbed star. The equations of motion include the gravitational acceleration of both stars, the centrifugal, Coriolis, gas pressure accelerations, and viscous coupling between volume elements. The method is illustrated for a grid of model binary systems with a 10 M$_\odot$ primary that is perturbed by a 6.97 M$_\odot$ companion in eccentric orbits (e=0 $-$ 0.7). The model is then applied to the heartbeat star MACHO 80.7443.1718. We find an increase by factors 10$^{-6}$ $-$10$^{-3}$ in tidal shear energy dissipation at periastron, consistent with the majority of observed heartbeat stars. The magnitude of the periastron effect correlates with the degree of departure from synchronicity: stars rotating much faster or much slower than the synchronous rate at periastron present the strongest effect. We confirm that for eccentricities $\leq$0.3, pseudo-synchronization occurs for 0.8$< \omega/\Omega_{ave} <$1, where $\Omega_{ave}$ is the average orbital angular velocity. However, we find that the rotation rate with minimum energy for e=0.5 and 0.7 occurs for $\omega/\Omega_{ave}>$1 . The tidal shear energy dissipation model reproduces from first principles the 23% maximum brightness enhancement at periastron of MACHO 80.7443.1718. The extraordinarily large hearbeat amplitude is likely due to a rotation rate that differs considerably from the synchronous rate at periastron.