Eccentric binaries: Periastron events and tidal heating

Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Ave. Universidad s/n, Chamilpa, Cuernavaca, Mexico
e-mail: gloria@icf.unam.mxe-mail: dtrujillo@icf.unam.mx

Received: 22 December 2023
Accepted: 29 February 2024

Abstract

Context. Binary stars cannot be fully understood without assessing the interaction effects between the two components and the impact of these effects on observational diagnostics. Periastron brightening events, also known as the heartbeat phenomenon, are a clear manifestation of this type of interaction.

Aims. We aim to explore the role of tidal shear energy dissipation in stars undergoing periastron brightening events.

Methods. We performed 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 “core” 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_⊙ primary that is perturbed by a 6.97 M_⊙ companion in eccentric orbits (e = 0 − 0.7). The model is then applied to the heartbeat star MACHO 80.7443.1718.

Results. 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 ≤0.3, pseudo-synchronization occurs for 0.8 < ω/Ω_ave < 1, where Ω_ave is the average orbital angular velocity. The minimum energy rotation rate (pseudo-synchronism) for e = 0.5 and 0.7 occurs for 1.0 < ω/Ω_ave < 1.15. The tidal shear energy dissipation model reproduces from first principles the ∼23% maximum brightness enhancement at periastron of MACHO 80.7443.1718.

Conclusions. Our results suggest that the magnitude and shape of the heartbeat signal may serve as diagnostics for the internal stellar rotation and turbulent viscosity values.