Structure and evolution of a tidally heated star
The shearing motion of tidal flows that are excited in non-equilibrium binary stars transform kinetic energy into heat via a process referred to as tidal heating. In this paper we aim to explore the way tidal heating affects the stellar structure. We used the TIDES code, which solves the equations of motion of the three-dimensional (3D) grid of volume elements that conform multiple layers of a rotating binary star to obtain an instantaneous value for the angular velocity, $ω''$, as a function of position in the presence of gravitational, centrifugal, Coriolis, gas pressure, and viscous forces. The released energy, $\dot{E,}$ was computed using a prescription for turbulent viscosity that depends on the instantaneous velocity gradients. The $\dot{E}$ values for each radius were injected into a MESA stellar structure calculation. The method is illustrated for a 1.0+0.8 M$_\odot$ binary system, with an orbital period of $P$=1.44d and departures from synchronous rotation of 5% and 10%. We find that heated models have a larger radius and surface luminosity, a smaller surface convection zone, and lower nuclear reaction rates than the equivalent standard stellar models, and their evolutionary tracks extend to higher temperatures. The magnitude of these effects depends on the amount of injected energy, which, for a fixed set of stellar, rotation and orbital parameters, depends on the perturbed star's density structure and turbulent viscosity. Tidal heating offers a possible alternative for describing phenomena such as bloated or overluminous binary components, age discrepancies, and aspherical mass ejection, as well as the extended main sequence turnoff in clusters. However, establishing its actual role requires 3D stellar structure models commensurate with the nonspherically symmetric properties of tidal perturbations.