Turbulent viscosity acting on the equilibrium tidal flow in convective stars

Abstract

Convection is thought to act as a turbulent viscosity in damping tidal flows and in driving spin and orbital evolution in close convective binary systems. This turbulent viscosity should be reduced, compared to mixing-length predictions, when the forcing (tidal) frequency $|{\omega }_t|$ exceeds the turnover frequency ${\omega }_{cv}$ of the dominant convective eddies. However, two contradictory scaling laws have been proposed and this issue remains highly disputed. To revisit this controversy, we conduct the first direct numerical simulations (DNS) of convection interacting with the equilibrium tidal flow in an idealized global model of a low-mass star. We present direct computations of the turbulent effective viscosity, ${\nu }_E$, acting on the equilibrium tidal flow. We unexpectedly report the coexistence of the two disputed scaling laws, which reconciles previous theoretical (and numerical) findings. We recover the universal quadratic scaling ${\nu }_E\propto (|{\omega }_t|/{\omega }_{cv}{)}^{-2}$ in the high-frequency regime $|{\omega }_t|/{\omega }_{cv}\gg 1$. Our results also support the linear scaling ${\nu }_E\propto (|{\omega }_t|/{\omega }_{cv}{)}^{-1}$ in an intermediate regime with $1\le |{\omega }_t|/{\omega }_{cv}=\mathcal{O}(10)$. Both regimes may be relevant to explain the observed properties of close binaries, including spin synchronization of solar-type stars and the circularization of low-mass stars. The robustness of these two regimes of tidal dissipation, and the transition between them, should be explored further in more realistic models. A better understanding of the interaction between convection and tidal flows is indeed essential to correctly interpret observations of close binary stars and short-period planetary orbits.

13 pages, 7 figures, 2 tables, published 2020 January 16 in ApJL, typos corrected

References in corpus (13)

• Tidal dissipation in stars and giant planets
• Scaling regimes in spherical shell rotating convection
• Tidal dissipation in binary systems
• Observational Evidence for Tidal Interaction in Close Binary Systems
• Tidal Synchronization and Differential Rotation of Kepler Eclipsing Binaries
• The EBLM Project IV. Spectroscopic orbits of over 100 eclipsing M dwarfs masquerading as transiting hot-Jupiters
• An Observational Study of Tidal Synchronization in Solar-Type Binary Stars in the Open Clusters M35 and M34
• Theory and simulations of rotating convection
• The EBLM Project V. Physical properties of ten fully convective, very-low-mass stars
• Tidal instability in a rotating and differentially heated ellipsoidal shell
• Tidal flows with convection: frequency-dependence of the effective viscosity and evidence for anti-dissipation
• Magnetic fields driven by tidal mixing in radiative stars
• Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits

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