scholarly journals Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

2020 ◽  
Vol 497 (4) ◽  
pp. 4472-4485 ◽  
Author(s):  
Jérémie Vidal ◽  
Adrian J Barker
Keyword(s):  
Frequency Spectrum ◽  
Effective Viscosity ◽  
Binary Systems ◽  
Tidal Flow ◽  
Orbital Evolution ◽  
Model Parameters ◽  
Turnover Frequency ◽  
Tidal Dissipation ◽  
Tidal Flows ◽  
Turbulent Cascade

ABSTRACT Turbulent convection is thought to act as an effective viscosity in damping equilibrium tidal flows, driving spin and orbital evolution in close convective binary systems. Compared to mixing-length predictions, this viscosity ought to be reduced when the tidal frequency |ωt| exceeds the turnover frequency ωcv of the dominant convective eddies, but the efficiency of this reduction has been disputed. We re-examine this long-standing controversy using direct numerical simulations of an idealized global model. We simulate thermal convection in a full sphere, and externally forced by the equilibrium tidal flow, to measure the effective viscosity νE acting on the tidal flow when |ωt|/ωcv ≳ 1. We demonstrate that the frequency reduction of νE is correlated with the frequency spectrum of the (unperturbed) convection. For intermediate frequencies below those in the turbulent cascade (|ωt|/ωcv ∼ 1−5), the frequency spectrum displays an anomalous 1/ωα power law that is responsible for the frequency reduction νE∝1/|ωt|α, where α < 1 depends on the model parameters. We then get |νE| ∝ 1/|ωt|δ with δ > 1 for higher frequencies, and δ = 2 is obtained for a Kolmogorov turbulent cascade. A generic |νE| ∝ 1/|ωt|2 suppression is next found for higher frequencies within the dissipation range of the convection (but with negative values). Our results indicate that a better knowledge of the frequency spectrum of convection is necessary to accurately predict the efficiency of tidal dissipation in stars and planets resulting from this mechanism.

scholarly journals Tidal flows with convection: frequency-dependence of the effective viscosity and evidence for anti-dissipation

2019 ◽  
Author(s):  
Craig D Duguid ◽  
Adrian J Barker ◽  
C A Jones
Keyword(s):  
High Frequency ◽  
Effective Viscosity ◽  
Large Scale ◽  
Binary Systems ◽  
Orbital Evolution ◽  
Turbulent Convection ◽  
Hot Jupiters ◽  
Tidal Flows ◽  
Tidal Frequency ◽  
Hydrodynamical Simulations

Abstract Tidal interactions are important in driving spin and orbital evolution in planetary and stellar binary systems, but the fluid dynamical mechanisms responsible remain incompletely understood. One key mechanism is the interaction between tidal flows and convection. Turbulent convection is thought to act as an effective viscosity in damping large-scale tidal flows, but there is a long-standing controversy over the efficiency of this mechanism when the tidal frequency exceeds the turnover frequency of the dominant convective eddies. This high frequency regime is relevant for many applications, such as for tides in stars hosting hot Jupiters. We explore the interaction between tidal flows and convection using hydrodynamical simulations within a local Cartesian model of a small patch of a convection zone of a star or planet. We adopt the Boussinesq approximation and simulate Rayleigh-Bénard convection, modelling the tidal flow as a background oscillatory shear flow. We demonstrate that the effective viscosity of both laminar and turbulent convection is approximately frequency-independent for low frequencies. When the forcing frequency exceeds the dominant convective frequency, the effective viscosity scales inversely with the square of the tidal frequency. We also show that negative effective viscosities are possible, particularly for high frequency tidal forcing, suggesting the surprising possibility of tidal anti-dissipation. These results are supported by a complementary high-frequency asymptotic analysis that extends prior work by Ogilvie & Lesur. We discuss the implications of these results for interpreting the orbital decay of hot Jupiters, and for several other astrophysical problems.

scholarly journals Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity

2020 ◽  
Vol 497 (3) ◽  
pp. 3400-3417 ◽  
Author(s):  
Craig D Duguid ◽  
Adrian J Barker ◽  
C A Jones
Keyword(s):  
Effective Viscosity ◽  
Turbulent Viscosity ◽  
Low Frequency ◽  
Giant Planets ◽  
Turbulent Convection ◽  
Tidal Dissipation ◽  
Orbital Decay ◽  
Tidal Theory ◽  
Tidal Flows ◽  
Hydrodynamical Simulations

ABSTRACT Turbulent convection is thought to act as an effective viscosity (νE) in damping tidal flows in stars and giant planets. However, the efficiency of this mechanism has long been debated, particularly in the regime of fast tides, when the tidal frequency (ω) exceeds the turnover frequency of the dominant convective eddies (ωc). We present the results of hydrodynamical simulations to study the interaction between tidal flows and convection in a small patch of a convection zone. These simulations build upon our prior work by simulating more turbulent convection in larger horizontal boxes, and here we explore a wider range of parameters. We obtain several new results: (1) νE is frequency dependent, scaling as ω−0.5 when ω/ωc ≲ 1, and appears to attain its maximum constant value only for very small frequencies (ω/ωc ≲ 10−2). This frequency reduction for low-frequency tidal forcing has never been observed previously. (2) The frequency dependence of νE appears to follow the same scaling as the frequency spectrum of the energy (or Reynolds stress) for low and intermediate frequencies. (3) For high frequencies (ω/ωc ≳ 1 − 5), νE ∝ ω−2. 4) The energetically dominant convective modes always appear to contribute the most to νE, rather than the resonant eddies in a Kolmogorov cascade. These results have important implications for tidal dissipation in convection zones of stars and planets, and indicate that the classical tidal theory of the equilibrium tide in stars and giant planets should be revisited. We briefly touch upon the implications for planetary orbital decay around evolving stars.

scholarly journals Fossil field decay due to nonlinear tides in massive binaries

2019 ◽  
Vol 629 ◽  
pp. A142 ◽  
Author(s):  
J. Vidal ◽  
D. Cébron ◽  
A. ud-Doula ◽  
E. Alecian
Keyword(s):  
Magnetic Fields ◽  
Binary Systems ◽  
Massive Stars ◽  
Tidal Flow ◽  
Magnetic Interaction ◽  
Nonlinear Regime ◽  
Close Binaries ◽  
Local Theory ◽  
Short Period ◽  
Tidal Flows

Context. Surface magnetic fields have been detected in 5–10% of isolated massive stars, hosting outer radiative envelopes. They are often thought to have a fossil origin, resulting from the stellar formation phase. Yet, magnetic massive stars are scarcer in (close) short-period binaries, as reported by the BinaMIcS (Binarity and Magnetic Interaction in various classes of Stars) Collaboration. Aims. Different physical conditions in the molecular clouds giving birth to isolated stars and binaries are commonly invoked. In addition, we propose that the observed lower magnetic incidence in close binaries may be due to nonlinear tides. Indeed, close binaries are probably prone to tidal instability, a fluid instability growing upon the equilibrium tidal flow via nonlinear effects. Yet, stratified effects have hitherto been largely overlooked. Methods. We theoretically and numerically investigate tidal instability in rapidly rotating, stably stratified fluids permeated by magnetic fields. We use the short-wavelength stability method to propose a comprehensive (local) theory of tidal instability at the linear onset, discussing damping effects. Then, we propose a mixing-length theory for the mixing generated by tidal instability in the nonlinear regime. We successfully assess our theoretical predictions against proof-of-concept, direct numerical simulations. Finally, we compare our predictions with the observations of short-period, double-lined spectroscopic binary systems. Results. Using new analytical results, cross-validated by a direct integration of the stability equations, we show that tidal instability can be generated by nonlinear couplings of inertia-gravity waves with the equilibrium tidal flow in short-period massive binaries, even against the Joule diffusion. In the nonlinear regime, a fossil magnetic field can be dissipated by the turbulent magnetic diffusion induced by the saturated tidal flows. Conclusions. We predict that the turbulent Joule diffusion of fossil fields would occur in a few million years for several short-period massive binaries. Therefore, turbulent tidal flows could explain the observed dearth of some short-period magnetic binaries.

scholarly journals Tidal interactions in rotating multiple stars and their impact on their evolution

2014 ◽  
Vol 9 (S307) ◽  
pp. 208-210
Author(s):  
P. Auclair-Desrotour ◽  
S. Mathis ◽  
C. Le Poncin-Lafitte
Keyword(s):  
Fluid Model ◽  
Orbital Evolution ◽  
Tidal Dissipation ◽  
Tidal Waves ◽  
Physical Mechanisms ◽  
Tidal Interactions ◽  
The Earth ◽  
Half Height ◽  
Multiple Stars ◽  
Stellar Interiors

AbstractTidal dissipation in stars is one of the key physical mechanisms that drive the evolution of binary and multiple stars. As in the Earth oceans, it corresponds to the resonant excitation of their eigenmodes of oscillation and their damping. Therefore, it strongly depends on the internal structure, rotation, and dissipative mechanisms in each component. In this work, we present a local analytical modeling of tidal gravito-inertial waves excited in stellar convective and radiative regions respectively. This model allows us to understand in details the properties of the resonant tidal dissipation as a function of the excitation frequencies, the rotation, the stratification, and the viscous and thermal properties of the studied fluid regions. Then, the frequencies, height, width at half-height, and number of resonances as well as the non-resonant equilibrium tide are derived analytically in asymptotic regimes that are relevant in stellar interiors. Finally, we demonstrate how viscous dissipation of tidal waves leads to a strongly erratic orbital evolution in the case of a coplanar binary system. We characterize such a non-regular dynamics as a function of the height and width of resonances, which have been previously characterized thanks to our local fluid model.

scholarly journals Tidal dissipation in rotating low-mass stars and implications for the orbital evolution of close-in planets

2017 ◽  
Vol 604 ◽  
pp. A112 ◽  
Author(s):  
F. Gallet ◽  
E. Bolmont ◽  
S. Mathis ◽  
C. Charbonnel ◽  
L. Amard
Keyword(s):  
Orbital Evolution ◽  
Low Mass Stars ◽  
Tidal Dissipation ◽  
Low Mass

scholarly journals Survival of planets around shrinking stellar binaries

2015 ◽  
Vol 112 (30) ◽  
pp. 9264-9269 ◽  
Author(s):  
Diego J. Muñoz ◽  
Dong Lai
Keyword(s):  
Binary Stars ◽  
Orbital Evolution ◽  
Eclipsing Binaries ◽  
Target List ◽  
Tidal Dissipation ◽  
Compact Binaries ◽  
Kepler Mission ◽  
Orbital Decay ◽  
Erratic Behavior ◽  
Circumbinary Planets

The discovery of transiting circumbinary planets by the Kepler mission suggests that planets can form efficiently around binary stars. None of the stellar binaries currently known to host planets has a period shorter than 7 d, despite the large number of eclipsing binaries found in the Kepler target list with periods shorter than a few days. These compact binaries are believed to have evolved from wider orbits into their current configurations via the so-called Lidov–Kozai migration mechanism, in which gravitational perturbations from a distant tertiary companion induce large-amplitude eccentricity oscillations in the binary, followed by orbital decay and circularization due to tidal dissipation in the stars. Here we explore the orbital evolution of planets around binaries undergoing orbital decay by this mechanism. We show that planets may survive and become misaligned from their host binary, or may develop erratic behavior in eccentricity, resulting in their consumption by the stars or ejection from the system as the binary decays. Our results suggest that circumbinary planets around compact binaries could still exist, and we offer predictions as to what their orbital configurations should be like.

scholarly journals Tidal evolution of circumbinary systems with arbitrary eccentricities: applications for Kepler systems

2020 ◽  
Vol 634 ◽  
pp. A12
Author(s):  
F. A. Zoppetti ◽  
A. M. Leiva ◽  
C. Beaugé
Keyword(s):  
Time Lag ◽  
Semimajor Axis ◽  
Tidal Flow ◽  
Orbital Evolution ◽  
Axis Ratio ◽  
Tidal Evolution ◽  
Tidal Interactions ◽  
Orbital Instability ◽  
Outward Migration ◽  
Circumbinary Planets

We present an extended version of the Constant Time Lag analytical approach for the tidal evolution of circumbinary planets introduced in our previous work. The model is self-consistent, in the sense that all tidal interactions between pairs are computed, regardless of their size. We derive analytical expressions for the variational equations governing the spin and orbital evolution, which are expressed as high-order elliptical expansions in the semimajor axis ratio but retain closed form in terms of the binary and planetary eccentricities. These are found to reproduce the results of the numerical simulations with arbitrary eccentricities very well, as well as reducing to our previous results in the low-eccentric case. Our model is then applied to the well-characterised Kepler circumbinary systems by analysing the tidal timescales and unveiling the tidal flow around each different system. In all cases we find that the spins reach stationary values much faster than the characteristic timescale of the orbital evolution, indicating that all Kepler circumbinary planets are expected to be in a sub-synchronous state. On the other hand, all systems are located in a tidal flow leading to outward migration; thus the proximity of the planets to the orbital instability limit may have been even greater in the past. Additionally, Kepler systems may have suffered a significant tidally induced eccentricity damping, which may be related to their proximity to the capture eccentricity. To help understand the predictions of our model, we also offer a simple geometrical interpretation of our results.

scholarly journals Statistics of Multiple Stars: Some Clues to Formation Mechanisms

2001 ◽  
Vol 200 ◽  
pp. 84-92 ◽  
Author(s):  
Andrei Tokovinin
Keyword(s):  
Observational Studies ◽  
Binary Systems ◽  
Close Binaries ◽  
Formation Mechanisms ◽  
Tidal Dissipation ◽  
Multiple Star ◽  
Star Catalogue ◽  
Multiple Stars ◽  
Available Information ◽  
Average Angle

The available information on the statistics of high multiplicity (3–6 components) systems is reviewed. The ratio of triple to binary systems is f3 ≍ 0.11, while fn ≍ 0.25 for higher n. Despite selection effects in the multiple star catalogue, the signatures of formation mechanisms are found in the distributions of period ratios and mass ratios. For example, the frequent occurrence of close sub-systems with periods less than 6 days can be explained by tidal dissipation in a 3-body system. In triple stars the angular momentum vectors of inner orbits are inclined to those of outer orbits by an average angle of 50°, hence the orbital spins are neither co-aligned nor completely random. Close binaries have a tendency to be found in higher-multiplicity systems, showing that close and wide binarity is statistically related. Future theoretical and observational studies are outlined.

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