Tidal dissipation in rotating low-mass stars and implications for the orbital evolution of close-in planets I. From the PMS to the RGB at solar metallicity

Star-planet interactions must be taken into account in stellar models to understand the dynamical evolution of close-in planets. The dependence of the tidal interactions on the structural and rotational evolution of the star is of peculiar importance and should be correctly treated. We quantify how tidal dissipation in the convective envelope of rotating low-mass stars evolves from the pre-main sequence up to the red-giant branch depending on the initial stellar mass. We investigate the consequences of this evolution on planetary orbital evolution. We couple the tidal dissipation formalism described in Mathis (2015) to the stellar evolution code STAREVOL and apply it to rotating stars with masses between 0.3 and 1.4 M$_\odot$. In addition, we generalize the work of Bolmont & Mathis (2016) by following the orbital evolution of close-in planets using the new tidal dissipation predictions for advanced phases of stellar evolution. On the PMS the evolution of tidal dissipation is controlled by the evolution of the internal structure of the contracting star. On the MS it is strongly driven by the variation of surface rotation that is impacted by magnetized stellar winds braking. The main effect of taking into account the rotational evolution of the stars is to lower the tidal dissipation strength by about four orders of magnitude on the main-sequence, compared to a normalized dissipation rate that only takes into account structural changes. The evolution of the dissipation strongly depends on the evolution of the internal structure and rotation of the star. From the pre-main sequence up to the tip of the red-giant branch, it varies by several orders of magnitude, with strong consequences for the orbital evolution of close-in massive planets. These effects are the strongest during the pre-main sequence, implying that the planets are mainly sensitive to the star's early history.Comment: 13 pages, 7 figures, accepted for publication in A&

Tides and angular momentum redistribution inside low-mass stars hosting planets: a first dynamical model

We introduce a general mathematical framework to model the internal transport of angular momentum in a star hosting a close-in planetary/stellar companion. By assuming that the tidal and rotational distortions are small and that the deposit/extraction of angular momentum induced by stellar winds and tidal torques are redistributed solely by an effective eddy-viscosity that depends on the radial coordinate, we can formulate the model in a completely analytic way. It allows us to compute simultaneously the evolution of the orbit of the companion and of the spin and the radial differential rotation of the star. An illustrative application to the case of an F-type main-sequence star hosting a hot Jupiter is presented. The general relevance of our model to test more sophisticated numerical dynamical models and to study the internal rotation profile of exoplanet hosts, submitted to the combined effects of tides and stellar winds, by means of asteroseismology are discussed.Comment: 32 pages, 10 figures, one table; accepted to Celestial Mechanics and Dynamical Astronomy, special issue on tide

Tidal resonance locks in inspiraling white dwarf binaries

We calculate the tidal response of helium and carbon/oxygen (C/O) white dwarf (WD) binaries inspiraling due to gravitational wave emission. We show that resonance locks, previously considered in binaries with an early-type star, occur universally in WD binaries. In a resonance lock, the orbital and spin frequencies evolve in lockstep, so that the tidal forcing frequency is approximately constant and a particular normal mode remains resonant, producing efficient tidal dissipation and nearly synchronous rotation. We show that analogous locks between the spin and orbital frequencies can occur not only with global standing modes, but even when damping is so efficient that the resonant tidal response becomes a traveling wave. We derive simple analytic formulas for the tidal quality factor Q and tidal heating rate during a g-mode resonance lock, and verify our results numerically. We find that Q ~ 10^7 for orbital periods ~ 1 - 2 hr in C/O WDs, and Q ~ 10^9 for P_orb ~ 3 - 10 hr in helium WDs. Typically tidal heating occurs sufficiently close to the surface that the energy should be observable as surface emission. Moreover, near an orbital period of ~ 10 min, the tidal heating rate reaches ~ 10^{-2} L_\sun, rivaling the luminosities of our fiducial WD models. Recent observations of the 13-minute double-WD binary J0651 are roughly consistent with our theoretical predictions. Tides naturally tend to generate differential rotation; however, we show that the fossil magnetic field strength of a typical WD can maintain solid-body rotation down to at least P_orb ~ 10 min even in the presence of a tidal torque concentrated near the WD surface.Comment: 24 pages, 8 figure

Tidal dissipation in evolving low-mass and solar-type stars with predictions for planetary orbital decay

We study tidal dissipation in stars with masses in the range 0.1–1.6 M⊙ throughout their evolution, including turbulent effective viscosity acting on equilibrium tides and inertial waves (IWs) in convection zones, and internal gravity waves in radiation zones. We consider a range of stellar evolutionary models and incorporate the frequency-dependent effective viscosity acting on equilibrium tides based on the latest simulations. We compare the tidal flow and dissipation obtained with the conventional equilibrium tide, which is strictly invalid in convection zones, finding that the latter typically overpredicts the dissipation by a factor of 2–3. Dissipation of IWs is computed using a frequency-averaged formalism accounting for realistic stellar structure for the first time, and is the dominant mechanism for binary circularization and synchronization on the main sequence. Dissipation of gravity waves in the radiation zone assumes these waves to be fully damped (e.g. by wave breaking), and is the dominant mechanism for planetary orbital decay. We calculate the critical planetary mass required for wave breaking as a function of stellar mass and age, and show that this mechanism predicts destruction of many hot Jupiters but probably not Earth-mass planets on the main sequence. We apply our results to compute tidal quality factors following stellar evolution, and tidal evolutionary time-scales, for the orbital decay of hot Jupiters, and the spin synchronization and circularization of binary stars. We also provide predictions for shifts in transit arrival times due to tidally driven orbital decay of hot Jupiters that may be detected with NGTS, TESS, or PLATO

On internal wave breaking and tidal dissipation near the centre of a solar-type star

We study the fate of internal gravity waves, which are excited by tidal forcing by a short-period planet at the interface of convection and radiation zones, approaching the centre of a solar-type star. We study at what amplitude these wave are subject to instabilities. These instabilities lead to wave breaking whenever the amplitude exceeds a critical value. Below this value, the wave reflects perfectly from the centre of the star. Wave breaking results in spinning up the central regions of the star, and the formation of a critical layer, which acts as an absorbing barrier for ingoing waves. As these waves are absorbed, the star is spun up from the inside out. This results in an important amplitude dependence of the tidal quality factor Q'. If the tidal forcing amplitude exceeds the value required for wave breaking, efficient dissipation results over a continuous range of tidal frequencies, leading to Q' \approx 10^5 (P/1day)^(8/3), for the current Sun. This varies by less than a factor of 5 throughout the range of G and K type main sequence stars, for a given orbit. We predict fewer giant planets with orbital periods of less than about 2 days around such stars, if they cause breaking at the centre, due to the efficiency of this process. This mechanism would, however, be ineffective in stars with a convective core, such as WASP-18, WASP-12 and OGLE-TR-56, perhaps partly explaining the survival of their close planetary companions.Comment: 22 pages, 10 figures, accepted in MNRAS, abstract shortened (!

Nonlinear Tides in Close Binary Systems

We study the excitation and damping of tides in close binary systems, accounting for the leading order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct effects: three-mode nonlinear interactions and nonlinear excitation of modes by the time-varying gravitational potential of the companion. This paper presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism is applicable to binaries containing stars, planets, or compact objects, we focus on solar type stars with stellar or planetary companions. Our primary results include: (1) The linear tidal solution often used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited gravity waves are unstable to parametric resonance for companion masses M' > 10-100 M_Earth at orbital periods P = 1-10 days. The nearly static equilibrium tide is, however, parametrically stable except for solar binaries with P < 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes waves to grow so rapidly that they must be treated as traveling waves rather than standing waves. (3) We find a novel form of parametric instability in which a single parent wave excites a very large number of daughter waves (N = 10^3[P / 10 days]) and drives them as a single coherent unit with growth rates that are ~N times faster than the standard three wave parametric instability. (4) Independent of the parametric instability, tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing; this coupling appears particularly efficient at draining energy out of the dynamical tide and may be more important than either wave breaking or parametric resonance at determining the nonlinear dissipation of the dynamical tide.Comment: 40 pages, 16 figures. Matches version published in ApJ; conclusions unchanged; some restructuring of sections; sect. 5 now provides simple physical estimates of the nonlinear growth rates that agree well with the detailed calculations given in the appendice

Detailed equilibrium and dynamical tides: impact on circularization and synchronization in open clusters

Binary stars evolve into chemically-peculiar objects and are a major driver of the Galactic enrichment of heavy elements. During their evolution they undergo interactions, including tides, that circularize orbits and synchronize stellar spins, impacting both individual systems and stellar populations. Using Zahn's tidal theory and MESA main-sequence model grids, we derive the governing parameters $\lambda_{lm}$ and $E_2$, and implement them in the new MINT library of the stellar population code BINARY_C. Our MINT equilibrium tides are 2 to 5 times more efficient than the ubiquitous BSE prescriptions while the radiative-tide efficiency drops sharply with increasing age. We also implement precise initial distributions based on bias-corrected observations. We assess the impact of tides and initial orbital-parameter distributions on circularization and synchronization in eight open clusters, comparing synthetic populations and observations through a bootstrapping method. We find that changing the tidal prescription yields no statistically-significant improvement as both calculations typically lie within 0.5$\sigma$. The initial distribution, especially the primordial concentration of systems at $\log_{10}(P/{\rm d}) \approx 0.8, e\approx 0.05$ dominates the statistics even when artificially increasing tidal strength. This confirms the inefficiency of tides on the main sequence and shows that constraining tidal-efficiency parameters using the $e-\log_{10}(P/{\rm d})$ distribution alone is difficult or impossible. Orbital synchronization carries a more striking age-dependent signature of tidal interactions. In M35 we find twice as many synchronized rotators in our MINT calculation as with BSE. This measure of tidal efficiency is verifiable with combined measurements of orbital parameters and stellar spins.Comment: 24 pages, 29 figures includings appendices. Accepted for publication in MNRA

Heartbeat Stars, Tidally Excited Oscillations, and Resonance Locking

Heartbeat stars are eccentric binary stars in short period orbits whose light curves are shaped by tidal distortion, reflection, and Doppler beaming. Some heartbeat stars exhibit tidally excited oscillations and present new opportunities for understanding the physics of tidal dissipation within stars. We present detailed methods to compute the forced amplitudes, frequencies, and phases of tidally excited oscillations in eccentric binary systems. Our methods i) factor out the equilibrium tide for easier comparison with observations, ii) account for rotation using the traditional approximation, iii) incorporate non-adiabatic effects to reliably compute surface luminosity perturbations, iv) allow for spin-orbit misalignment, and v) correctly sum over contributions from many oscillation modes. We also discuss why tidally excited oscillations are more visible in hot stars with surface temperatures $T \! \gtrsim \! 6500 \, {\rm K}$, and we derive some basic probability theory that can be used to compare models with data in a statistical manner. Application of this theory to heartbeat systems can be used to determine whether observed tidally excited oscillations can be explained by chance resonances with stellar oscillation modes, or whether a resonance locking process is operating.Comment: Published in MNRA