Binary stars are places of complex stellar interactions. While all binaries are in principle converging towards a state of circularization, many eccentric systems are found even in advanced stellar phases. In this work we discuss the sample of binaries with a red-giant component, discovered from observations of the NASA Kepler space mission. We first discuss which effects and features of tidal interactions are detectable in photometry, spectroscopy and the seismic analysis. In a second step, the sample of binary systems observed with Kepler, is compared to the well studied sample of Verbunt & Phinney (1995, hereafter VP95). We find that this study of circularization of systems hosting evolving red-giant stars with deep convective envelopes is also well applicable to the red-giant binaries in the sample of Kepler stars.
Tidal forces are important for understanding how close binary stars and compact exoplanetary systems form and evolve. However, tides are difficult to model and significant uncertainties exist about the strength of tides. Here, we investigate tidal circularization in close binaries using a large sample of well-characterised eclipsing systems. We searched TESS photometry from the southern hemisphere for eclipsing binaries. We derive best-fit orbital and stellar parameters by jointly modelling light curves and spectral energy distributions. To determine the eccentricity distribution of eclipsing …
A gas giant planet which survives the giant branch stages of evolution at a distance of many au and then is subsequently perturbed sufficiently close to a white dwarf will experience orbital shrinkage and circularization due to star-planet tides. The circularization timescale, when combined with a known white dwarf cooling age, can place coupled constraints on the scattering epoch as well as the active tidal mechanisms. Here, we explore this coupling across the entire plausible parameter phase space by computing orbit shrinkage and potential self-disruption due to chaotic f-mode excitation and…
Tidal dissipation is responsible for circularizing the orbits and synchronizing the spins of solar-type close binary stars, but the mechanisms responsible are not fully understood. Previous work has indicated that significant enhancements to the theoretically-predicted tidal dissipation rates are required to explain the observed circularization periods ($P_\mathrm{circ}$) in various stellar populations, and their evolution with age. This was based partly on the common belief that the dominant mechanism of tidal dissipation in solar-type stars is turbulent viscosity acting on equilibrium tides …
All the studies of the interaction between tides and a convective flow assume that the large scale tides can be described as a mean shear flow which is damped by small scale fluctuating convective eddies. The convective Reynolds stress is calculated using mixing length theory, accounting for a sharp suppression of dissipation when the turnover timescale is larger than the tidal period. This yields tidal dissipation rates several orders of magnitude too small to account for the circularization periods of late-type binaries or the tidal dissipation factor of giant planets. Here, we argue that th…
The rate of tidal circularization is predicted to be faster for relatively cool stars with convective outer layers, compared to hotter stars with radiative outer layers. Observing this effect is challenging, because it requires large and well-characterized samples including both hot and cool stars. Here we seek evidence for the predicted dependence of circularization upon stellar type, using a sample of 945 eclipsing binaries observed by Kepler. This sample complements earlier studies of this effect, which employed smaller samples of better-characterized stars. For each Kepler binary we measur…
We re-analyze the pristine eclipsing binary data from the $\textit{Kepler}$ and TESS missions, focusing on eccentricity measurements at short orbital periods to emperically constrain tidal circularization. We find an average circularization period of $~$6 days, as well as a short circularization period of $\sim$3 days for the $\textit{Kepler}$/TESS field binaries. We argue previous spectroscopic binary surveys reported longer circularization periods due to small sample sizes, which were contaminated by an abundance of binaries with circular orbits out to $\sim$10 days, but we re-affirm their d…
We examine the consequences of, and apply, the formalism developed in Terquem (2021) for calculating the rate $D_R$ at which energy is exchanged between fast tides and convection. In this previous work, $D_R$ (which is proportional to the gradient of the convective velocity) was assumed to be positive in order to dissipate the tidal energy. Here we argue that, even if energy is intermittently transferred from convection to the tides, it must ultimately return to the convective flow and transported efficiently to the stellar surface on the convective timescale. This is consistent with, but much…
In the standard theory of equilibrium tides, hydrodynamic turbulence is considered. In this paper we study the effect of magnetic fields on equilibrium tides. We find that the turbulent Ohmic dissipation associated with a tidal flow is much stronger than the turbulent viscous dissipation such that a magnetic field can greatly speed up the tidal evolution of a binary system. We then apply the theory to three binary systems: the orbital migration of 51 Pegasi b, the orbital decay of WASP-12b, and the circularization of close binary stars. Theoretical predictions are in good agreement with observ…
Context. With the detection of thousands of exoplanets, characterising their dynamical evolution in detail represents a key step in the understanding of their formation. Studying the dissipation of tides occurring both in the host star and in the planets is of great relevance in order to investigate the distribution of the angular momentum occurring among the objects populating the system and to studying the evolution of the orbital parameters. From a theoretical point of view, the dissipation of tides throughout a body may be studied by relying on the so-called phase or time-lag equilibrium t…
We study the effect of dynamical tides associated with the excitation of gravity waves in an interior radiative region of the central star on orbital evolution in observed systems containing Hot Jupiters. We consider WASP-43, Ogle-tr-113, WASP-12, and WASP-18 which contain stars on the main sequence (MS). For these systems there are observational estimates regarding the rate of change of the orbital period. We also investigate Kepler-91 which contains an evolved giant star. We adopt the formalism of Ivanov et al. for calculating the orbital evolution. For the MS stars we determine expected rat…
Short-period binary star systems dissipate orbital energy through tidal interactions that lead to tighter, more circular orbits. When at least one star in a binary has evolved off of the main sequence, orbital circularization occurs for longer-period (~100 day) systems. Past work by (Verbunt & Phinney 1995) has shown that the orbital parameters and the circularization periods of a small sample of binary stars with evolved-star members can be understood within the context of standard tidal circularization theory. Using a sample of binaries with subgiant, giant, and red clump star members that i…
We study orbital evolution of multi-planet systems with masses in the terrestrial planet regime induced through tidal interaction with a protoplanetary disk assuming that this is the dominant mechanism for producing orbital migration and circularization. We develop a simple analytic model for a system that maintains consecutive pairs in resonance while undergoing orbital circularization and migration. Migration times for each planet may be estimated once planet masses, circularization times and the migration time for the innermost planet are given. We applied it to a model system with the curr…
We study tidal dissipation in stars with masses in the range $0.1-1.6 M_\odot$ throughout their evolution, including turbulent effective viscosity acting on equilibrium tides and inertial waves 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 typi…
Recent observation of the tidally-excited stellar oscillations in the main-sequence binary KOI-54 by the KEPLER satellite provides a unique opportunity for studying dynamical tides in eccentric binary systems. We develop a general theory of tidal excitation of oscillation modes of rotating binary stars, and apply our theory to tidally excited gravity modes (g-modes) in KOI-54. The strongest observed oscillations, which occur at 90 and 91 times the orbital frequency, are likely due to prograde m=2 modes (relative to the stellar spin axis) locked in resonance with the orbit. The remaining flux o…
We systematically searched for gravity- and Rossby-mode period spacing patterns in Kepler eclipsing binaries with $γ$ Doradus pulsators. These stars provide an excellent opportunity to test the theory of tidal synchronisation and angular momentum transport in F- and A-type stars. We discovered 35 systems that show clear patterns, including the spectroscopic binary KIC 10080943. Combined with 45 non-eclipsing binaries with $γ$ Dor components that have been found using pulsation timing, we measured their near-core rotation rates and asymptotic period spacings. We find that many stars are tidally…
Tidal interaction governs the redistribution of angular momentum in close binary stars and planetary systems and determines the systems evolution towards the possible equilibrium state. Turbulent friction acting on the equilibrium tide in the convective envelope of low-mass stars is known to have a strong impact on this exchange of angular momentum in binaries. Moreover, theoretical modelling in recent literature as well as presented in this paper suggests that the dissipation of the dynamical tide, constituted of tidal inertial waves propagating in the convective envelope, is weak compared to…
Although tidal dissipation in binary stars has been studied for over a century, theoretical predictions have yet to match the observed properties of binary populations. This work quantitatively examines the recent proposal of tidal circularization by resonance locking, where tidal dissipation arises from resonances between the star's natural oscillation frequencies and harmonics of the orbital frequency, and where resonances are `locked' for an extended period of time due to concurrent stellar evolution. We focus on tidal resonances with axi-symmetric gravity-modes, and examine binaries with p…
Tidal dissipation due to convective turbulent viscosity shapes the evolution of a variety of astrophysical binaries. For example, this type of dissipation determines the rate of orbital circularization in a binary with a post-main sequence star that is evolving toward a common envelope phase. Viscous dissipation can also influence binaries with solar-type stars, or stars with a close-in giant planet. In general, the effective viscosity in a convective stellar envelope depends on the tidal forcing frequency $ω_{\rm tide}$; when $ω_{\rm tide}$ is larger than the turnover frequency of convective …
Context. Kepler-444 is one of the oldest planetary systems known thus far. Its peculiar configuration consisting of five sub-Earth-sized planets orbiting the companion to a binary stellar system makes its early history puzzling. Moreover, observations of HI-Ly-$\rm α$ variations raise many questions about the potential presence of escaping atmospheres today. Aims. We aim to study the orbital evolution of Kepler-444-d and Kepler-444-e and the impact of atmospheric evaporation on Kepler-444-e. Methods. Rotating stellar models of Kepler-444-A were computed with the Geneva stellar evolution code a…
Tidal friction has long been recognized to circularize the orbits of binary stars over time. In this study, we use the observed distribution of orbital eccentricities in populations of binary stars to probe tidal dissipation. In contrast to previous studies, we incorporate a host of physical effects often neglected in other analyses, provide a much more general description of tides, model individual systems in detail (in lieu of population statistics), and account for all observational uncertainties. The goal is to provide a reliable measurement of the properties of tidal dissipation that is f…
The advent of space-based photometry missions such as CoRoT, Kepler and TESS has sparkled the development of asteroseismology and exoplanetology. The advent of PLATO will further strengthen such multi-disciplinary studies. Testing asteroseismic modelling and its importance for our understanding of planetary systems is crucial. We carried out a detailed modelling of Kepler-93, an exoplanet host star observed by Kepler. This star is particularly interesting as it is very similar to the PLATO benchmark target (G spectral type, ~ 6000K, ~ 1 Msun and ~ 1 Rsun) and provides a real-life testbed for p…
KIC 5773205 is the least luminous eclipsing M dwarf found in the Villanova catalog of eclipsing binaries detected by the {\it Kepler} mission. We processed and analyzed the three available quarters of mission data for this star and discovered a persistent periodic variation of the light curve with a period, which is in exact 4:5 commensurability to the orbital period. Three routes of interpretation are considered: 1) non-radial pulsations excited by the tidal interaction at a specific eigenfrequency; 2) a high-order spin-orbit resonance caused by the tides; 3) an ellipsoidal deformation caused…
We report on the properties of eclipsing binaries from the Kepler mission with a newly developed photometric modeling code, which uses the light curve, spectral energy distribution of each binary, and stellar evolution models to infer stellar masses without the need for radial velocity measurements. We present solutions and posteriors to orbital and stellar parameters for 728 systems, forming the largest homogeneous catalogue of full Kepler binary parameter estimates to date. Using comparisons to published radial velocity measurements, we demonstrate that the inferred properties (e.g., masses)…
The discovery of many planets using the Kepler telescope includes ten planets orbiting eight binary stars. Three binaries, Kepler-16, Kepler-47, and Kepler-453, have at least one planet in the circumbinary habitable-zone (BHZ). We constrain the level of high-energy radiation and the plasma environment in the BHZ of these systems. With this aim, BHZ limits in these Kepler binaries are calculated as a function of time, and the habitability lifetimes are estimated for hypothetical terrestrial planets and/or moons within the BHZ. With the time-dependent BHZ limits established, a self-consistent mo…
With 16-month Kepler data, 14 long-period (40 d - 265 d) eclipsing binaries on highly eccentric orbits (minimum e between 0.5 and 0.85) are recognized from their closely separated primary and secondary eclipses (Δt_I,II = 3 d - 10 d). These systems confirm the existence of a previously hinted binary population situated near a constant angular momentum track at P(1-e^2)^(3/2) ~ 15 d, close to the tidal circularization period P_circ. They may be presently migrating due to tidal dissipation and form a steady-state stream (~1% of stars) feeding the close-binary population (few percent of stars). I…
Here we present CAFein, a new computational tool for investigating radiative dissipation of dynamic tides in close binaries and of non-adiabatic, non-radial stellar oscillations in isolated stars in the linear regime. For the latter, CAFein computes the non-adiabatic eigenfrequencies and eigenfunctions of detailed stellar models. The code is based on the so-called Riccati method, a numerical algorithm that has been successfully applied to a variety of stellar pulsators, and which doesn't suffer of the major drawbacks of commonly used shooting and relaxation schemes. Here we present an extensio…
Evolution of binary objects under the influence of tides drastically affects the expected observational properties of the system. With the discovery of a large number of close-in hot Jupiter systems and eclipsing binaries from missions such as Kepler and TESS, it has become imperative to understand the extent of tidal influence on their formation and observed properties. In the case of binary systems, an efficient tidal dissipation can lead to either spin up or spin down of the stars and/or spin-orbit synchronization, depending upon the exchange of angular momentum between the star and the orb…
Apsidal motion is a gradual shift in the position of periastron. The impact of dynamic tides on apsidal motion has long been debated, because the contribution could not be quantified due to the lack of high quality observations. KIC 4544587 with tidally excited oscillations has been observed by \textit{Kepler} high-precision photometric data based on long time baseline and short-cadence schema. In this paper, we compute the rate of apsidal motion that arises from the dynamic tides as $19.05\pm 1.70$ mrad yr$^{-1}$ via tracking the orbital phase shifts of tidally excited oscillations. We also c…
Heartbeat stars (HB stars) are a class of eccentric binary stars with close periastron passages. The characteristic photometric HB signal evident in their light curves is produced by a combination of tidal distortion, heating, and Doppler boosting near orbital periastron. Many HB stars continue to oscillate after periastron and along the entire orbit, indicative of the tidal excitation of oscillation modes within one or both stars. These systems are among the most eccentric binaries known, and they constitute astrophysical laboratories for the study of tidal effects. We have undertaken a radia…
We explore the tidal excitation of stellar modes in binary systems using Kepler observations of the remarkable eccentric binary KOI-54 (HD 187091; KIC 8112039), which displays strong ellipsoidal variation as well as a variety of linear and nonlinear pulsations. We report the amplitude and phase of over 120 harmonic and anharmonic pulsations in the system. We use pulsation phases to determine that the two largest-amplitude pulsations, the 90th and 91st harmonics, most likely correspond to axisymmetric m=0 modes in both stars, and thus cannot be responsible for resonance locks as had been recent…
Kepler photometry of the hot Neptune host star HAT-P-11 suggests that its spot latitude distribution is comparable to the Sun's near solar maximum. We search for evidence of an activity cycle in the CaII H & K chromospheric emission $S$-index with archival Keck/HIRES spectra and observations from the echelle spectrograph on the ARC 3.5 m Telescope at APO. The chromospheric emission of HAT-P-11 is consistent with a $\gtrsim 10$ year activity cycle, which plateaued near maximum during the Kepler mission. In the cycle that we observed, the star seemed to spend more time near active maximum than m…
Few observational constraints exist for the tidal synchronization rate of late-type stars, despite its fundamental role in binary evolution. We visually inspected the light curves of 2278 eclipsing binaries (EBs) from the Kepler Eclipsing Binary Catalog to identify those with starspot modulations, as well as other types of out-of-eclipse variability. We report rotation periods for 816 EBs with starspot modulations, and find that 79% of EBs with orbital periods less than ten days are synchronized. However, a population of short period EBs exists with rotation periods typically 13% slower than s…
We have discovered a class of eccentric binary systems within the Kepler data archive that have dynamic tidal distortions and tidally-induced pulsations. Each has a uniquely shaped light curve that is characterized by periodic brightening or variability at time scales of 4-20 days, frequently accompanied by shorter period oscillations. We can explain the dominant features of the entire class with orbitally-varying tidal forces that occur in close, eccentric binary systems. The large variety of light curve shapes arises from viewing systems at different angles. This hypothesis is supported by s…
The study of young Sun-like stars is of fundamental importance to understand the magnetic activity and rotational evolution of the Sun. Space-borne photometry by the Kepler telescope provides unprecedented datasets to investigate these phenomena in Sun-like stars. We present a new analysis of the entire Kepler photometric time series of the moderately young Sun-like star Kepler-17 that is accompanied by a transiting hot Jupiter. We applied a maximum-entropy spot model to the long-cadence out-of-transit photometry of the target to derive maps of the starspot filling factor versus the longitude …
In recent years it has been shown that the tidal coupling between extrasolar planets and their stars could be an important mechanism leading to orbital evolution. Both the tides the planet raises on the star and vice versa are important and dissipation efficiencies ranging over four orders of magnitude are being used. In addition, the discovery of extrasolar planets extremely close to their stars has made it clear that the estimates of the tidal quality factor, Q, of the stars based on Jupiter and its satellite system and on main sequence binary star observations are too low, resulting in life…
We examine how tides, stellar evolution, and magnetic braking shape the rotation period (P$_{rot}$) evolution of low-mass stellar binaries up to orbital periods (P$_{orb}$) of 100 d across a wide range tidal dissipation parameters using two common equilibrium tidal models. We find that many binaries with P$_{orb} < 20$ d tidally lock, and most with $P_{orb} < 4$ d tidally lock into synchronous rotation on circularized orbits. At short P$_{orb}$, tidal torques produce a population of fast rotators that single-star only models of magnetic braking fail to produce. In many cases, we show that the …
This paper reports on the discovery that an eclipsing binary system, EPIC 202843107 , has a δ Scuti variable component. The phased light curve from Kepler space telescope presents a detached configuration. The binary modelling indicates that the two component stars have almost the same radius and may have experienced orbital circularization. Frequency analyses are performed for the residual light curve after subtracting the binary variations. The frequency spectrum reveals that one component star is a δ Scuti variable. A large frequency separation is cross-identified with the histogram graph, …
Kepler observations of the star HD 187091 (KID 8112039, hereafter KOI-54) revealed a remarkable light curve exhibiting sharp periodic brightening events every 41.8 days with a superimposed set of oscillations forming a beating pattern in phase with the brightenings. Spectroscopic observations revealed that this is a binary star with a highly eccentric orbit, e=0.83. We are able to match the Kepler light curve and radial velocities with a nearly face-on (i=5.5 degree) binary star model in which the brightening events are caused by tidal distortion and irradiation of nearly identical A stars dur…
We analyze the full $\mathit{Kepler}$ phase curve of KOI-964, a binary system consisting of a hot white dwarf on an eclipsing orbit around an A-type host star. Using all 18 quarters of long-cadence photometry, we carry out a joint light curve fit and obtain improved phase curve amplitudes, occultation depths, orbital parameters, and transit ephemeris over the previous results of Carter et al. 2011. A periodogram of the residuals from the phase curve fit reveals an additional stellar variability signal from the host star with a characteristic period of $0.620276\pm0.000011$ days and a full ampl…
Tidal forces in eccentric binary stars known as heartbeat stars excite detectable oscillations that shed light on the processes of tidal synchronization and circularization. We examine the pulsation phases of tidally excited oscillations (TEOs) in heartbeat binary systems. The target list includes four published heartbeat binaries and four additional systems observed by {\it Kepler}. To the first order, the pulsation phases of TEOs can be explained by the geometric effect of the dominant $l=2$, $m=0$, or $\pm 2$ modes assuming pulsations are adiabatic. We found that this simple theoretical int…
We measure the sky-projected stellar obliquities (λ) in the multiple-transiting planetary systems KOI-94 and Kepler-25, using the Rossiter-McLaughlin effect. In both cases the host stars are well-aligned with the orbital planes of the planets. For KOI-94 we find λ=-11+-11 deg, confirming a recent result by Hirano and coworkers. Kepler-25 was a more challenging case because the transit depth is unusually small (0.13 %). To obtain the obliquity it was necessary to use prior knowledge of the star's projected rotation rate, and apply two different analysis methods to independent wavelength regions…
The occurrence distribution of the shortest period giant exoplanets as found by Kepler show a drop-off that is a remarkable match to the drop-off expected by taking migration due to tides in the star. We present a comparison that can show the level of tidal dissipation (friction) as a function of the distribution of the ages of the star and planet system, with known dependencies on basic star and planet parameters. Use of this relation enables constraints to be put on the value of the tidal dissipation, constraints that will be improved as the distribution of the ages are determined. For the g…
What powers the most energetic flares in the Kepler field? Revisiting the superflaring star KIC 2852961
Konkoly Observatory, HUN-REN Research Centre for Astronomy and Earth Sciences（孔科利天文台，匈牙利研究与教育网络天文学与地球科学研究中心）；HUN-REN CSFK, MTA Centre of Excellence（匈牙利研究与教育网络科学院研究所，马塔卓越中心）；Eötvös Loránd University（厄特沃什·罗兰大学）；Institute of Physics/IGAM, University of Graz（格拉茨大学物理研究所/IGAM）
Several classes of stellar binaries with post-main sequence (post-MS) components - millisecond pulsars with the white dwarf companions (MSP+WD) and periods P_b~30 d, binaries hosting post-asymptotic giant branch (post-AGB) stars or barium stars with P_b~several yr - feature high eccentricities (up to 0.4) despite the expectation of their efficient tidal circularization during the AGB phase. It was suggested that the eccentricities of these binaries can be naturally excited by their tidal coupling to the circumbinary disk, formed by the material ejected from the binary. Here we critically reass…
Eccentric binaries known as heartbeat stars experience strong dynamical tides as the stars pass through periastron, providing a laboratory to study tidal interactions. We measure the rotation periods of 24 heartbeat systems, using the Kepler light curves to identify rotation peaks in the Fourier transform. Where possible, we compare the rotation period to the pseudosynchronization period derived by Hut 1981. Few of our heartbeat stars are pseudosynchronized with the orbital period. For four systems, we were able to identify two sets of rotation peaks, which we interpret as the rotation from bo…
Context. Thanks to the high-precision photometry from space missions such as Kepler and TESS, tidal perturbations and tilting of pulsations have been detected in more than a dozen binary systems. However, only two of these were g-mode pulsators. Aims. We aim to detect tidally perturbed g modes in additional binary systems and characterise them observationally. Methods. We perform a custom data reduction of the available Kepler and TESS photometry of a well-studied sample of 35 binary systems with gamma Doradus pulsators. For each target, we model the binary signal using a sum of 100 sine waves…
