Tidally Driven Oscillations in KIC 4544587: a δ Scuti Binary System

Binary modelling techniques and frequency analysis have been applied to the Kepler photometric observations of KIC 4544587 to determine information about the orbital characteristics, individual components and tidal interactions. The system contains an early A-type δ Scuti variable, which pulsates in both pressure and gravity modes, and a late F- to early G-type star, which is possibly a solar-like oscillator. The Wilson-Devinney code was used to model the Quarter 3.2 data and PHOEBE was used to model the Quarter 7 data; the results of these two methods were then compared. Using PHOEBE the rate of apsidal advance was determined to be 0.0001179(1) rad d-1, which gives 145.9(1) yr for a complete precession. Subsequently the binary model light curve was subtracted from the original data and frequency analysis was performed on the residuals. Fifteen frequencies were identified that are harmonics of the orbital period, 9 of which are in the g mode regime and 6 in the p mode regime. It was concluded that these frequencies are not an artifact of the model fit and thus are a signature of tidal resonance. It was also determined that many of the frequencies in the p mode regime are separated from the two dominant p modes by a multiple of the orbital frequency; six of the identified modes demonstrate this separation to an accuracy of 3 σ. As they are not orbital harmonics, the origin of these frequencies remains unknown. Currently we know of no other star demonstrating these characteristics

Accelerated Tidal Circularization Via Resonance Locking in KIC 8164262

Tidal dissipation in binary star and planetary systems is poorly understood. Fortunately, eccentric binaries known as heartbeat stars often exhibit tidally excited oscillations, providing observable diagnostics of tidal circularization mechanisms and timescales. We apply tidal theories to observations of the heartbeat star KIC 8164262, which contains an F-type primary in a very eccentric orbit that exhibits a prominent tidally excited oscillation. We demonstrate that the prominent oscillation is unlikely to result from a chance resonance between tidal forcing and a stellar oscillation mode. However, the oscillation has a frequency and amplitude consistent with the prediction of resonance locking, a mechanism in which coupled stellar and orbital evolution maintain a stable resonance between tidal forcing and a stellar oscillation mode. The resonantly excited mode produces efficient tidal dissipation (corresponding to an effective tidal quality factor $Q \sim 5 \times 10^4$), such that tidal orbital decay/circularization proceeds on a stellar evolution time scale.Comment: Published in MNRAS Letters. For an interactive 3D model of the system, go to http://www.glowscript.org/#/user/slantburns/folder/Public/program/KIC816426

The Pseudosynchronization of Binary Stars Undergoing Strong Tidal Interactions

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 both stars in the binary. The majority of the systems have a rotation period that is approximately 3/2 times the pseudosynchronization period predicted by Hut 1981, suggesting that other physical mechanisms influence the stars' rotation, or that stars typically reach tidal spin equilibrium at a rotation period slightly longer than predicted.Comment: 9 pages, 4 figures, 1 table

Heartbeat Stars and the Ringing of Tidal Pulsations

With the advent of high precision photometry from satellites such as the Kepler satellite, a whole new collection of interesting astronomical features and objects has been revealed: heartbeat stars are prime example of this. Heartbeat stars are eccentric ellipsoidal variables that undergo strong tidal interactions at periastron, when the stars are close to each other. These interactions induce the deformation of the stars, which causes a change in the cross-sectional area and temperature variations over the stellar surface. In the precise Kepler data, these changes cause a notable variation in the light curve in the form of a tidal pulse. In this work I present novel modelling tools produced specifically to model heartbeat stars. These include the bayes-todcor software, which generates radial velocities and fundamental stellar parameters from spectra using a combination of emcee and todcor; and software created for modelling heartbeat stars, which is a combination of phoebe, emcee and my own codes. One of the features added to the phoebe modelling software is the ability to model tidally induced pulsations simultaneously with the binary star features, enabling a complete and accurate heartbeat star model to be determined. Tidally induced pulsations are stellar oscillations driven by the tidal force of the companion star. Approximately 20% of our sample of 173 Kepler heartbeat stars show prominent tidally induced pulsations, which present in the light curve as oscillations at precise multiples of the orbital frequency. In this work I present a selection of heartbeat stars, modelled with the aforementioned codes. The majority of these show tidally induced pulsations. Additional features include rapid apsidal motion, tidally resonant modes, solar-like oscillations and tidally influenced pressure modes. I also applied my codes to a binary star presenting a strong case of frequency modulation, the Doppler shift of the stellar pulsation frequencies as the pulsating star moves towards and away from the observer. Combined, these objects form the majority of heartbeat stars that have been studied in detail in the literature today

Physics Of Eclipsing Binaries. II. Towards the Increased Model Fidelity

The precision of photometric and spectroscopic observations has been systematically improved in the last decade, mostly thanks to space-borne photometric missions and ground-based spectrographs dedicated to finding exoplanets. The field of eclipsing binary stars strongly benefited from this development. Eclipsing binaries serve as critical tools for determining fundamental stellar properties (masses, radii, temperatures and luminosities), yet the models are not capable of reproducing observed data well either because of the missing physics or because of insufficient precision. This led to a predicament where radiative and dynamical effects, insofar buried in noise, started showing up routinely in the data, but were not accounted for in the models. PHOEBE (PHysics Of Eclipsing BinariEs; http://phoebe-project.org) is an open source modeling code for computing theoretical light and radial velocity curves that addresses both problems by incorporating missing physics and by increasing the computational fidelity. In particular, we discuss triangulation as a superior surface discretization algorithm, meshing of rotating single stars, light time travel effect, advanced phase computation, volume conservation in eccentric orbits, and improved computation of local intensity across the stellar surfaces that includes photon-weighted mode, enhanced limb darkening treatment, better reflection treatment and Doppler boosting. Here we present the concepts on which PHOEBE is built on and proofs of concept that demonstrate the increased model fidelity.Comment: 60 pages, 15 figures, published in ApJS; accompanied by the release of PHOEBE 2.0 on http://phoebe-project.or

KIC 4142768: An Evolved Gamma Doradus/Delta Scuti Hybrid Pulsating Eclipsing Binary with Tidally Excited Oscillations

We present the characterization of KIC 4142768, an eclipsing binary with two evolved A-type stars in an eccentric orbit with a period of 14 days. We measure the fundamental parameters of the two components (M₁ = 2.05M_⊙, R₁ = 2.96R_⊙ and M₂ = 2.05M_⊙, R₂ = 2.51R_⊙) by combining Kepler photometry and spectra from the Keck HIRES. The measured surface rotation rates are only one-fifth of the pseudo-synchronous rate of the eccentric orbit. The Fourier spectrum of the light curve reveals hybrid pulsations of δ Scuti and γ Doradus type, with pulsation frequencies at about 15–18 day⁻¹ for p modes and about 0.2–1.2 day⁻¹ for low-frequency g modes. Some of the g modes are exact orbital harmonics and are likely tidally excited. Their pulsation amplitudes and phases both agree with predictions from linear tidal theory for l = 2, m = 2 prograde modes. We examine the period spacing patterns in the self-driven g modes and identify them mostly as prograde sectoral dipole modes. The unstable frequency range and frequency spacing of the p modes and the inferred asymptotic g-mode period spacings both agree with the stellar model for the primary star evolved to a late stage of the main sequence. The inferred rotation rate of the convective core boundary is very slow, similar to the small surface rotation rate inferred from the spectroscopy. The measured surface and near-core rotation rates provide constraints for testing the mechanism of angular momentum transfer and tidal synchronization in evolved eccentric binary star systems