A new class of pulsating binary stars was recently discovered, whose pulsation amplitudes are strongly modulated with orbital phase. Stars in close binaries are tidally distorted, so we examine how a star's tidally induced asphericity affects its oscillation mode frequencies and eigenfunctions. We explain the pulsation amplitude modulation via tidal mode coupling such that the pulsations are effectively confined to certain regions of the star, e.g., the tidal pole or the tidal equator. In addition to a rigorous mathematical formalism to compute this coupling, we provide a more intuitive semi-analytic description of the process. We discuss three resulting effects: 1. Tidal alignment, i.e., the alignment of oscillation modes about the tidal axis rather than the rotation axis; 2. Tidal trapping, e.g., the confinement of oscillations near the tidal poles or the tidal equator; 3. Tidal amplification, i.e., increased flux perturbations near the tidal poles where acoustic modes can propagate closer to the surface of the star. Together, these phenomena can account for the pulsation amplitude and phase modulation of the recently discovered class of "tidally tilted pulsators." We compare our theory to the three tidally tilted pulsators HD 74423, CO Cam, and TIC 63328020, finding that tidally trapped modes that are axisymmetric about the tidal axis can largely explain the first two, while a non-axisymmetric tidally aligned mode is present in the latter. Finally, we discuss implications and limitations of the theory, and we make predictions for the many new tidally tilted pulsators likely to be discovered in the near future.
Stellar components in binaries are subject to tidal forces which influence asteroseismic properties. Tidally pertubed pulsations have been reported for different objects but none of these are in their pre-main sequence phase of evolution. This makes RS Cha, consisting of two $δ$ Scuti stars and with pulsational characteristics influenced by tidal effects , the first such object observed. We aim to investigate the pulsational properties of the eclipsing binary RS Cha in terms of the theory of tidally perturbed pulsations. Based on photometric time series obtained from the TESS satellite, we per…
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 present the analysis of KIC 8164262, a heartbeat star with a high-amplitude (~1 mmag), tidally resonant pulsation (a mode in resonance with the orbit) at 229 times the orbital frequency and a plethora of tidally induced g-mode pulsations (modes excited by the orbit). The analysis combines Kepler light curves with follow-up spectroscopic data from the Keck telescope, KPNO (Kitt Peak National Observatory) 4-m Mayal telescope and the 2.7-m telescope at the McDonald observatory. We apply the binary modelling software, PHOEBE, to the Kepler light curve and radial velocity data to determine a det…
RR Lyn is a detached eclipsing binary with a 9.95 d orbit containing two A-stars: one metallic-lined and one possibly metal-poor. We use the light curve from the TESS satellite and two sets of published radial velocity measurements to determine the properties of the system to high precision. We find masses of 1.939 +/- 0.007 and 1.510 +/- 0.003 Msun, and radii of 2.564 +/- 0.019 and 1.613 +/- 0.013 Rsun. After adjusting published effective temperatures upwards by 200 K we find a good agreement with theoretical models for a solar chemical composition and an age of 1 Gyr, and a distance slightly…
Tidally tilted pulsators (TTPs) are an intriguing new class of oscillating stars in binary systems; in such stars, the pulsation axis coincides with the line of apsides, or semi-major axis, of the binary. All three TTPs discovered so far have been $δ$~Scuti stars. In this Letter, we report the first conclusive discovery of tidally tilted pulsations in a subdwarf B (sdB) star. HD 265435 is an sdB--white dwarf binary with a 1.65-hr period that has been identified and characterized as the nearest potential Type Ia supernova progenitor. Using TESS 20-s cadence data from Sectors 44 and 45, we show …
Tidally Trapped Two-pole Pulsations Discovered in a Close Binary with a Massive $β$ Cephei Star
Yunnan Observatories, Chinese Academy of Sciences (CAS)（中国科学院云南天文台）；University of Chinese Academy of Sciences（中国科学院大学）；School of Physics and Astronomy, Yunnan University（云南大学物理与天文学院）
It has long been suspected that tidal forces in close binary stars could modify the orientation of the pulsation axis of the constituent stars. Such stars have been searched for, but until now never detected. Here we report the discovery of tidally trapped pulsations in the ellipsoidal variable HD 74423 in TESS space photometry data. The system contains a Delta Scuti pulsator in a 1.6-d orbit, whose pulsation mode amplitude is strongly modulated at the orbital frequency, which can be explained if the pulsations have a much larger amplitude in one hemisphere of the star. We interpret this as an…
We report the discovery of the third tidally tilted pulsator, TIC 63328020. Observations with the TESS satellite reveal binary eclipses with an orbital period of 1.1057 d, and $δ$ Scuti-type pulsations with a mode frequency of 21.09533 d$^{-1}$. This pulsation exhibits a septuplet of orbital sidelobes as well as a harmonic quintuplet. Using the oblique pulsator model, the primary oscillation is identified as a sectoral dipole mode with $l = 1, |m| = 1$. We find the pulsating star to have $M_1 \simeq 2.5\, {\rm M}_\odot$, $R_1 \simeq 3 \, {\rm R}_\odot$, and $T_{\rm eff,1} \simeq 8000$ K, while…
Context. Many well-known bright stars have been observed by the ongoing Transiting Exoplanet Survey Satellite (TESS) space mission. For several of them, these new data reveal previously unobserved variability, such as tidally perturbed pulsations in close binary stars. Aims. Using newly detected gravity-mode (g-mode) pulsations in V456 Cyg, we aim to determine the global stellar properties of this short-period eclipsing binary and evaluate the interaction between these pulsations and the tides. Methods. We model the binary orbit and determine the physical properties of the component stars usin…
KIC 3230227 is a short period ($P\approx 7.0$ days) eclipsing binary with a very eccentric orbit ($e=0.6$). From combined analysis of radial velocities and {\it Kepler} light curves, this system is found to be composed of two A-type stars, with masses of $M_1=1.84\pm 0.18M_{\odot}$, $M_2=1.73\pm 0.17M_{\odot}$ and radii of $R_1=2.01\pm 0.09R_{\odot}$, $R_2=1.68\pm 0.08 R_{\odot}$ for the primary and secondary, respectively. In addition to an eclipse, the binary light curve shows a brightening and dimming near periastron, making this a somewhat rare eclipsing heartbeat star system. After removi…
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…
We present TESS photometry of the triple star system V1031 Ori (AB)C, which exhibits short-period oscillations superimposed on an eclipsing light curve. The high-quality data were analyzed in detail and combined with the published spectroscopic measurements to obtain the fundamental stellar parameters of the program target. The masses and radii of the eclipsing pair (AB) were determined to about 0.5 \% and 0.7 \% precision, respectively. We found 23 significant frequencies in two ranges of $<$ 2 day$^{-1}$ and 10.9$-$12.7 day$^{-1}$ from the eclipse-subtracted residuals. Among them, sixteen in…
The interior physics of stars is currently not well constrained for early-type stars. This is particularly pertinent for multiple systems as binary interaction becomes more prevalent for more massive stars, which strongly affects their evolution. High-precision photometry from the Transiting Exoplanet Survey Satellite (TESS) mission offers the opportunity to remedy the dearth of observations of pulsating stars that show evidence of binary interaction, specifically pulsating mass-accreting components of semi-detached Algol-type eclipsing binary (oEA) systems. We present the TESS light curve of …
Oscillating eclipsing Algols (oEAs) are remarkable systems which allow us to determine accurate fundamental stellar parameters (mass, radius) and probe the stellar interiors through pulsations. TZ\,Dra is an oEA system containing a $δ$ Scuti component. To examine particular characteristics of such close systems including pulsations and mass transfer, we present a detailed photometric and spectroscopic study of TZ\,Dra. With the analysis of high-resolution spectra, the orbital parameters were determined by the radial velocity analysis and the atmospheric parameters were derived for the primary …
IM Per is a triple star system whose eclipsing pair masses and radii are accurate to within 1 \%. The TESS light curve of the program target exhibits partial eclipses and multiple oscillations with mmag-level amplitudes. It is found that the oscillations affect eclipse timing measurements. Binary modeling of the high-quality TESS data indicates that the eclipsing components of the triple system are twin dwarfs with parameters of $M_2$/$M_1$ = 0.995, $R_2$/$R_1$ = 0.901, and $Δ$($T_{\rm eff,1}$--$T_{\rm eff,2}$) = 12 K in an eccentric ($e$ = 0.049), detached configuration. The third light of $l…
The tidally tilted pulsators are a new type of oscillating star in close binary systems that have their pulsation axis in the orbital plane because of the tidal distortion caused by their companion. We describe this group of stars on the basis of the first three representatives discovered and illustrate the basic methods used for their analysis. Their value for astrophysical study is rooted in the combination of the strengths of binary star and asteroseismic analyses; pulsational mode identifications can be achieved because the oscillations are visible over nearly 360 degrees of aspect through…
WASP-33 is one of the few $δ$ Sct stars with a known planetary companion. By analyzing the stellar oscillations, we search for possible star-planet interactions in the pattern of the pulsation. We made use of the Transit and Light Curve Modeller (TLCM) to solve the light curve from the Transiting Exoplanet Survey Satellite (TESS). We include gravity darkening into our analysis. The stellar oscillation pattern of WASP-33 clearly shows signs of several tidally perturbed modes. We find that there are peaks in the frequency spectrum that are at or near the $3$rd, $12$th and $25$th orbital harmonic…
Heartbeat stars are eccentric (e > 0.2) ellipsoidal variables whose light curves resemble a cardiogram. We present the observations and corresponding model of KIC 3749404, a highly eccentric (e = 0.66), short period (P = 20.3 d) heartbeat star with tidally induced pulsations. A binary star model was created using PHOEBE, which we modified to include tidally induced pulsations and Doppler boosting. The morphology of the photometric periastron variation (heartbeat) depends strongly on the eccentricity, inclination and argument of periastron. We show that the inclusion of tidally induced pulsatio…
Context. Unambiguous examples of the influence of tides on self-excited, free stellar pulsations have recently been observationally detected in space-based photometric data. Aims. We aim to investigate U Gru and contextualise it within the growing class of tidally influenced pulsators. Initial analysis of U Gru revealed frequencies spaced by the orbital frequency that are difficult to explain by currently proposed tidal mechanisms. Methods. We re-investigate the TESS photometry of U Gru alongside new uves spectroscopy. We analyse the uves spectroscopy with least-squares deconvolution and spect…
TIC 435850195: The Second Tri-Axial, Tidally Tilted Pulsator
Massachusetts Institute of Technology（麻省理工学院）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；SETI Institute（搜寻地外文明研究所）；California Institute of Technology（加州理工学院）；North-West University（西北大学）；University of Central Lancashire（中央兰开夏大学）；Phillips Academy（菲利普斯学院）
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 ($M_1=2.05M_{\odot}, R_1=2.96R_{\odot}$ and $M_2=2.05M_{\odot}, R_2=2.51R_{\odot}$) by combining {\it Kepler} photometry and spectra from {\it Keck} HIRES. The measured surface rotation rates are only one-fifth of the pseudo-synchronous rate of the eccentric orbit. Fourier spectrum of the light curve reveals hybrid pulsations of $δ$ Scuti and $γ$ Doradus type, with pulsation frequencies at a…
V453 Cyg is an eclipsing binary containing 14 Msun and 11 Msun stars in an eccentric short-period orbit. We have discovered $β$ Cep-type pulsations in this system using TESS data. We identify seven significant pulsation frequencies, between 2.37 and 10.51 d$^{-1}$, in the primary star. These include six frequencies which are separated by yet significantly offset from harmonics of the orbital frequency, indicating they are tidally-perturbed modes. We have determined the physical properties of the system to high precision: V453 Cyg A is the first $β$ Cep pulsator with a precise mass measurement.…
We briefly review the current status of the study of tidally excited oscillations (TEOs) in heartbeat binary stars. Particular attention is paid to correctly extracting the TEOs when the Fourier spectrum also contains other types of pulsations and variabilities. We then focus on the theoretical modeling of the TEO amplitudes and phases. Pulsation amplitude can be modeled by a statistical approach, and pulsation phases can help to identify the azimuthal number m of pulsation modes. We verify the results by an ensemble study of ten systems. We discuss some future prospects, including the secular…
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…
Mercury-manganese (HgMn) stars are late-B upper main sequence chemically peculiar stars distinguished by large overabundances of heavy elements, slow rotation, and frequent membership in close binary systems. These stars lack strong magnetic fields typical of magnetic Bp stars but occasionally exhibit non-uniform surface distributions of chemical elements. The physical origin and the extent of this spot formation phenomenon remains unknown. Here we use 2-min cadence light curves of 64 HgMn stars observed by the TESS satellite during the first two years of its operation to investigate the incid…
We report a new subdwarf B (sdB) pulsator, PG1142-037, discovered during the first full-length campaign of K2, the two-gyro mission of the Kepler space telescope. Fourteen periodicities have been detected between 0.9 and 2.5 hours with amplitudes below 0.35 ppt. We have been able to associate all of the pulsations with low-degree, ell<=2 modes. Follow-up spectroscopy of PG1142 has revealed it to be in a binary with a period of 0.54 days. Phase-folding the K2 photometry reveals a two-component variation including both Doppler boosting and ellipsoidal deformation. Perhaps the most surprising and…
We seek signatures of the current experimental $^{12}$C$(α,γ)^{16}$O reaction rate probability distribution function in the pulsation periods of carbon-oxygen white dwarf models. We find that adiabatic g-modes trapped by the interior carbon-rich layer offer potentially useful signatures of this reaction rate probability distribution function. Probing the carbon-rich region is relevant because it forms during the evolution of low-mass stars under radiative helium burning conditions, mitigating the impact of convective mixing processes. We make direct quantitative connections between the pulsati…
We present an analysis of the high-mass eclipsing binary system VV Ori based on photometry from the TESS satellite. The primary star (B1V, 9.5 Msun) shows beta Cephei pulsations and the secondary (B7V, 3.8 Msun) is possibly a slowly-pulsating B star. We detect 51 significant oscillation frequencies, including two multiplets with separations equal to the orbital frequency, indicating that the pulsations are tidally perturbed. We analyse the TESS light curve and published radial velocities to determine the physical properties of the system. Both stars are only the second of their pulsation type …
We present both binarity and pulsation of KIC 6220497 from the {\it Kepler} observations. The light curve synthesis shows that the eclipsing system is a semi-detached Algol with parameters of $q$ = 0.243$\pm$0.001, $i$ = 77.3$\pm$0.3 deg, and $ΔT$ = 3,372$\pm$58 K, in which the detached primary component fills its Roche lobe by $\sim$87\%. A multiple frequency analysis of the eclipse-subtracted light residuals reveals 33 frequencies in the range of 0.75$-$20.22 d$^{-1}$ with amplitudes between 0.27 and 4.56 mmag. Among these, four are pulsation frequencies in fundamental ($f_1$, $f_5$) and $p$…
$η$ Car is a massive, eccentric binary with a rich observational history. We obtained the first high-cadence, high-precision light curves with the BRITE-Constellation nanosatellites over 6 months in 2016 and 6 months in 2017. The light curve is contaminated by several sources including the Homunculus nebula and neighboring stars, including the eclipsing binary CPD$-$59$^\circ$2628. However, we found two coherent oscillations in the light curve. These may represent pulsations that are not yet understood but we postulate that they are related to tidally excited oscillations of $η$ Car's primary …
In close binary stars, the tidal excitation of pulsations typically dissipates energy, causing the system to evolve towards a circular orbit with aligned and synchronized stellar spins. However, for stars with self-excited pulsations, we demonstrate that tidal interaction with unstable pulsation modes can transfer energy in the opposite direction, forcing the spins of the stars away from synchronicity, and potentially pumping the eccentricity and spin-orbit misalignment angle. This "inverse" tidal process only occurs when the tidally forced mode amplitude is comparable to the mode's saturation…
We report the ${\it Kepler}$ photometry of KIC 11401845 displaying multiperiodic pulsations, superimposed on binary effects. Light-curve synthesis represents that the binary star is a short-period detached system with a very low mass ratio of $q$ = 0.070 and filling factors of $F_1$ = 45 % and $F_2$ = 99 %. Multiple frequency analyses were applied to the light residuals after subtracting the synthetic eclipsing curve from the observed data. We detected 23 frequencies with signal to noise amplitude ratios larger than 4.0, of which the orbital harmonics ($f_4$, $f_6$, $f_9$, $f_{15}$) in the low…
The study of pulsating stars in eclipsing binaries holds the promise of combining two different ways of measuring the physical properties of a star to obtain improved constraints on stellar theory. Gravity (g) mode pulsations such as those found in $γ$ Doradus stars can be used to probe rotational profiles, mixing and magnetic fields. Until recently few $γ$ Doradus stars in eclipsing binaries were known. We have discovered g-mode pulsations in four detached eclipsing binary systems from light curves obtained by the Transiting Exoplanet Survey Satellite (TESS) and present an analysis of their e…
National Astronomical Observatory of Japan, National Institutes of Natural Sciences（日本国立天文台，国立自然科学研究院）；Department of Astronomy, Graduate University for Advanced Studies（高级研究大学院大学天文学系）
Using ASAS-SN data, we find that the bright ($V{\sim}13.5$ mag) variable star MACHO 80.7443.1718 (ASASSN-V J052624.38-684705.6) is the most extreme heartbeat star yet discovered. This massive binary, consisting of at least one early B-type star, has an orbital period of $P_{\rm ASAS-SN}=32.83627\pm0.00846\,{\rm d},$ and is located towards the LH58 OB complex in the LMC. Both the ASAS-SN and TESS light curves show extreme brightness variations of ${\sim}40\%$ at periastron and variations of ${\sim}10\%$ due to tidally excited oscillations outside periastron. We fit an analytical model of the va…
Binary systems anchor many of the fundamental relations relied upon in asteroseismology. Masses and radii are rarely constrained better than when measured via orbital dynamics and eclipse depths. Pulsating binaries have much to offer. They are clocks, moving in space, that encode orbital motion in the Doppler-shifted pulsation frequencies. They offer twice the opportunity to obtain an asteroseismic age, which is then applicable to both stars. They enable comparative asteroseismology -- the study of two stars by their pulsation properties, whose only fundamental differences are the mass and rot…
我们提出了一个比较周期搜索的结果在不同的时间尺度和建模的ZZ鲸鱼座（DAV）星GD 154。我们确定了六个频率的正常模式和四个旋转的双峰周围的最大振幅。在807.62和861.56微赫兹的两个正常模式以前从未报道过。一个严格的测试显示显着的固有振幅的频率在839.14和861.56微赫兹超过50天的时间尺度的变化。此外，在观测结束时，多模式脉动变为单周期脉动，主频率为843.15微赫兹。检测到的2.76微赫兹平均旋转分裂导致GD 154的2.1 d旋转周期的确定。我们寻找模型的解决方案，有效的温度和日志g接近光谱确定的。通过网格搜索得到的最佳拟合模型的M_H在6.3 x 10^-5和6.3 x 10^-7 M* 之间，这意味着氢层比之前的研究所认为的要厚。我们的研究表明，模式捕获不一定在所有观察到的模式和捕获模式的最佳候选人是在2484微赫兹。
We study the flux variation in helium white dwarfs (WDs) induced by dynamical tides for a variety of WD models with effective temperatures ranging from $T$=10 kK to $T$=26 kK. At linear order, we find the dynamical tide can significantly perturb the observed flux in hot WDs. If the temperature $T\gtrsim14$ kK, then the dynamical tide may induce a fractional change in the flux by >1% when the orbital period is $P_{\rm orb}\simeq 20-60\,{\rm min}$. The ratio between the flux modulation due to the dynamical tide and that due to the equilibrium tide (i.e., ellipsoidal variability) increases as the…
