Continuous and precise space-based photometry has made it possible to measure the orbital frequency modulation of pulsating stars in binary systems with extremely high precision over long time spans. Frequency modulation caused by binary orbital motion manifests itself as a multiplet with equal spacing of the orbital frequency in the Fourier transform. The amplitudes and phases of the peaks in these multiplets reflect the orbital properties, hence the orbital parameters can be extracted by analysing such precise photometric data alone. We derive analytically the theoretical relations between the multiplet properties and the orbital parameters, and present a method for determining these parameters, including the eccentricity and the argument of periapsis, from a quintuplet or a higher order multiplet. This is achievable with the photometry alone, without spectroscopic radial velocity measurements. We apply this method to Kepler mission data of KIC8264492, KIC9651065, and KIC10990452, each of which is shown to have an eccentricity exceeding 0.5. Radial velocity curves are also derived from the Kepler photometric data. We demonstrate that the results are in good agreement with those obtained by another technique based on the analysis of the pulsation phases.
Some pulsating stars are good clocks. When they are found in binary stars, the frequencies of their luminosity variations are modulated by the Doppler effect caused by orbital motion. For each pulsation frequency this manifests itself as a multiplet separated by the orbital frequency in the Fourier transform of the light curve of the star. We derive the theoretical relations to exploit data from the Fourier transform to derive all the parameters of a binary system traditionally extracted from spectroscopic radial velocities, including the mass function which is easily derived from the amplitud…
The unparalleled photometric data obtained by NASA's Kepler space telescope led to an improved understanding of red giant stars and binary stars. Seismology allows us to constrain the properties of red giants. In addition to eclipsing binaries, eccentric non-eclipsing binaries, exhibiting ellipsoidal modulations, have been detected with Kepler. We aim to study the properties of eccentric binary systems containing a red giant star and derive the parameters of the primary giant component. We apply asteroseismic techniques to determine masses and radii of the primary component of each system. For…
The orbital parameters of binaries at intermediate periods ($10^2$--$10^3$ d) are difficult to measure with conventional methods and are very incomplete. We have undertaken a new survey, applying our pulsation timing method to {\it Kepler} light curves of 2224 main-sequence A/F stars and found 341 non-eclipsing binaries. We calculate the orbital parameters for 317 PB1 systems (single-pulsator binaries) and 24 PB2s (double-pulsators). The method reaches down to small mass ratios $q=0.02$ and yields a highly homogeneous sample. We parametrize the mass-ratio distribution using both inversion and …
KIC 8569819 is an eclipsing binary star with an early F primary and G secondary in a 20.85-d eccentric orbit. The primary is a delta Sct - gamma Dor star pulsating in both p modes and g modes. Using 4 years of Kepler Mission photometric data we independently model the light curve using the traditional technique with the modelling code PHOEBE, and we study the orbital characteristics using the new frequency modulation (FM) technique. We show that both methods provide the equivalent orbital period, eccentricity and argument of periastron, thus illustrating and validating the FM technique. In the…
BE Lyncis: A Pulsating Star in the Most Eccentric Binary with a Massive Unseen Companion
Institute of Theoretical Physics, Shanxi University（山西大学理论物理研究所）；State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University（山西大学量子光学技术与器件国家重点实验室）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）；Department of Physics, Taiyuan Normal University（太原师范学院物理系）；Institute of Computational and Applied Physics, Taiyuan Normal University（太原师范学院计算与应用物理研究所）；Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology（山西省智能优化计算与区块链技术重点实验室）
We present candidates for non-pulsating stars lying in the classical Cepheid instability strip based on OGLE photometric maps combined with Strömgren photometry obtained with the 4.1-m SOAR telescope, and Gaia DR2 data in four fields in the Large Magellanic Cloud. We selected 19 candidates in total. After analysis of their light curves from OGLE surveys we found that all these stars appear to be photometrically stable at the level of a few mmag. Our results show that non-pulsating stars might constitute to about 21%-30% of the whole sample of giant stars located in the classical instability st…
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…
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…
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…
The predicted width of the upper main sequence in stellar evolution models depends on the empirical calibration of the convective overshooting parameter. Despite decades of discussions, its precise value is still unknown and further observational constraints are required to gauge it. Based on a photometric and preliminary asteroseismic analysis, we show that the mid B-type giant 18 Peg is one of the most evolved members of the rare class of slowly pulsating B-stars and, thus, bears tremendous potential to derive a tight lower limit for the width of the upper main sequence. In addition, 18 Peg …
We present a method for finding binaries among pulsating stars that were observed by the Kepler Mission. We use entire four-year light curves to accurately measure the frequencies of the strongest pulsation modes, then track the pulsation phases at those frequencies in 10-d segments. This produces a series of time-delay measurements in which binarity is apparent as a periodic modulation whose amplitude gives the projected light travel time across the orbit. Fourier analysis of this time-delay curve provides the parameters of the orbit, including the period, eccentricity, angle of ascending nod…
Mutual gravitation between a pulsating star and an orbital companion leads to a time-dependent variation in path length for starlight traveling to Earth. These variations can be used for coherently pulsating stars, such as the δ Scuti variables, to constrain the masses and orbits of their companions. Observing these variations for δ Scuti stars has previously relied on subdividing the light curve and measuring the average pulsation phase in equally sized subdivisions, which leads to under-sampling near periapsis. We introduce a new approach that simultaneously forward-models each sample in the…
We combine variability information from the MAssive Compact Halo Objects (MACHO) survey of the Large Magellanic Cloud (LMC) with infrared photometry from the Spitzer Space Telescope Surveying the Agents of a Galaxy's Evolution (SAGE) survey to create a dataset of ~30 000 variable red sources. We photometrically classify these sources as being on the first ascent of the Red Giant Branch (RGB), or as being in one of three stages along the Asymptotic Giant Branch (AGB): oxygen-rich, carbon-rich, or highly reddened with indeterminate chemistry ("extreme" AGB candidates). We present linear period-l…
The analysis of eclipsing binaries containing non-radial pulsators allows: i) to combine two different and independent sources of information on the internal structure and evolutionary status of the components, and ii) to study the effects of tidal forces on pulsations. KIC 3858884 is a bright Kepler target whose light curve shows deep eclipses, complex pulsation patterns with pulsation frequencies typical of δ Sct, and a highly eccentric orbit. We present the result of the analysis of Kepler photometry and of high resolution phaseresolved spectroscopy. Spectroscopy yielded both the radial vel…
The project Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS (muchfuss) aims to discover subdwarf-B stars with massive compact companions such as overmassive white dwarfs (M > 1.0 M_sun), neutron stars or black holes. From the 127 subdwarfs with substantial radial-velocity variations discovered in the initial survey, a number of interesting objects have been selected for extensive follow-up. After an initial photometry run with BUSCA revealed that FBS 0117+396 is photometrically variable both on long and short timescales, we chose it as an auxiliary target during a 6-night …
Eclipsing systems are essential objects for understanding the properties of stars and stellar systems. Eclipsing systems with pulsating components are furthermore advantageous because they provide accurate constraints on the component properties, as well as a complementary method for pulsation mode determination, crucial for precise asteroseismology. The outcome of space missions aiming at delivering high-accuracy light curves for many thousands of stars in search of planetary systems has also generated new insights in the field of variable stars and revived the interest of binary systems in g…
We report the discovery of rapid periodic signals in the light curves of two cataclysmic variables with prominent white-dwarf components in their spectra, SDSS J1457+51 and BW Sculptoris. These stars therefore appear to be new members of the GW Lib class of variable star, in which the fast periodic (and non-commensurate with the orbital period) signals are believed to arise from non-radial pulsations in the underlying white dwarf. The power spectra of both stars show complex signals with primary periods near 10 and 20 minutes. These signals change in frequency by a few percent on a timescale o…
Pulsating stars in eclipsing binary systems are powerful tools to test stellar models. Binarity enables to constrain the pulsating component physical parameters, whose knowledge drastically improves the input physics for asteroseismic studies. The study of stellar oscillations allows us, in its turn, to improve our understanding of stellar interiors and evolution. The space mission CoRoT discovered several promising objects suitable for these studies, which have been photometrically observed with unprecedented accuracy, but needed spectroscopic follow-up. A promising target was the relatively …
Red-giant stars are an incredible source of information for testing models of stellar evolution, as asteroseismology has opened up a window into their interiors. Such insights are a direct result of the unprecedented data from space missions Kepler and CoRoT as well as recent theoretical advances. Eclipsing binaries are also fundamental astrophysical objects, and when coupled with asteroseismology, binaries would provide two independent methods to obtain masses and radii and exciting opportunities to develop highly constrained stellar models. The possibility of discovering pulsating red giants…
We searched for circumbinary planets orbiting NY Vir in historical eclipse times including our long-term CCD data. Sixty-eight times of minimum light with accuracies better than 10 s were used for the ephemeris computations. The best fit to those timings indicated that the orbital period of NY Vir has varied due to a combination of two sinusoids with periods of $P_3$=8.2 yr and $P_4$=27.0 yr and semi-amplitudes of $K_3$=6.9 s and $K_4$=27.3 s, respectively. The periodic variations most likely arise from a pair of light-time effects due to the presence of third and fourth bodies that are gravit…
There is a small group of peculiar early-type stars on the main sequence that show different rotation velocities from different spectral lines. This inconsistency might be due to the binary nature of these objects. We aim to verify this hypothesis by a more detailed spectroscopic and photometric investigation of one such object: HD 183986. We obtained 151 high and medium resolution spectra that covered an anticipated long orbital period. There is clear evidence of theorbital motion of the primary component. We uncovered a very faint and broad spectrum of the secondary component. The correspond…
Orbital and stellar parameter determination of eclipsing $β$ Cep pulsators
University of Nigeria, Nsukka（尼日利亚恩苏卡大学）；Çanakkale Onsekiz Mart University（恰纳卡莱十月马特大学）；Villanova University（维拉诺瓦大学）；Royal Observatory of Belgium（比利时皇家天文台）；Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）
HD172189 is a spectroscopic eclipsing binary system with a rapidly-rotating pulsating delta Scuti component. It is also a member of the open cluster IC4756. These combined characteristics make it an excellent laboratory for asteroseismic studies. To date, HD172189 has been analysed in detail photometrically but not spectroscopically. For this reason we have compiled a set of spectroscopic data to determine the absolute and atmospheric parameters of the components. We determined the radial velocities (RV) of both components using four different techniques. We disentangled the binary spectra usi…
KIC 8560861 (HD 183648) is a marginally eccentric (e=0.05) eclipsing binary with an orbital period of P_orb=31.973d, exhibiting mmag amplitude pulsations on time scales of a few days. We present the results of the complex analysis of high and medium-resolution spectroscopic data and Kepler Q0 -- Q16 long cadence photometry. The iterative combination of spectral disentangling, atmospheric analysis, radial velocity and eclipse timing variation studies, separation of pulsational features of the light curve, and binary light curve analysis led to the accurate determination of the fundamental stell…
$τ^{9}$ Eri is a Bp star that was previously reported to be a single-lined spectroscopic binary. Using 17 ESPaDOnS spectropolarimetric (Stokes $V$) observations we identified the weak spectral lines of the secondary component and detected a strong magnetic field in the primary. We performed orbital analysis of the radial velocities of both components to find a slightly eccentric orbit ($e= 0.129$) with a period of $5.95382(2)$ days. The longitudinal magnetic field ($B_\ell$) of the primary was measured from each of the Stokes $V$ profiles, with typical error bars smaller than 10 G. Equivalent …
We present a survey of variable stars detected in K2 Campaign 13 within the massive intermediate age ($\sim1$ Gyr) open cluster NGC 1817. We identify a complete sample of 44 red clump stars in the cluster, and have measured asteroseismic quantities ($ν_{\rm max}$ and/or $Δν$) for 29 of them. Five stars showed suppressed dipole modes, and the occurrence rates indicate that mode suppression is unaffected by evolution through core helium burning. A subset of the giants in NGC 1817 (and in the similarly aged cluster NGC 6811) have $ν_{\rm max}$ and $Δν$ values at or near the maximum observed for c…
Among the competing evolution theories for subdwarf-B (sdB) stars is the binary evolution scenario. EC~20117-4014 (=V4640~Sgr) is a spectroscopic binary system consisting of a pulsating sdB star and a late F main-sequence companion (O'Donoghue et al. 1997), however the period and the orbit semi-major axes have not been precisely determined. This paper presents orbital characteristics of the EC 20117-4014 binary system using 20 years of photometric data. Periodic Observed minus Calculated (O-C) variations were detected in the two highest amplitude pulsations identified in the EC 20117-4014 powe…
We present a variability study of 4646 massive stars in the Small Magellanic Cloud (SMC) with known spectral types from the catalog of Bonanos et al. (2010) using the light curves from the OGLE-III database. The goal is to exploit the time domain information available through OGLE-III to gain insight into the processes that govern the evolution of massive stars. This variability survey of massive stars with known spectral types is larger than any previous survey by a factor of 7. We find that 60% of our sample (2766 stars) show no significant variability and 40% (1880 stars) exhibit variabilit…
This work provides a statistical analysis of the massive star binary characteristics in the Cygnus OB2 Association using radial velocity information of 114 B3-O3 primary stars and orbital properties for the 24 known binaries. We compare these data to a series of Monte Carlo simulations to infer the intrinsic binary fraction and distributions of mass ratios, periods, and eccentricities. We model the distribution of mass ratio, log-period, and eccentricity as power-laws and find best fitting indices of alpha=0.1+/-0.5, beta=0.2+/-0.4, and gamma=-0.6+/-0.3 respectively. These distributions indica…
High-mass binary stars are known to show an unexplained discrepancy between the dynamical masses of the individual components and those predicted by models. In this work, we study Sigma Scorpii, a double-lined spectroscopic binary system consisting of two B-type stars residing in an eccentric orbit. The more massive primary component is a Beta Cep-type pulsating variable star. Our analysis is based on a time-series of some 1000 high-resolution spectra collected with the CORALIE spectrograph in 2006, 2007, and 2008. We use two different approaches to determine the orbital parameters of the star…
Pulsating stars in binary systems are ideal laboratories to test stellar evolution and pulsation theory, since a direct, model-independent determination of component masses is possible. The high-precision CoRoT photometry allows a detailed view of the frequency content of pulsating stars, enabling detection of patterns in their distribution. The object HD 51844 is such a case showing periastron brightening instead of eclipses. We present a comprehensive study of the HD 51844 system, where we derive physical parameters of both components, the pulsation content and frequency patterns. Additional…
$\varepsilon$ Lupi A is a binary system consisting of two main sequence early B-type stars Aa and Ab in a short period, moderately eccentric orbit. The close binary pair is the only doubly-magnetic massive binary currently known. Using photometric data from the BRITE-Constellation we identify a modest heartbeat variation. Combining the photometry with radial velocities of both components we determine a full orbital solution including empirical masses and radii. These results are compared with stellar evolution models as well as interferometry and the differences discussed. We also find additio…
The star HD 51844 was observed in CoRoT LRa02 as a Seismo target which turned out to be an SB2 system. The 117 days long light curve revealed delta Scuti pulsation in the range of 6 to 15 d^{-1} where four frequencies have amplitudes larger than 1.4 mmag and a rich frequency spectrum with amplitudes lower than 0.6 mmag. Additionally, the light curve exhibits a brightening event recurring every 33.5 days with a maximum of 3 mmag and a duration of about 5 days. Thus, this star can be considered as a heartbeat candidate. The radial velocities from spectroscopy confirmed an eccentric binary system…
AQ Col (EC 05217-3914) is one of the first detected pulsating subdwarf B (sdB) stars and has been considered to be a single star. Photometric monitoring of AQ Col reveals a pulsation timing variation with a period of 486 days, interpreted as time-delay due to reflex motion in a wide-binary formed with an unseen companion with expected mass larger than 1.05 $M_\odot$. The optical spectra and color-Magnitude diagram of the system suggested that the companion is not a main sequence star but a white dwarf or neutron star. The pulsation timing variation also shows that the system has an eccentricit…
We present the analysis of an eccentric, partially eclipsing long-period ($P=19.23$ d) binary system KIC 9777062 that contains main sequence stars near the turnoff of the intermediate age open cluster NGC 6811. The primary is a metal-lined Am star with a possible convective blueshift to its radial velocities, and one star (probably the secondary) is likely to be a $γ$ Dor pulsator. The component masses are $1.603\pm0.006$(stat.)$\pm0.016$(sys.) and $1.419\pm0.003\pm0.008 M_\odot$, and the radii are $1.744\pm0.004\pm0.002$ and $1.544\pm0.002\pm0.002 R_\odot$. The isochrone ages of the stars are…
We present a detailed study of the classical Cepheid in the double-lined, highly eccentric eclipsing binary system OGLE-LMC562.05.9009. The Cepheid is a fundamental mode pulsator with a period of 2.988 days. The orbital period of the system is 1550 days. Using spectroscopic data from three 4-8-m telescopes and photometry spanning 22 years, we were able to derive the dynamical masses and radii of both stars with exquisite accuracy. Both stars in the system are very similar in mass, radius and color, but the companion is a stable, non-pulsating star. The Cepheid is slightly more massive and bigg…
Continuous photometry with up to three BRITE satellites was obtained for 12 targets and subjected to a period search. Contemporaneous high-resolution optical spectroscopy with STELLA was used to obtain radial velocities through cross correlation with template spectra as well as to determine astrophysical parameters through a comparison with model spectra. The Capella red light curve was found to be constant over 176 days with a root mean square of 1 mmag, but the blue light curve showed a period of 10.1$\pm$0.6 d, which we interpret to be the rotation period of the G0 component. The BRITE ligh…
Asteroseismic Detection of a Massive Unseen Companion to the $δ$ Scuti Star TIC 160582982
Xinjiang Astronomical Observatory, Chinese Academy of Sciences（中国科学院新疆天文台）；Instituto de Astrofísica de Andalucía - CSIC（安达卢西亚天体物理研究所-西班牙国家研究委员会）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Chinese Academy of Sciences South America Center for Astronomy（中国科学院南美天文中心）
TESS Pulsation Timing Reveals the JWST Calibration Star HD 158485 as a Double-pulsator Binary
Xinjiang Astronomical Observatory, Chinese Academy of Sciences（中国科学院新疆天文台）；Instituto de Astrofísica de Andalucía - CSIC（安达卢西亚天体物理研究所-西班牙国家研究委员会）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Chinese Academy of Sciences South America Center for Astronomy（中国科学院南美天文中心）
本研究通过 TESS 脉冲计时，发现 JWST 校准星 HD 158485 为双脉冲星双星，测得其轨道参数，盲预测验证了轨道可靠性，还发现未分辨伴星会影响分光光度预测。
