We present results of comprehensive seismic modelling of the B-type main-sequence pulsator $ν$ Eridani, which consists in parallel fitting of the pulsational frequencies and corresponding values of the complex, nonadiabatic parameter $f$, defined by the bolometric flux perturbation. This kind of studies, which we call {\it complex asteroseismology}, provides a unique test of stellar opacities. Our results indicate a preference for the OPAL data.
We undertake another attempt towards seismic modelling of the most intensive studied main sequence pulsators of the early B spectral type, $ν$ Eridani. Our analysis is extended by a requirement of fitting not only pulsational frequencies but also the complex amplitude of the bolometric flux variation, $f$, related to each mode frequency. This approach, called {\it complex asteroseismology}, provides a unique test of stellar parameters, atmospheres and opacities. In particular, the concordance of the empirical and theoretical values of $f$ we obtained for the high-order g mode opens a new gate …
The analysis of the BRITE oscillation spectrum of the main sequence early B-type star $ν$ Eridani is presented. Only models with the modified mean opacity profile can account for the observed frequency ranges as well as for the values of some individual frequencies. The number of the $κ$ modified seismic models is constrained by the nonadiabatic parameter $f$, which is very sensitive to the opacity changes in the subphotospheric layers where the pulsations are driven. We present an example of the model that satisfies all the above conditions. It seems that the OPLIB opacities are preferred ove…
The simultaneous presence of variability due to both pulsations and binarity is no rare phenomenon. Unfortunately, the complexities of dealing with even one of these sources of variability individually means that the other signal is often treated as a nuisance and discarded. However, both types of variability offer means to probe fundamental stellar properties in robust ways through asteroseismic and binary modelling. We present an efficient methodology that includes both binary and asteroseismic information to estimate fundamental stellar properties based on a grid-based modelling approach. W…
Pulsating hot B subdwarf (sdB) stars, which are core-He burning objects, are one of the showcases of asteroseismology. Thanks to the combination of rich pulsation spectra and state-of-the-art modeling tools it is possible to tightly constrain fundamental parameters such as the stellar mass. There are on the contrary very few hotter sdO pulsators, which are in a more advanced evolutionary stage. Some of them are identified in Globular Clusters (GCs), but they are extremely rare in the field. Recently, it was suggested that PB8783, one of the very first sdB pulsators discovered in 1997, may in f…
We present the discovery and asteroseismic analysis of a new g-mode hot B subdwarf (sdB) pulsator, EC 21494-7018 (TIC 278659026), monitored in TESS first sector using 120-second cadence. The light curve analysis reveals that EC 21494-7018 is a sdB pulsator counting up to 20 frequencies associated with independent g-modes. The seismic analysis singles out an optimal model solution in full agreement with independent measurements provided by spectroscopy (atmospheric parameters derived from model atmospheres) and astrometry (distance evaluated from Gaia DR2 trigonometric parallax). Several key pa…
Is a 1D perturbative method sufficient for asteroseismic modelling of $β$ Cephei pulsators? Implications for measurements of rotation and internal magnetic fields
We report an analysis of the first known Beta Cep pulsator observed by the TESS mission, the runaway star PHL 346 = HN Aqr. The star, previously known as a singly-periodic pulsator, has at least 34 oscillation modes excited, 12 of those in the g-mode domain and 22 p modes. Analysis of archival data implies that the amplitude and frequency of the dominant mode and the stellar radial velocity were variable over time. A binary nature would be inconsistent with the inferred ejection velocity from the Galactic disc of 420 km/s, which is too large to be survivable by a runaway binary system. A kinem…
51 Eri is well known for hosting a directly-imaged giant planet and for its membership to the $β$ Pictoris moving group. Using two-minute cadence photometry from the Transiting Exoplanet Survey Satellite (TESS), we detect multi-periodic variability in 51 Eri that is consistent with pulsations of Gamma Doradus ($γ$ Dor) stars. We identify the most significant pulsation modes (with frequencies between $\sim$0.5-3.9 cycles/day and amplitudes ranging between $\sim$1-2 mmag) as dipole and quadrupole gravity-modes, as well as Rossby modes, as previously observed in Kepler $γ$ Dor stars. Our results …
We present a comprehensive seismic study of the three pulsating stars of $β$ Cep/SPB type: $ν$ Eridani, 12 Lacertae and $γ$ Pegasi. Models with the modified mean opacity profile are constructed in order to account for both the observed frequency range and the values of some individual frequencies. To decrease the number of possible solutions, we make use of the non-adiabatic parameter $f$, whose value is very sensitive to subphotospheric layers where pulsations are driven. This complex seismic modelling show the need for a significant modification of the opacity profile.
Pulsating binary stars are ideal targets for testing the theory of stellar structure and evolution. Fundamental parameters can be derived to high precision from binary modelling and provide crucial constraints for seismic modelling. High-order gravity modes are sensitive to the conditions near the convective core and therefore allow for a determination of parameters describing interior physics, especially the convective-core overshooting parameter. KIC\,10080943 is a binary system that contains two gravity- and pressure-mode hybrid pulsators. A detailed observational study has provided fundame…
Context. In asteroseismology the pulsation mode frequencies of a star are the fundamental data that are compared to theoretical predictions to determine a star's interior physics. Recent significant advances in the numerical, theoretical and statistical asteroseismic methods applied to main sequence stars with convective cores have renewed the interest in investigating the propagation of observational uncertainties within a forward asteroseismic modelling framework. Aims. We aim to quantify the impact of various choices made throughout the observational aspects of extracting pulsation mode fre…
We present examples of an extended asteroseismic modelling in which we aim at fitting not only pulsational frequencies but also certain complex parameter related to each frequency. This kind of studies, called \textbf{complex asteroseismology}, has been successfully applied to a few main sequence B-type pulsators and provided, in particular, plausible constraints on \textbf{stellar opacities}. Here, we briefly describe our results for three early B-type stars.
This article reviews the present knowledge on oscillating main sequence A/F stars that belong to more than one class of pulsator. Due to recent results of asteroseismic space missions, we now know of many Delta Scuti/Gamma Doradus stars. However, Gamma Doradus variability was also detected in a rapidly oscillating Ap star, and solar-like oscillations were discovered in a Delta Scuti star. The astrophysical information that can be gained from these pulsators is discussed, and confronted with what is believed to be known about pulsational driving.
Asteroseismology is a powerful tool to infer fundamental stellar properties. The use of these asteroseismic-inferred properties in a growing number of astrophysical contexts makes it vital to understand their accuracy. Consequently, we performed a hare-and-hounds exercise where the hares simulated data for 6 artificial main-sequence stars and the hounds inferred their properties based on different inference procedures. To mimic a pipeline such as that planned for the PLATO mission, all hounds used the same model grid. Some stars were simulated using the physics adopted in the grid, others a di…
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…
We present the discovery of three new $β$ Cep pulsators, three new pulsators with frequency groupings, and frequency patterns in a B3Ib star, all of which show pulsations with frequencies as high as about 17 d$^{-1}$, with K2 space mission photometry. Based on a Fourier analysis and iterative pre-whitening we present a classification and evaluate the potential for asteroseismic modelling. We include the lists of pulsation frequencies for three new $β$ Cep pulsators, CD-28 12286, CD-27 10876, LS 3978, and additional pulsation mode frequencies for the known $β$ Cep pulsator HD 164741. In additio…
Context: The central star of the HR 8799 system is a gamma Doradus-type pulsator. The system harbours four planetary-mass companions detected by direct imaging, and is a good solar system analogue. The masses of the companions are not known accurately, because the estimation depends strongly on the age of the system, which is also not known with sufficient accuracy. Asteroseismic studies of the star might help to better constrain the age of HR 8799. We organized an extensive photometric and multi-site spectroscopic observing campaign for studying the pulsations of the central star. Aims: The a…
$ν$ Eridani is a well known multiperiodic $β$ Cephei pulsator which exhibits also the SPB (Slowly Pulsating B-type stars) type modes. Recent frequency analysis of the BRITE photometry of $α$ Lupi showed that the star is also a hybrid $β$ Cep/SPB pulsator, in which both high and low frequencies were detected. We construct complex seismic models in order to account for the observed frequency range, the values of the frequencies themselves and the non-adiabatic parameter $f$ for the dominant mode. Our studies suggest, that significant modifications of the opacity profile at the temperature range …
We present results of a {\bf comprehensive} asteroseismic modelling of the $β$ Cephei variable $θ$ Ophiuchi. {\bf We call these studies {\it complex asteroseismology} because our goal is to reproduce both pulsational frequencies as well as corresponding values of a complex, nonadiabatic parameter, $f$, defined by the radiative flux perturbation.} To this end, we apply the method of simultaneous determination of the spherical harmonic degree, $\ell$, of excited pulsational mode and the corresponding nonadiabatic $f$ parameter from combined multicolour photometry and radial velocity data. Using …
The present work performs an asteroseismic study of a gamma Doradus star member of the open cluster NGC 2506. This work conjugates the observational information of the star and the strong constraints imposed by the cluster membership, with the latest developed theoretical asteroseismic tools for the modelling of this type of objects, in particular the Frequency Ratio Method (FRM) and Time-Dependent Convection (TDC), to study the gamma Dor stars found in the NGC 2506 stellar cluster. The use of both techniques gives us the opportunity of constructing a self-consistent procedure, allowing the mo…
The short-period (P $\approx1.7$ d), Algol-type eclipsing binary KIC 7385478 consists of an F-type primary star ($M_1 \approx 1.71M_{\odot}$) and an evolved K-type secondary ($M_2 \approx 0.37M_{\odot}$) (Ozdarcan \& Ali Dal 2017). We study the variability of the {\it Kepler} light curve and attribute many frequency peaks in the Fourier spectrum to the spot modulation. These frequencies are in the form of orbital harmonics and are highly variable in amplitude. They are most likely from the mass-accreting primary star. In addition, we identify a series prograde dipole g-modes from the primary s…
Context. gamma Doradus (gamma Dor) are late A and F-type stars pulsating with high order gravity modes (g-modes). The existence of different evolutionary phases crossing the gamma Dor instability strip raises the question of the existence of pre-main sequence (PMS) gamma Dor stars. Aims. We intend to study the differences between the asteroseismic behaviour of PMS and main sequence (MS) gamma Dor pulsators as it is predicted by the current theory of stellar evolution and stability. Methods. We explore the adiabatic and non-adiabatic properties of high order g-modes in a grid of PMS and MS mode…
I review the properties of pulsators located on the upper main sequence in the HR diagram and discuss asteroseismic inferences on the internal structure of stars of spectral type A and B. Special attention is given to the problem of uncertainties in stellar opacities in modelling.
A promising way of testing the impact of a magnetic field on internal mixing (core overshooting, internal rotation) in main-sequence B-type stars is to perform asteroseismic studies of a sample of magnetic pulsators. The CoRoT satellite revealed that the B3IV star HD 43317 is a hybrid SPB/beta Cep-type pulsator that has a wealth of pulsational constraints on which one can perform a seismic modelling, in particular, probing the extent of its convective core and mixing processes. Moreover, indirect indicators of a magnetic field in the star were observed: rotational modulation due to chemical or…
The NASA's Transiting Exoplanet Survey Satellite (TESS) is about to provide full-frame images of almost the entire sky. The amount of stellar data to be analysed represents hundreds of millions stars, which is several orders of magnitude above the amount of stars observed by CoRoT, Kepler, or K2 missions. We aim at automatically classifying the newly observed stars, with near real-time algorithms, to better guide their subsequent detailed studies. In this paper, we present a classification algorithm built to recognise solar-like pulsators among classical pulsators, which relies on the global a…
B-type stars are promising targets for asteroseismic modelling, since their frequency spectrum is relatively simple. We deduce and summarise observational constraints for the hybrid pulsator, HD50230, earlier reported to have deviations from a uniform period spacing of its gravity modes. The combination of spectra and a high-quality light curve measured by the CoRoT satellite allow a combined approach to fix the position of HD50230 in the HR diagram. To describe the observed pulsations, classical Fourier analysis was combined with short-time Fourier transformations and frequency spacing analys…
Can Asteroseismic Structure Inversions Be Performed in Structure-Dependent Coordinates?
University of Hawaiʻi（夏威夷大学）；Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney（悉尼大学物理学院天体物理学研究所(SIfA)）；Yale University（耶鲁大学）；KU Leuven（荷语天主教鲁汶大学）
KIC~8262223 is an eclipsing binary with a short orbital period ($P=1.61$ d). The {\it Kepler} light curves are of Algol-type and display deep and partial eclipses, ellipsoidal variations, and pulsations of Delta Scuti type. We analyzed the {\it Kepler} photometric data, complemented by phase-resolved spectra from the R-C Spectrograph on the 4-meter Mayall telescope at Kitt Peak National Observatory and determined the fundamental parameters of this system. The low mass and oversized secondary ($M_2=0.20M_{\odot}$, $R_2=1.31R_{\odot}$) is the remnant of the donor star that transferred most of it…
Multi-dimensional (magneto-)hydrodynamical simulations of physical processes in stellar interiors depend on a multitude of uncalibrated free parameters, which set the spatial and time scales of their computations. We aim to provide an asteroseismic calibration of the wave and convective Rossby numbers, and of the stiffness at the interface between the convective core and radiative envelope of intermediate-mass stars. We deduce these quantities for rotating dwarfs from the observed properties of their identified gravity and gravito-inertial modes. We rely on near-core rotation rates and asteros…
The first asteroseismic studies of pre-main sequence (pre-MS) pulsators have been conducted based on data from the space telescopes MOST and CoRoT with typical time bases of less than 40 days. With these data, a relation between the pulsational properties of pre-MS delta Scuti stars and their relative evolutionary phase on their way from the birthline to the zero-age main sequence was revealed. But it is evident from comparison with the more evolved pulsators in their main sequence or post-main sequence stages observed by the main Kepler mission, that many more questions could be addressed wit…
Gamma Doradus and delta Scuti pulsators cover the transition region between low mass and massive main-sequence stars, and as such, are critical for testing stellar models. When they reside in binary systems, we can combine two independent methods to derive critical information, such as precise fundamental parameters to aid asteroseismic modelling. In the Kepler light curve of KIC10080943, clear signatures of gravity- and pressure-mode pulsations have been found. Ground-based spectroscopy revealed this target to be a double-lined binary system. We present the analysis of four years of Kepler ph…
Among the known groups of pulsating stars, $δ$ Sct stars are one of the least understood. Theoretical models do not predict the oscillation frequencies that observations reveal. Complete asteroseismic studies are necessary to improve these models and better understand the internal structure of these targets. We study the $δ$ Sct star HD 41641 with the ultimate goal of understanding its oscillation pattern. The target was simultaneously observed by the CoRoT space telescope and the HARPS high-resolution spectrograph. The photometric data set was analyzed with the software package PERIOD04, whil…
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 …
A noticeable fraction of subdwarf B stars shows either short-period (p-mode) or long-period (g-mode) luminosity variations, with two objects so far known to exhibit hybrid behaviour, i.e. showing both types of modes at the same time. The pulsating subdwarf B star V391 Pegasi (or HS2201+2610), which is close to the two known hybrid pulsators in the log g - Teff plane, has recently been discovered to host a planetary companion. In order to learn more about the planetary companion and its possible influence on the evolution of its host star (subdwarf B star formation is still not well understood)…
Rossby modes are the oscillations in a rotating fluid, whose restoring force is the Coriolis force. They provide an additional diagnostic to understand the rotation of stars, which complicates asteroseismic modelling. We report 82 $γ$\,Doradus stars for which clear period spacing patterns of both gravity and Rossby modes have been detected. The period spacings of both show a quasi-linear relation with the pulsation period but the slope is negative for the gravity modes and positive for the Rossby modes. Most Rossby modes have $k=-2, m=-1$. For only one star a series of $k=-1,m=-1$ modes is see…
Comparing models and data of pulsating stars is a powerful way to understand the stellar structure better.βHyi is an evolved solar-type pulsator with mixed modes in its frequency spectrum, making it very interesting for asteroseismic studies.The goal of this work is to search for the best model of the solar-type star βHyi, based on up-to-date non-seismic and seismic data.We present a revised list of frequencies for 33 modes, which we produced by analysing the power spectrum of the published observations again using a new weighting scheme that minimises the daily sidelobes.We ran several grids …
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…
Recent progress in the seismic interpretation of field beta Cep stars has resulted in improvements of the physics in the stellar structure and evolution models of massive stars. Further asteroseismic constraints can be obtained from studying ensembles of stars in a young open cluster, which all have similar age, distance and chemical composition. We present an observational asteroseismology study based on the discovery of numerous multi-periodic and mono-periodic B-stars in the open cluster NGC 884. We describe a thorough investigation of the pulsational properties of all B-type stars in the c…
The $β$ Cephei pulsators are massive main-sequence stars, presenting low radial-order modes. These modes probe in particular the chemical gradient at the edge of the convective core. They hence give constraints on macroscopic processes, such as hydrodynamic or magnetic instabilities. Yet, it is not clear to what extent the seismic inferences depend on the physics employed for the stellar modelling or on the observational dataset. We investigate the observational constraints which are necessary to provide accurate constraints on the mixing processes in $β$ Cephei stars. We explore the importanc…
