According to the rotational splitting law of g modes, the frequency spectra of EE Cam can be disentangled only with oscillation modes of $\ell$ = 0, 1, and 2. Fifteen sets of rotational splits are found, containing five sets of $\ell=1$ multiplets and ten sets of $\ell=2$ multiplets. The rotational period of EE Cam is deduced to be $P_{\rm rot}$ = $1.84_{-0.05}^{+0.07}$ days. When we do model fittings, we use two nonradial oscillation modes ($f_{11}$ and $f_{32}$) and the fundamental radial mode $f_{1}$. The fitting results show that $χ^{2}$ of the best-fitting model is much smaller than those of other theoretical models. The physical parameters of the best-fitting model are $M$ = 2.04 $M_{\odot}$, $Z=0.028$, $T_{\rm eff}$ = 6433 K, $\log L/L_{\odot}$ = 1.416, $R$ = 4.12 $R_{\odot}$, $\log g$ = 3.518, and $χ^{2}$ = 0.00035. Furthermore, we find $f_{11}$ and $f_{32}$ are mixed mode, which mainly characterize the features of the helium core. The fundamental radial mode $f_{1}$ mainly restrict the features of the stellar envelope. Finally, the acoustic radius $τ_{0}$ and the period separation $Π_{0}$ are determined to be 5.80 hr and 463.7 s respectively, and the size of the helium core of EE Cam is estimated to be $M_{\rm He}$ = 0.181 $M_{\odot}$ and $R_{\rm He}$ = 0.0796 $R_{\odot}$.
In the last years, space missions such as COROT, Kepler or MOST have provided very accurate photometric observational data. In the particular case of $δ$ Scuti stars, the observed frequency spectra have hundreds (if not thousands) of modes and a clear amplitude distribution. In this work we present new techniques for modelling these observations and the results obtained. We searched for regular patterns in the observational data, which yields something resembling the large separation. This allows to reduce the possible positions of the star in the HR diagram, yielding a value of the mean densi…
We present the results of analysis and modelling of the eclipsing binary system, KIC 10661783. The Fourier analysis of the Kepler light curve, corrected for the binary effects, reveals 750 frequency peaks in both p and g-mode regions. Those with the highest amplitudes concentrate in the range of 20-30 d$^{-1}$. To reproduce observed spectrum of frequencies we construct seismic models accounting for the mode instability. In order to obtain instabilities in the g-mode regime we modify the opacity tables data near the Z-bump. In order to reproduce system parameters, we construct evolutionary mode…
The present work concerns the Asteroseismology of the Kepler detached eclipsing binary KIC 8504570. Particularly, it focuses on the pulsational behaviour of the oscillating component of this system and the estimation of its physical parameters in order to enrich the so far poor sample of this kind of systems. Using spectroscopic observations, the spectral type of the primary component was determined and used to create accurate light curves models and estimate its absolute parameters. The light curve residuals were subsequently analysed using Fourier transformation techniques to obtain the puls…
We present an analysis of the δ-Scuti star object HD 174936 (ID 7613) observed by CoRoT during the first short run SRc01 (27 days). A total number of 422 frequencies we are extracted from the light curve using standard prewhitening techniques. This number of frequencies was obtained by considering a spectral significance limit of sig = 10 using the software package SigSpec. Our analysis of the oscillation frequency spectrum reveals a spacing periodicity of around 52 \muHz. Although modes considered here are not in the asymptotic regime, a comparison with stellar models confirms that this signa…
Statistical analysis of asteroseismic indices and stellar parameters of TESS-observed $δ$ Scuti stars
Xinjiang Astronomical Observatory, Chinese Academy of Sciences（中国科学院新疆天文台）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文学与空间科学学院）；Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick（华威大学物理学院聚变、太空与天体物理学中心）；Institute of Geophysics, University of Tehran（德黑兰大学地球物理学研究所）；Department of Physics, Faculty of Science, University of Qom（库姆大学理学院物理系）；Instituto de Astrofísica de Andalucía - CSIC（安达卢西亚天体物理研究所-西班牙国家科研委员会）；Departamento de Física Teórica y del Cosmos, Universidad de Granada（格拉纳达大学理论与宇宙物理学系）；Ulugh Beg Astronomical Institute, Uzbekistan Academy of Sciences（乌兹别克斯坦科学院乌鲁格别克天文研究所）
It is known that the observed distribution of frequencies in CoRoT and Kepler δ Scuti stars has no parallelism with any theoretical model. Pre-whitening is a widespread technique in the analysis of time series with gaps from pulsating stars located in the classical instability strip such as δ Scuti stars. However, some studies have pointed out that this technique might introduce biases in the results of the frequency analysis. This work aims at studying the biases that can result from pre-whitening in asteroseismology. The results will depend on the intrinsic range and distribution of frequenc…
HD 144277 was previously discovered by MOST space photometry to be a young and hot delta Scuti star showing regular groups of pulsation frequencies. The first asteroseismic models required lower than solar metallicity to fit the observed frequency range based on a purely photometric analysis. High-resolution, high S/N spectroscopic data obtained with the HARPS spectrograph were used to determine the fundamental parameters and chemical abundances of HD 144277. These values were put into context alongside the results from asteroseismic models. The effective temperature, Teff, of HD 144277 was de…
Pulsating extremely low-mass pre-white dwarf stars (pre-ELMV), with masses between ~0.15 Msun and ~0.30 Msun, constitute a new class of variable stars showing g- and possibly p-mode pulsations with periods between 320 and 6000 s, while main sequence delta Scuti stars, with masses between 1.2-2.5 Msun, pulsate in low-order g and p modes with periods in the range [700-28800] s. Interestingly enough, the instability strips of pre-ELM white dwarf and delta Scuti stars nearly overlap in the Teff vs. log g diagram, leading to a degeneracy when spectroscopy is the only tool to classify the stars and …
We review recent research on Delta Scuti stars from an observer's viewpoint. First, some signposts helping to lead the way through the Delta Scuti jungle are placed. Then, some problems in studying individual pulsators in the framework of asteroseismology are given before a view on how the study of these variables has benefited (or not) from past and present high-precision asteroseismic space missions is presented. Some possible pitfalls in the analysis of data with a large dynamical range in pulsational amplitudes are pointed out, and a strategy to optimize the outcome of asteroseismic studie…
Thanks to relatively firm mode identification, possible based on period ratios only, High Amplitude Delta Scuti Stars pulsating in at least three radial modes are promising targets for asteroseismic inference. In this study we used the most numerous sample of HADS from the OGLE inner bulge fields that likely pulsate in either three or four radial modes simultaneously. We have computed a grid of pulsation models along evolutionary tracks and determined the physical parameters of stars by matching their pulsation periods and period ratios. For 176 HADS we determined physical parameters, i.e. mas…
We present high-precision time-series photometry of the classical delta Scuti star HD 144277 obtained with the MOST (Microvariability and Oscillations of STars) satellite in two consecutive years. The observed regular frequency patterns are investigated asteroseismologically. HD 144277 is a hot A-type star that is located on the blue border of the classical instability strip. While we mostly observe low radial order modes in classical delta Scuti stars, HD 144277 presents a different case. Its high observed frequencies, i.e., between 59.9c/d (693.9 microHz) and 71.1c/d (822.8microHz), suggest …
The evolutionary stage of the delta Scuti star 44 Tau has been unclear. Recent asteroseismic studies have claimed models on the main sequence, as well as in the expansion phase of the post-main sequence evolution. However, these models could not reproduce all of the observed frequencies, the mode instability range, and the fundamental stellar parameters simultaneously. A recent photometric study has increased the number of detected independent modes in 44 Tau to 15, and a newly found gravity mode at 5.30 c/d extends the observed frequency range. Aims. One of the possible evolutionary stages of…
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）
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…
We perform mode identification for five $δ$ Scuti stars in the Pleiades star cluster, using custom light curves from K2 photometry. By creating échelle diagrams, we identify radial and dipole mode ridges, comprising a total of 28 radial and 16 dipole modes across the five stars. We also suggest possible identities for those modes that lie offset from the radial and dipole ridges. We calculate non-rotating stellar pulsation models to verify our mode identifications, finding good agreement within the age and metallicity constraints of the cluster. We also find that for all stars, the least dense…
We present a photometric, spectroscopic, asteroseismic, and evolutionary analysis of the Algol-type eclipsing binary KIC 12268220. We find the O'Connell effect and anticorrelated eclipse timing variations in the Kepler light curve, revealing the presence of large starspots. Radial velocities and atmospheric parameters are obtained from ground-based spectroscopic observations. Combined with the radial velocity measurements and Gaia-derived total luminosity, our light-curve modeling yields the solution of the physical parameters for both the primary and secondary components. We find 14 independe…
Hybrid $δ$ Scuti-$γ$ Doradus pulsating stars show acoustic ($p$) oscillation modes typical of $δ$ Scuti variable stars, and gravity ($g$) pulsation modes characteristic of $γ$ Doradus variable stars simultaneously excited. Observations from space missions like MOST, CoRoT, and \emph{Kepler} have revealed a large number of hybrid $δ$ Scuti-$γ$ Doradus pulsators, thus paving the way for a exciting new channel for asteroseismic studies. We perform a detailed asteroseismological modeling of five hybrid $δ$ Scuti-$γ$ Doradus stars. We employ a grid-based modeling approach to sound the internal stru…
Hybrid stars of the γ Doradus and δ Scuti pulsation types have great potential for asteroseismic analysis to explore their interior structure. To achieve this, mode identi- fications of pulsational frequencies observed in the stars must be made, a task which is far from simple. In this work we begin the analysis by scrutinizing the frequencies found in the CoRoT photometric satellite measurements and ground-based high-resolution spectroscopy of the hybrid star HD 49434. The results show almost no consistency between the frequencies found using the two techniques and no characteristic period sp…
We present the first asteroseismic results for $δ$ Scuti and $γ$ Doradus stars observed in Sectors 1 and 2 of the TESS mission. We utilise the 2-min cadence TESS data for a sample of 117 stars to classify their behaviour regarding variability and place them in the Hertzsprung-Russell diagram using Gaia DR2 data. Included within our sample are the eponymous members of two pulsator classes, $γ$ Doradus and SX Phoenicis. Our sample of pulsating intermediate-mass stars observed by TESS also allows us to confront theoretical models of pulsation driving in the classical instability strip for the fir…
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.
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…
Metallic-line A (Am) stars are main-sequence stars of around twice the mass of the Sun that show element abundance peculiarities in their spectra. The radiative levitation and diffusive settling processes responsible for these abundance anomalies should also deplete helium from the region of the envelope that drives delta Scuti pulsations. Therefore, these stars are not expected to be delta Scuti stars, which pulsate in multiple radial and nonradial modes with periods of around 2 hours. As part of the NASA TESS Guest Investigator Program, we proposed photometric observations in 2-minute cadenc…
The Kepler space mission provided a wealth of δ Sct-γ Dor hybrid candidates. While some may be genuine hybrids, others might be misclassified due to the presence of a binary companion or to rotational modulation caused by magnetism and related surface inhomogeneities. In particular, the Kepler δ Sct-γ Dor hybrid candidate HD 188774 shows a few low frequencies in its light and radial velocity curves, whose origin is unclear. In this work, we check for the presence of a magnetic field in HD 188774. We obtained two spectropolarimetric measurements with ESPaDOnS at CFHT. The data were analysed wit…
We aim at studying the theoretical properties of the regular spacings found in the oscillation spectra of delta Scuti stars. We performed a multi-variable analysis covering a wide range of stellar structure and seismic properties and model parameters representative of intermediate-mass, main sequence stars. The work-flow is entirely done using a new Virtual Observatory tool: TOUCAN (the VO gateway for asteroseismic models), which is presented in this paper. A linear relation between the large separation and the mean density is predicted to be found in the low frequency frequency domain (i.e. r…
Asteroseismology is witnessing a revolution thanks to high-precise asteroseismic space data (MOST, CoRoT, Kepler, BRITE), and their large ground-based follow-up programs. Those instruments have provided an unprecedented large amount of information, which allows us to scrutinize its statistical properties in the quest for hidden relations among pulsational and/or physical observables. This approach might be particularly useful for stars whose pulsation content is difficult to interpret. This is the case of intermediate-mass classical pulsating stars (i.e. gamma Dor, delta Scuti, hybrids) for wh…
Modelling $δ$ Scuti pulsations: A new grid of p, g, and f modes across pre-main-sequence to post-main-sequence evolution
Centre for Astrophysics, University of Southern Queensland（南昆士兰大学天体物理中心）；Sydney Institute for Astronomy, School of Physics, University of Sydney（悉尼大学物理学院悉尼天文研究所）
The present work contains light curve, spectroscopic and asteroseismic analyses for KIC 04851217 and KIC 10686876. These systems are detached eclipsing binaries hosting a pulsating component of delta Scuti type and have been observed with the unprecedented accuracy of the Kepler space telescope. Using ground based spectroscopic observations, the spectral types of the primary components of the systems were estimated as A6V and A5V for KIC 04851217 and KIC 10686876, respectively, with an uncertainty of one subclass. The present spectral classification together with literature radial velocities c…
The large separation in the low radial order regime is considered as a highly valuable observable to derive mean densities of $δ$ Scuti stars, due to its independence with rotation. Up to now, theoretical studies of this $Δν$-${\bar ρ}$ relation have been limited to 1D non-rotating models, and 2D pseudo-evolutionary models. The present work aims at completing this scenario by investigating quantitatively the impact of rotation in this relation on a large grid of 1D asteroseismic models representative of $δ$ Scuti stars. These include rotation effects on both the stellar evolution and the inter…
We study the $δ$ Scuti -- red giant binary KIC9773821, the first double-pulsator binary of its kind. It was observed by \textit{Kepler} during its four-year mission. Our aims are to ascertain whether the system is bound, rather than a chance alignment, and to identify the evolutionary state of the red giant via asteroseismology. An extension of these aims is to determine a dynamical mass and an age prior for a $δ$ Sct star, which may permit mode identification via further asteroseismic modelling. We determine spectroscopic parameters and radial velocities (RVs) for the red giant component usin…
We concentrate on an asteroseismological study of HD 261711, a rather hot delta Scuti type pulsating member of the young open cluster NGC 2264 located at the blue border of the instability region. HD 261711 was discovered to be a pre-main sequence delta Scuti star using the time series photometry obtained by the MOST satellite in 2006. High-precision, time-series photometry of HD 261711 was obtained by the MOST and CoRoT satellites in 4 separate new observing runs that are put into context with the star's fundamental atmospheric parameters obtained from spectroscopy. With the new MOST data set…
Despite a century of remarkable progress in understanding stellar interiors, we know surprisingly little about the inner workings of stars spinning near their critical limit. New interferometric imaging of these so-called ``rapid rotators'' combined with breakthroughs in asteroseismology promise to lift this veil and probe the strongly latitude-dependent photospheric characteristics and even reveal the internal angular momentum distribution of these luminous objects. Here, we report the first high precision photometry on the low-amplitude delta cuti variable star Rasalhague (alpha Oph, A5IV, 2…
This paper reports the discovery of an Algol system KIC 10736223 that just past the rapid mass transfer stage. From the light curve and radial-velocity modelling we find KIC 10736223 to be a detached Algol system with the less-massive secondary nearly filling its Roche lobe. Based on the short-cadence Kepler data, we analyzed intrinsic oscillations of the pulsator and identified six secured independent $δ$ Scuti-type pulsation modes ($f_{1}$, $f_3$, $f_{9}$, $f_{19}$, $f_{42}$, and $f_{48}$). We compute two grids of theoretical models to reproduce the $δ$ Scuti freqiencies, and find fitting re…
In this work we aim at constraining the age of the young open cluster Melotte 20, known as $α$ Per, using seismic indices. The method consists of the following steps: 1) Extract the frequency content of a sample of stars in the field of an open cluster. 2) Search for possible regularities in the frequency spectra of $δ$ Scuti candidates, using different techniques, such as the Fourier transform, the autocorrelation function, the histogram of frequency differences and the échelle diagram. 3) Constrain the age of the selected stars by both the physical parameters and seismic indices by comparing…
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…
We propose that KIC 1573174 is a quadruple-mode $δ$ Scuti star with pulsation amplitudes between those of the HADS (high-amplitude Delta Scuti star) group and average low-amplitude pulsators. The radial modes detected in this star provide a unique opportunity to exploit asteroseismic techniques up to their limits. Detailed frequency analysis is given for the light curve from the Kepler mission. The variation of the light curve is dominated by the strongest mode with a frequency of F0 = 7.3975 $\rm{d^{-1}}$, as shown by Fourier analysis of long cadence data (Q1-Q17, spanning 1460 days), indicat…
Many stars exhibit stellar pulsations, favoring them for asteroseismic analyses. Interpreting the oscillations requires some knowledge of the oscillation mode geometry (spherical degree, radial and azimuthal orders). The delta Scuti stars (1.5 - 2.5 M_sol) often show just one or few pulsation frequencies. Although this may promise a successful seismological analysis, we may not know enough about either the mode or the star to use the oscillation frequency to improve the determination of the stellar model, or probe the star's structure. For the observed frequencies to be used successfully as se…
Context. This research paper contains light curve modelling, spectroscopy and detailed asteroseismic studies for four out of five in total semidetached eclipsing binaries with a delta Scuti component, that have been detected to date through Kepler mission, namely KIC 06669809, KIC 10581918, KIC 10619109 and KIC 11175495. Aims. The goal is to study the pulsational characteristics of the oscillating stars of the systems as well as to estimate their absolute parameters and enrich the so far poor sample of this kind of systems. Methods. Ground based spectroscopic observations provide the means to …
The physics of early stellar evolution (e.g. accretion processes) is often not properly included in the calculations of pre-main-sequence models, leading to insufficient model grids and hence systematic errors in the results. We aim to investigate current and improved approaches for the asteroseismic modelling of pre-main-sequence delta Scuti stars. We calculated an extensive grid of pre-main-sequence models including the early accretion phase and used the resulting equilibrium models as input to calculate theoretical frequency spectra. These spectra were used to investigate different approach…
Based on the two-minutes TESS data, we analyzed intrinsic oscillations of the primary component and identified seven confident independent $δ$ Scuti frequencies ($f_1$, $f_2$, $f_3$, $f_4$, $f_7$, $f_{11}$, and $f_{12}$). Both of single-star evolutionary models and mass-accreting models are computed to reproduce the $δ$ Scuti freqiencies. Fitting results of them match well with each other. The stellar parameters of the primary star yielded by asteroseismology are $M$ = $1.92^{+0.10}_{-0.02}$ $M_{\odot}$, $Z$ = 0.011$^{+0.006}_{-0.001}$, $R$ = $2.068^{+0.050}_{-0.007}$ $R_{\odot}$, $\log g$ = $…
Discovery of the First Octupole Pulsation Mode in a delta Scuti Star: A Stationary l = 3 Sectoral Mode
HUN–REN–SZTE Stellar Astrophysics Research Group（匈牙利科学院-塞格德大学恒星天体物理学研究组）；Department of Physics, Kavli Institute for Astrophysics and Space Research, M.I.T.（麻省理工学院物理系卡弗里天体物理学与空间研究研究所）；Department of Astronomy, Cornell University（康奈尔大学天文学系）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文中心）；Centre for Space Research, North-West University（西北大学太空研究中心）；Jeremiah Horrocks Institute, University of Lancashire（兰开夏大学杰里迈亚·霍克斯研究所）；Harvard University（哈佛大学）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）；TAPIR, Mailcode 350-17, California Institute of Technology（加州理工学院TAPIR（邮件代码350-17））；Baja Astronomical Observatory of University of Szeged（塞格德大学巴亚天文台）；Konkoly Observatory, Research Centre for Astronomy and Earth Sciences（匈牙利科学院地球科学研究中心孔科利天文台）；ELTE Eötvös Loránd University, Gothard Astrophysical Observatory（罗兰大学哥塔德天体物理观测站）
Very high precision seismic space missions such as CoRoT and Kepler provide the means for testing the modelling of transport processes in stellar interiors. For some stars, such as $δ$ Scuti $γ$ Doradus and Be stars, for instance, the observed pulsation spectra are modified by rotation to such an extent that it prevents any fruitful interpretation. Our aim is to characterise acoustic pulsation spectra of realistic stellar models in order to be able to interpret asteroseismic data from such stars. The 2-dimensional oscillation code ACOR, which treats rotation in a non-perturbative manner, is us…
