Recent asteroseismic analyses have revealed the presence of strong (B $\gtrsim 10^5$ G) magnetic fields in the cores of many red giant stars. Here, we examine the implications of these results for the evolution of stellar magnetic fields, and we make predictions for future observations. Those stars with suppressed dipole modes indicative of strong core fields should exhibit moderate but detectable quadrupole mode suppression. The long magnetic diffusion times within stellar cores ensure that dynamo-generated fields are confined to mass coordinates within the main sequence convective core, and the observed sharp increase in dipole mode suppression rates above $1.5 \, M_\odot$ may be explained by the larger convective core masses and faster rotation of these more massive stars. In clump stars, core fields of $\sim10^5 \, {\rm G}$ can suppress dipole modes, whose visibility should be equal to or less than the visibility of suppressed modes in ascending red giants. High dipole mode suppression rates in low-mass ($M \lesssim 2 \, M_\odot$) clump stars would indicate that magnetic fields generated during the main sequence can withstand subsequent convective phases and survive into the compact remnant phase. Finally, we discuss implications for observed magnetic fields in white dwarfs and neutron stars, as well as the effects of magnetic fields in various types of pulsating stars.
Asteroseismic forward modelling techniques are being used to determine fundamental properties (e.g. mass, radius, and age) of solar-type stars. The need to take into account all possible sources of error is of paramount importance towards a robust determination of stellar properties. We present a study of 34 solar-type stars for which high signal-to-noise asteroseismic data is available from multi-year Kepler photometry. We explore the internal systematics on the stellar properties, that is, associated with the uncertainty in the input physics used to construct the stellar models. In particula…
With four years of nearly-continuous photometry from Kepler, we are finally in a good position to apply asteroseismology to $γ$ Doradus stars. In particular several analyses have demonstrated the possibility to detect non-uniform period spacings, which have been predicted to be directly related to rotation. In the present work, we define a new seismic diagnostic for rotation in $γ$ Doradus stars that are too rapidly rotating to present rotational splittings. Based on the non uniformity of their period spacings, we define the observable $Σ$ as the slope of the period spacing when plotted as a f…
Asteroseismic observations of internal stellar rotation have indicated a substantial lack of angular momentum transport in theoretical models of subgiant and red-giant stars. Accurate core and surface rotation rate measurements are therefore needed to constrain internal transport processes included in the models. We eliminate substantial systematic errors of asteroseismic surface rotation rates found in previous studies. We propose a new objective function for the Optimally Localized Averages method of rotational inversions for red-giant stars, which results in more accurate envelope rotation …
Is a 1D perturbative method sufficient for asteroseismic modelling of $β$ Cephei pulsators? Implications for measurements of rotation and internal magnetic fields
Asteroseismology has emerged as the best way to characterize the global and internal properties of nearby stars. Often, this characterization is achieved by fitting stellar evolution models to asteroseismic observations. The star under investigation is then assumed to have the properties of the best-fitting model, such as its age. However, the models do not fit the observations perfectly. This is due to incorrect or missing physics in stellar evolution calculations, resulting in predicted stellar structures that are discrepant with reality. Through an inverse analysis of the asteroseismic data…
We have discovered rotationally split core g-mode triplets and surface p-mode triplets and quintuplets in a terminal age main sequence A star, KIC 11145123, that shows both $δ$ Sct p-mode pulsations and $γ$ Dor g-mode pulsations. This gives the first robust determination of the rotation of the deep core and surface of a main sequence star, essentially model-independently. We find its rotation to be nearly uniform with a period near 100 d, but we show with high confidence that the surface rotates slightly faster than the core. A strong angular momentum transfer mechanism must be operating to pr…
Asteroseismic rotation rates of hot subdwarf B stars hint at transient accretion from leftover common envelope matter
Yunnan Observatories, Chinese Academy of Sciences（中国科学院云南天文台）；Heidelberger Institut für Theoretische Studien (HITS)（海德堡理论研究所）；Center for Astronomy (ZAH/LSW), Heidelberg University（海德堡大学天文学中心）；Institute of Astronomy, KU Leuven（鲁汶大学天文学研究所）；London Centre for Stellar Astrophysics（伦敦恒星天体物理学中心）；University of Oxford（牛津大学）；Thüringer Landessternwarte Tautenburg（图林根州陶滕堡天文台）
Transport of angular momentum in stellar interiors is currently not well understood. Asteroseismology can provide us with estimates of internal rotation of stars and thereby advances our understanding of angular momentum transport. We can measure core-rotation rates in red-giant stars and we can place upper bounds on surface-rotation rates using measurements of dipole ($l=1$) modes. Here, we aim to determine the theoretical sensitivity of modes of different spherical degree towards the surface rotation. Additionally, we aim to identify modes that can potentially add sensitivity at intermediate…
We present an asteroseismic approach to study the dynamics of the stellar interior in red-giant stars by asteroseismic inversion of the splittings induced by the stellar rotation on the oscillation frequencies. We show preliminary results obtained for the red giant KIC4448777 observed by the space mission Kepler.
HD 129929 is a slowly-rotating $β$ Cephei pulsator with a rich spectrum of detected oscillations, including two rotational multiplets. The asteroseismic interpretation revealed the presence of radial differential rotation in this massive star of $\sim$9.35 M . The stellar core is indeed estimated to spin $\sim$3.6 times faster than the surface. The surface rotation was consequently derived as $\sim$2 km/s. This massive star represents an ideal counter-part to the wealth of space-based photometry results for main-sequence and evolved low-mass stars. Those latter have revealed a new, and often u…
DA-type white dwarfs account for 80% of all white dwarfs and represent, for most of them, the ultimate outcome of the typical evolution of low-to-intermediate mass stars. Their internal chemical stratification is strongly marked by passed, often uncertain, stellar evolution processes that occurred during the helium (core and shell) burning phases, i.e., from the horizontal branch through AGB and post-AGB stages. Pulsating white dwarfs, in particular the "cool" DA-type ZZ Ceti variables, offer an outstanding opportunity to dig into these stars by fully exploiting their asteroseismic potential. …
We present a method for measuring internal stellar structure based on asteroseismology that we call "inversions for agreement." The method accounts for imprecise estimates of stellar mass and radius as well as the relatively limited oscillation mode sets that are available for distant stars. By construction, the results of the method are independent of stellar models. We apply this method to measure the isothermal sound speeds in the cores of the solar-type stars 16 Cyg A and B using asteroseismic data obtained from Kepler observations. We compare the asteroseismic structure that we deduce aga…
We present the results of the asteroseismic analysis of the hydrogen-deficient white dwarf PG 0112+104 from the $Kepler$-2 field. Our seismic procedure using the forward method based on physically sound, static models, includes the new core parameterization leading us to reproduce the periods of this star near the precision of the observations. This new fit outperforms current state-of-the-art standards by order of magnitudes. We precisely establish the internal structure and unravel the inner C/O stratification of its core. This opens up interesting perspectives on better constraining key pro…
Context: Asteroseismic measurements reveal that an unknown efficient angular momentum (AM) transport mechanism is needed for subgiant and red giant stars. A revised prescription for AM transport by the magnetic Tayler instability has been recently proposed as a possible candidate for such a missing mechanism. Results: The revised prescription for the transport by the Tayler instability leads to low core rotation rates after the main sequence that are in better global agreement with asteroseismic measurements than those predicted by models with purely hydrodynamic processes or with the original…
Observations of magnetic activity cycles in other stars provide a broader context for our understanding of the 11-year sunspot cycle. The discovery of short activity cycles in a few stars, and the recognition of analogous variability in the Sun, suggest that there may be two distinct dynamos operating in different regions of the interior. Consequently, there is a natural link between studies of magnetic activity and asteroseismology, which can characterize some of the internal properties that are relevant to dynamos. I provide a brief historical overview of the connection between these two fie…
Turbulent processes in the convective envelopes of the sun and stars have been shown to be a source of internal acoustic excitations. In single stars, acoustic waves having frequencies below a certain cutoff frequency propagate nearly adiabatically and are effectively trapped below the photosphere where they are internally reflected. This reflection essentially occurs where the local wavelength becomes comparable to the pressure scale height. In close binary stars, the sound speed is a constant on equipotentials, while the pressure scale height, which depends on the local effective gravity, va…
In this paper we study the dynamics of the stellar interior of the early red-giant star KIC 4448777 by asteroseismic inversion of 14 splittings of the dipole mixed modes obtained from {\it Kepler} observations. In order to overcome the complexity of the oscillation pattern typical of red-giant stars, we present a procedure which involves a combination of different methods to extract the rotational splittings from the power spectrum. We find not only that the core rotates faster than the surface, confirming previous inversion results generated for other red giants (Deheuvels et al. 2012,2014), …
The advent of space-based photometry observations provided high-quality asteroseismic data for a large number of stars. These observations enabled the adaptation of advanced techniques, until then restricted to helioseismology, to study the best asteroseismic targets. Amongst these, the 16Cyg binary system holds a special place, being the brightest solar twins observed by Kepler. For this system, modellers have access to high-quality asteroseismic, spectroscopic and interferometric data, making it the perfect testbed for the limitations of stellar models. We aim to further constrain the intern…
The internal structures and properties of oscillating red-giant stars can be accurately inferred through their global oscillation modes (asteroseismology). Based on 1460 days of Kepler observations we perform a thorough asteroseismic study to probe the stellar parameters and evolutionary stages of three red giants in eclipsing binary systems. We present the first detailed analysis of individual oscillation modes of the red-giant components of KIC 8410637, KIC5640750 and KIC9540226. We obtain estimates of their asteroseismic masses, radii, mean densities and logarithmic surface gravities by usi…
Oscillation frequencies of even the best stellar models differ from those of the stars they represent, and the difference is predominantly a function of frequency. This difference is caused by limitations of modeling the near-surface layers of a star. This frequency-dependent frequency error, usually referred to as the "surface term" can result in erroneous interpretation of the oscillation frequencies unless treated properly. Several techniques have been developed to minimize the effect of the surface term; it is either subtracted out, or frequency combinations insensitive to the surface term…
Space observatories such as $\textit{Kepler}$ have provided data that can potentially revolutionise our understanding of stars. Through detailed asteroseismic analyses we are capable of determining fundamental stellar parameters and reveal the stellar internal structure with unprecedented accuracy. However, such detailed analyses, known as peak bagging, have so far been obtained for only a small percentage of the observed stars while most of the scientific potential of the available data remains unexplored. One of the major challenges in peak bagging is identifying how many solar-like oscillat…
The advent of space-based photometry missions in the early 21st century enabled the application to asteroseismic data of advanced inference techniques until then restricted to the field of helioseismology. The high quality of the observations, the discovery of mixed modes in evolved solar-like oscillators and the need for an improvement in the determination of stellar fundamental parameters such as mass, radius and age led to the development of sophisticated modelling tools, amongst which seismic inversions play a key role. In this review, we will discuss the existing inversion techniques for …
Asteroseismic Imprints of Mass Transfer in Binary Stars: Probing the Interiors of Donors and Accretors with Gravity and Acoustic Modes
Yunnan Observatories, Chinese Academy of Sciences（中国科学院云南天文台）；Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences（中国科学院天体结构与演化重点实验室）；International Centre of Supernovae, Yunnan Key Laboratory（云南省超新星国际研究中心）；University of Chinese Academy of Sciences（中国科学院大学）；Center for Astronomical Mega-Science, Chinese Academy of Sciences（中国科学院天文大科学中心）；Institute of Astronomy (IvS), KU Leuven（荷语鲁汶大学天体物理研究所）；Department of Applied Mathematics, School of Mathematics, University of Leeds（利兹大学数学学院应用数学系）
We compare evolved stellar models, which match Procyons mass and position in the HR diagram, to current ground-based asteroseismic observations. Diffusion of helium and metals along with two conventional core overshoot descriptions and the Kuhfuss nonlocal theory of convection are considered. We establish that one of the two published asteroseismic data reductions for Procyon, which mainly differ in their identification of even versus odd l-values, is a significantly more probable and self-consistent match to our models than the other. The most probable models according to our Bayesian analysi…
In the asymptotic parameterisation of mode frequencies, the phase function $ε(ν)$ completely specifies the detailed structure of the frequency eigenvalues. In practice, however, this function of frequency is reduced to a single scalar $ε$, defined, particularly by observers, as the intercept of a least-squares fit to the frequencies against radial order, or via the central value of this function. The procedure by which this is done is not unique. We derive a few simple expressions relating various observational estimators of $ε$ for radial modes to each other, and to the underlying theoretical…
Asteroseismology can provide joint constraints on masses and radii of individual stars. While this approach has been extensively tested for red giant branch (RGB) stars, it has been more difficult to test for helium core-burning red-clump (RC) giants because of the lack of fundamental calibrators. To provide independent mass estimates, we utilize a number of widely used horizontal-branch (HB) models in the literature, and derive photometric masses from a comparison with $griBVI_CJHK_s$ photometry. Our selected models disagree with each other on the predicted mass-luminosity-temperature relatio…
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）
The goal of stellar evolution theory is to predict the structure of stars throughout their lifetimes. Usually, these predictions can be assessed only indirectly, for example by comparing predicted and observed effective temperatures and luminosities. Thanks now to asteroseismology, which can reveal the internal structure of stars, it becomes possible to compare the predictions from stellar evolution theory to actual stellar structures. In this work, we present an inverse analysis of the oscillation data from the solar-type star KIC 6225718, which was observed by the \emph{Kepler} space observa…
HD 176465 is a binary system whose both components are solar-like pulsators and whose oscillation frequencies were observed by the \kepler\ mission. In this paper we have modeled the asteroseismic and spectroscopic data of the stars, and have determined their convection-zone helium abundances using the signatures left by the He{\sc ii} ionization zone on the mode frequencies. As expected we find that the components of the binary have the same age within uncertainties ($3.087 \pm 0.580$ Gyr and $3.569 \pm 0.912$ Gyr); they also have the same initial helium abundance (Y$_{\mathrm{init}}$=0.253 $…
Context: The internal characteristics of stars, such as their core rotation rates, are obtained via asteroseismic observations. A comparison of core rotation rates found in this way with core rotation rates as predicted by stellar evolution models demonstrate a large discrepancy. This means that there must be a process of angular momentum transport missing in the current theory of stellar evolution. A new formalism was recently proposed to fill in for this missing process, which has the Tayler instability as its starting point (hereafter referred to as `Fuller-formalism'). Aims: We investigate…
The distributions of the frequencies of the maximum oscillation Power (ν_max) and the large frequency separation ( Δν) of red giant stars observed by CoRoT have a dominant peak. Miglio et al. (2009) identified that the stars are red-clump stars. Using stellar population synthesis method, we studied the effects of Reimers mass loss, binary interactions, star formation rate and the mixing-length parameter on the distributions of the ν_max and Δν of red-clump stars. The Reimers mass loss can result in an increase in the ν_max and Δν of old population which lost a considerable amount of mass. Howe…
Detailed modeling of stellar evolution requires a better understanding of the (magneto-)hydrodynamic processes which mix chemical elements and transport angular momentum. Understanding these pro- cesses is crucial if we are to accurately interpret observations of chemical abundance anomalies, surface rotation measurements and asteroseismic data. Here, we use two-dimensional hydrodynamic simula- tions of the generation and propagation of internal gravity waves (IGW) in an intermediate mass star to measure the chemical mixing induced by these waves. We show that such mixing can generally be trea…
Context: The observations of solar-like oscillations in evolved stars have brought important constraints on their internal rotation rates. To correctly reproduce these data, an efficient transport mechanism is needed in addition to meridional circulation and shear instability. Aims: We study the efficiency of the transport of angular momentum during the subgiant phase. Results: The precise asteroseismic measurements of both core and surface rotation rates available for the six Kepler targets enable a precise determination of the efficiency of the transport of angular momentum needed for each o…
During the past 10 years the unprecedented quality and frequency resolution of asteroseismic data provided by space photometry has revolutionized the study of red-giant stars providing us with the possibility to probe the interior of thousands of these targets. Our aim is to present an asteroseismic tool which allows to determine the total angular momentum of stars, without a priori inference of their internal rotational profile. We adopt and adapt to red giants the asteroseismic inversion technique developed for the case of the Sun. The method has been tested assuming different artificial set…
The Kepler space telescope has provided time series of red giants of such unprecedented quality that a detailed asteroseismic analysis becomes possible. For a limited set of about a dozen red giants, the observed oscillation frequencies obtained by peak-bagging together with the most recent pulsation codes allowed us to reliably determine the core/envelope rotation ratio. The results so far show that the current models are unable to reproduce the rotation ratios, predicting higher values than what is observed and thus indicating that an efficient angular momentum transport mechanism should be …
HR\,8799 is a $λ$ Bootis, $γ$ Doradus star hosting a planetary system and a debris disk with two rings. This makes this system a very interesting target for asteroseismic studies. In particular, this work is devoted to the determination of the internal metallicity of this star, linked with its $λ$ Bootis nature, and its age, taking the advantage of its $γ$ Doradus-type pulsations. To do so we have used the equilibrium code CESAM and the non-adiabatic pulsational code GraCo. We have applied the Frequency Ratio Method and the Time Dependent Convection theory to estimate the mode identification, …
Asteroseismology of solar-like oscillators: emulating individual mode frequencies with a branching neural network
School of Physics & Astronomy, University of Birmingham（伯明翰大学物理与天文学院）；Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University（奥胡斯大学物理与天文系恒星天体物理学中心）；Advanced Research Computing, University of Birmingham（伯明翰大学高级计算研究中心）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学前沿天文与天体物理研究所）；Department of Astronomy, Beijing Normal University（北京师范大学天文系）；Sydney Institute for Astronomy, School of Physics, University of Sydney（悉尼大学物理学院悉尼天体物理研究所）
Current stellar model predictions of adiabatic oscillation frequencies differ significantly from the corresponding observed frequencies due to the non-adiabatic and poorly understood near-surface layers of stars. However, certain combinations of frequencies -- known as frequency ratios -- are largely unaffected by the uncertain physical processes as they are mostly sensitive to the stellar core. Furthermore, the seismic signature of helium ionization provides envelope properties while being almost independent of the outermost layers. We have developed an advanced stellar modelling approach in …
During most of their life, stars fuse hydrogen into helium in their cores. The mixing of chemical elements in the radiative envelope of stars with a convective core is able to replenish the core with extra fuel. If effective, such deep mixing allows stars to live longer and change their evolutionary path. Yet localized observations to constrain internal mixing are absent so far. Gravity modes probe the deep stellar interior near the convective core and allow us to calibrate internal mixing processes. Here we provide core-to-surface mixing profiles inferred from observed dipole gravity modes in…
Thanks to asteroseismology, constraints on the core rotation rate are available for hundreds of low- and intermediate-mass stars in evolved phases. Current physical processes tested in stellar evolution models cannot reproduce the evolution of these core rotation rates. We investigate the efficiency of the internal angular momentum redistribution in red giants during the hydrogen shell and core-helium burning phases based on the asteroseismic determinations of their core rotation rates. We compute stellar evolution models with rotation and model the transport of angular momentum by the action …
It is well known that asteroseismology is the unique technique permitting the study of the internal structure of pulsating stars using their pulsational frequencies, which is per se very important. It acquires an additional value when the star turns out to be a planet host. In this case, the asteroseismic study output may be a very important input for the study of the planetary system. With this in mind, we use the large time-span of the Kepler public data obtained for the star system HAT-P-7, first to perform an asteroseismic study of the pulsating star using Time-Dependent-Convection (TDC) m…
Turbulent mixing of chemical elements by convection has fundamental effects on the evolution of stars. The standard algorithm at present, mixing-length theory (MLT), is intrinsically local, and must be supplemented by extensions with adjustable parameters. As a step toward reducing this arbitrariness, we compare asteroseismically inferred internal structures of two Kepler slowly pulsating B stars (SPB's; $M\sim 3.25 M_\odot$) to predictions of 321D turbulence theory, based upon well-resolved, truly turbulent three-dimensional simulations (Arnett , et al. 2015, Christini, et al. 2016) which inc…
Recent asteroseismic advances have allowed for direct measurements of the internal rotation rates of many sub-giant and red giant stars. Unlike the nearly rigidly rotating Sun, these evolved stars contain radiative cores that spin faster than their overlying convective envelopes, but slower than they would in the absence of internal angular momentum transport. We investigate the role of internal gravity waves in angular momentum transport in evolving low mass stars. In agreement with previous results, we find that convectively excited gravity waves can prevent the development of strong differe…
Regions of rapid variation in the internal structure of a star are often referred to as acoustic glitches since they create a characteristic periodic signature in the frequencies of p modes. Here we examine the localized disturbance arising from the helium second ionization zone in red giant branch and clump stars. More specifically, we determine how accurately and precisely the parameters of the ionization zone can be obtained from the oscillation frequencies of stellar models. We use models produced by three different generation codes that not only cover a wide range of stages of evolution a…
