About 10 per cent of intermediate- and high-mass dwarf stars are observed to host a strong large-scale magnetic field at their surface, which is thought to be of fossil field origin. However, there are few inferences as to the magnetic field strength and geometry within the deep interiors of stars. Considering that massive stars harbour a convective core whilst on the main sequence, asteroseismology of gravity (g) modes is able to provide constraints on their core masses, yet it has so far not been used to probe the strength of their interior magnetic fields. Here we use asteroseismology to constrain an upper limit for the magnetic field strength in the near-core region of the pulsating and magnetic B star HD 43317, based on the expected interaction of a magnetic field and its g modes. We find a magnetic field strength of order $5 \times 10^5$ G is sufficient to suppress high-radial order g modes and reproduce the observed frequency spectrum of HD 43317, which contains only high-frequency g modes. This result is the first inference of the magnetic field strength inside a main-sequence star.
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…
As it is long known, the presence of a convective region creates a discontinuity in the chemical profile of a star, which in turn translates into a sharp variation of the adiabatic sound speed. This variation produces an oscillatory behavior of the pulsation frequencies, to which low degree p-modes are sensitive. We investigate the possibility of detecting the signature related to the presence of a convective core in the frequency spectrum of low-mass stars by means of suitable frequency combinations (such as separations and ratios)
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…
The asteroseismic modelling of period spacing patterns from gravito-inertial modes in stars with a convective core is a high-dimensional problem. We utilise the measured period spacing pattern of prograde dipole gravity modes (acquiring $Π_0$), in combination with the effective temperature ($T_{\rm eff}$) and surface gravity ($\log g$) derived from spectroscopy, to estimate the fundamental stellar parameters and core properties of 37 $γ~$Doradus ($γ~$Dor) stars whose rotation frequency has been derived from $\textit{Kepler}$ photometry. We make use of two 6D grids of stellar models, one with s…
We have analyzed 18 quarters of long-cadence data of KIC 9145955 provided by \emph{Kepler}, and extracted 61 oscillation frequencies from these high precision photometric data. The oscillation frequencies include 7 $l = 0$ modes, 44 $l = 1$ modes, 7 $l = 2$ modes, and 3 $l = 3$ modes. We identify $l = 0$ modes as p modes and $l = 2$ modes as p-dominated modes. For $l = 1$ modes, all of them are identified as mixed modes. These mixed modes can be used to determine the size of the helium core. We conduct a series of asteroseismic models and the size of the helium core is determined to be $M_{\rm…
Slowly pulsating B stars (SPB) and $γ$ Dor stars pulsate in high-order gravity (g-) modes. The frequencies of g-modes are sensitive to the detailed structure and evolution history of stars having convective cores. Receding convective cores in OB-type stars leave behind a chemically inhomogenous $\nabla_μ>0$ radiative zone. Once a g-mode has radial nodes near the boundaries of these layers, the mode gets trapped and its period deviates from asymptotic period spacing. Careful study of such trapped modes allows constraining the extent of such layers by fitting individual pulsation frequencies. We…
Transport of angular momentum has been a challenging topic within the stellar evolution community, even more since the recent asteroseismic surveys. All published studies on rotation using asteroseismic observations show a discrepancy between the observed and calculated rotation rates, indicating there is an undetermined process of angular momentum transport active in these stars. We aim to constrain the efficiency of this process by investigating rotation rates of 2.5 M$_{\odot}$ stars. First, we investigated whether the Tayler-Spruit dynamo could be responsible for the extra transport of ang…
We have found a rotationally split series of core g-mode triplets and surface p-mode multiplets in a main sequence F star, KIC 9244992. Comparison with models shows that the star has a mass of about 1.45 M$_\odot$, and is at an advanced stage of main sequence evolution in which the central hydrogen abundance mass fraction is reduced to about 0.1. This is the second case, following KIC 11145123, of an asteroseismic determination of the rotation of the deep core and surface of an A-F main-sequence star. We have found, essentially model-independently, that the rotation near the surface, obtained …
The Kepler Asteroseismic Legacy Project provided frequencies, separation ratios, error estimates, and covariance matrices for 66 Kepler main sequence targets. Most of the previous analysis of these data was focused on fitting standard stellar models. We present results of direct asteroseismic inversions using the method of optimally localized averages (OLA), which effectively eliminates the surface effects and attempts to resolve the stellar core structure. The inversions are presented for various structure properties, including the density stratification and sound speed. The results show that…
The $α$ Cen stellar system is the closest neighbour to our Sun. Its main component is a binary composed of two main-sequence stars, one more massive than the Sun and one less massive. The system's bright magnitude led to a wealth of astronomical observations over a long period, making it an appealing testbed for stellar physics. In particular, detection of stellar pulsations in both $α$ Cen A and B has revealed the potential of asteroseismology for determining its fundamental stellar parameters. Asteroseismic studies have also focused on the presence of a convective core in the A component, bu…
We propose a methodological framework to perform forward asteroseismic modeling of stars with a convective core, based on gravity-mode oscillations. These probe the near-core region in the deep stellar interior. The modeling relies on a set of observed high-precision oscillation frequencies of low-degree coherent gravity modes with long lifetimes and their observational uncertainties. Identification of the mode degree and azimuthal order is assumed to be achieved from rotational splitting and/or from period spacing patterns. This paper has two major outcomes. The first is a comprehensive list …
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…
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 …
Stellar mergers are important processes in stellar evolution, dynamics, and transient science. However, it is difficult to identify merger remnant stars because they cannot easily be distinguished from single stars based on their surface properties. We demonstrate that merger remnants can potentially be identified through asteroseismology of red giant stars using measurements of the gravity mode period spacing together with the asteroseismic mass. For mergers that occur after the formation of a degenerate core, remnant stars have over-massive envelopes relative to their cores, which is manifes…
All evolved stars with masses $M_\star\lesssim 2M_\odot$ undergo a helium(He)-core flash at the end of their first stage as a giant star. Although theoretically predicted more than 50 years ago, this core-flash phase has yet to be observationally probed. We show here that gravity modes (g modes) stochastically excited by He-flash driven convection are able to reach the stellar surface, and induce periodic photometric variabilities in hot-subdwarf stars with amplitudes of the order of a few mmag. As such they can now be detected by space-based photometry with the Transiting Exoplanet Survey Sat…
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…
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…
Asteroseismology of non-radial pulsations in Hot B Subdwarfs (sdB stars) offers a unique view into the interior of core-helium-burning stars. Ground-based and space-borne high precision light curves allow for the analysis of pressure and gravity mode pulsations to probe the structure of sdB stars deep into the convective core. As such asteroseismological analysis provides an excellent opportunity to test our understanding of stellar evolution. In light of the newest constraints from asteroseismology of sdB and red clump stars, standard approaches of convective mixing in 1D stellar evolution mo…
Aims. We investigate the s-process during the AGB phase of stellar models whose cores are enforced to rotate at rates consistent with asteroseismology observations of their progenitors and successors. Methods. We calculated new 2M$_{\odot}$, Z=0.01 models, rotating at 0, 125, and 250 km/s at the start of main sequence. An artificial, additional viscosity was added to enhance the transport of angular momentum in order to reduce the core rotation rates to be in agreement with asteroseismology observations. We compared rotation rates of our models with observed rotation rates during the MS up to …
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）
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. …
Aims: We investigate the thermal and chemical structure in the near-core region of stars with a convective core by means of gravito-inertial modes. We do so by determining the probing power of different asteroseismic observables and fitting methodologies. We focus on the case of the B-type star KIC$\,$7760680, rotating at a quarter of its critical rotation velocity. Methods: We compute grids of 1D stellar structure and evolution models for two different prescriptions of the temperature gradient and mixing profile in the near-core region. We determine which of these prescriptions is preferred a…
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), …
Using asteroseismic data and stellar evolution models we make the first detection of a convective core in a Kepler field main-sequence star, putting a stringent constraint on the total size of the mixed zone and showing that extra mixing beyond the formal convective boundary exists. In a slightly less massive target the presence of a convective core cannot be conclusively discarded, and thus its remaining main-sequence life time is uncertain. Our results reveal that best-fit models found solely by matching individual frequencies of oscillations corrected for surface effects do not always prope…
KIC 10526294 is a very slowly rotating and slowly pulsating late B-type star. Its 19 consecutive dipole gravity modes constitute a series with almost constant period spacing. This unique collection of identified modes probes the near-core environment of this star and holds the potential to reveal the size and structure of the overshooting zone on top of the convective core, as well as the mixing properties of the star. We pursue forward seismic modelling based on adiabatic eigenfrequencies of equilibrium models for eight extensive evolutionary grids tuned to KIC 10526294, by varying the initia…
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 …
Extending asteroseismic magnetometry across the diverse landscape of magnetic structures
Princeton University（普林斯顿大学）；Northwestern University（西北大学）；University of Sydney（悉尼大学）；Institute of Science and Technology Austria（奥地利科学技术研究所）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Université Paris-Saclay（巴黎萨克雷大学）；Université Paris Cité（巴黎西岱大学）
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…
The influence of rotational mixing on the global parameters and asteroseismic properties of red giant stars is reviewed. While red giants are generally characterised by low surface rotational velocities, they may have been rotating much more rapidly during the main sequence, so that the rotational history of a star has a large impact on its properties during the red giant phase. For stars massive enough to ignite helium burning in non-degenerate conditions, rotational mixing leads to a significant increase of the stellar luminosity and shifts the location of the core helium burning phase to a …
The frequency ratios and of HD 49933 exhibit an increase at high frequencies. This behavior also exists in the ratios of other stars, which is considered to result from the low signal-to-noise ratio and the larger line width at the high-frequency end and could not be predicted by stellar models in previous work. Our calculations show that the behavior not only can be reproduced by stellar models, but can be predicted by asymptotic formulas of the ratios. The frequency ratios of the Sun, too, can be reproduced well by the asymptotic formulas. The increased behavior derives from the fact that th…
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…
In this study, we explore the evolution of lithium in giant stars based on data assembled from the literature on asteroseismology and Li abundances for giants. Our final sample of 187 giants consists of 44 red giant branch (RGB), 140 core He-burning (CHeB) and three giants with an unclassified evolutionary phase. For all 187 stars, the seismic parameters $ν\rm_{max}$ (frequency of maximum oscillation power) and $Δν$ (large frequency spacing) are available, while $ΔΠ\rm_{1}$ (the asymptotic gravity-mode period spacing) is available for a subset of 64. For some of the CHeB giants, mass estimates…
Asteroseismic measurements enable inferences of the underlying stellar structure, such as the density and the speed of sound at various points within the interior of the star. This provides an opportunity to test stellar evolution theory by assessing whether the predicted structure of a star agrees with the measured structure. Thus far, this kind of inverse analysis has only been applied to the Sun and three solar-like main-sequence stars. Here we extend the technique to stars on the subgiant branch, and apply it to one of the best-characterized subgiants of the Kepler mission, HR 7322. The ob…
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…
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…
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…
The TESS space mission provides us with high-precision photometric observations of bright stars over more than 70% of the entire sky, allowing us to revisit and characterise well-known stars. We aim to conduct an asteroseismic analysis of the gamma Doradus star HD112429 using both the available ground-based spectroscopy and TESS photometry, and assess the conditions required to measure the near-core rotation rate and buoyancy travel time. We collect and reduce the available five sectors of short-cadence TESS photometry of this star, as well as 672 legacy observations from six medium- to high-r…
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…
Motivated by the recent detection of stochastically excited modes in the massive star V1449 Aql (Belkacem et al., 2009b), already known to be a $β$ Cephei, we theoretically investigate the driving by turbulent convection. By using a full non-adiabatic computation of the damping rates, together with a computation of the energy injection rates, we provide an estimate of the amplitudes of modes excited by both the convective region induced by the iron opacity bump and the convective core. Despite uncertainties in the dynamical properties of such convective regions, we demonstrate that both are ab…
The influence of rotation on the properties of red giants is studied in the context of the asteroseismic modelling of these stars. While red giants exhibit low surface rotational velocities, we find that the rotational history of the star has a large impact on its properties during the red giant phase. In particular, for stars massive enough to ignite He burning in non-degenerate conditions, rotational mixing induces a significant increase of the stellar luminosity and shifts the location of the core helium burning phase to a higher luminosity in the HR diagram. This of course results in a cha…
In order to clarify the properties of the secondary clump star HD 226808 (KIC 5307747), we combined four years of data from Kepler space photometry with high-resolution spectroscopy of the High Efficiency and Resolution Mercator Échelle Spectrograph mounted on the Mercator telescope. The fundamental atmospheric parameters, radial velocities, rotation velocities, and elemental abundance for Fe and Li were determined by analyzing line strengths and fitting-line profiles, based on a 1D local thermodynamic equilibrium model atmosphere. Second, we analyzed a photometric light curve obtained by Kepl…
We develop a novel method based on machine learning principles to achieve optimal initiation of CPU-intensive computations for forward asteroseismic modeling in a multi-D parameter space. A deep neural network is trained on a precomputed asteroseismology grid containing about 62 million coherent oscillation-mode frequencies derived from stellar evolution models. These models are representative of the core-hydrogen burning stage of intermediate-mass and high-mass stars. The evolution models constitute a 6D parameter space and their predicted low-degree pressure- and gravity-mode oscillations ar…
Core helium burning primary red clump (RC) stars are evolved red giant stars which are excellent standard candles. As such, these stars are routinely used to map the Milky Way or determine the distance to other galaxies among other things. However distinguishing RC stars from their less evolved precursors, namely red giant branch (RGB) stars, is still a difficult challenge and has been deemed the domain of asteroseismology. In this work, we use a sample of 1,676 RGB and RC stars which have both single epoch infrared spectra from the APOGEE survey and asteroseismic parameters and classification…
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…
The space-borne missions CoRoT and Kepler have opened a new era in stellar physics, especially for evolved stars, with precise asteroseismic measurements that help determine precise stellar parameters and perform ensemble astero seismology. This paper deals with the quality of the information that we can retrieve from the oscillations. It focusses on the conditions for obtaining the most accurate measurement of the radial and non-radial oscillation patterns. This accuracy is a prerequisite for making the best with asteroseismic data. From radial modes, we derive proxies of the stellar mass and…
