Localised modelling error in the near-surface layers of evolutionary stellar models causes the frequencies of their normal modes of oscillation to differ from those of actual stars with matching interior structures. These frequency differences are referred to as the asteroseismic surface term. Global stellar properties estimated via detailed constraints on individual mode frequencies have previously been shown to be robust with respect to different parameterisations of this surface term. It has also been suggested that this may be true of a broader class of nonparametric treatments. We examine systematic differences in inferred stellar properties with respect to different surface-term treatments, both for a statistically large sample of main-sequence stars, as well as for a sample of red giants, for which no such characterisation has previously been done. For main-sequence stars, we demonstrate that while masses and radii, and hence ages, are indeed robust to the choice of surface term, the inferred initial helium abundance $Y_0$ is sensitive to the choice of surface correction. This implies that helium-abundance estimates returned from detailed asteroseismology are methodology-dependent. On the other hand, for our red giant sample, nonparametric surface corrections return dramatically different inferred stellar properties than parametric ones. The nature of these differences suggests that such nonparametric methods should be preferred for evolved stars; this should be verified on a larger sample.
We present our preliminary results of the modelling of the F5 star Procyon A. The frequencies predicted by our models are compared with the frequencies extracted through a global fit to the power spectrum obtained by the latest ground-based observations, which provides two different mode identification scenarios.
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 detection and analysis of oscillations in binary star systems is critical in understanding stellar structure and evolution. This is partly because such systems have the same initial chemical composition and age. Solar-like oscillations have been detected by Kepler in both components of the asteroseismic binary HD 176465. We present an independent modelling of each star in this binary system. Stellar models generated using MESA (Modules for Experiments in Stellar Astrophysics) were fitted to both the observed individual frequencies and complementary spectroscopic parameters. The individual …
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…
With the success of the Kepler and CoRoT missions, the number of stars with detected solar-like oscillations has increased by several orders of magnitude, for the first time we are able to perform large-scale ensemble asteroseismology of these stars. In preparation for this golden age of asteroseismology we have computed expected values of various asteroseismic observables from models of varying mass and metallicity. The relationships between these asteroseismic observables, such as the separations between mode frequencies, are able to significantly constrain estimates of the ages and masses o…
We model the oscillations of the SONG target $μ$ Herculis to estimate the parameters of the star. The $\ell$ = 1 mixed modes of $μ$ Her provide strong constraints on stellar properties. The mass and age given by our asteroseismic modelling are 1.10$^{+0.11}_{-0.06}$ M$_{\odot}$ and 7.55$^{+0.96}_{-0.79}$ Gyr. The initial helium abundance is also constrained at around $Y_{\rm{init}}$ = 0.28, suggesting a ratio in the elements enrichment law ($ΔY/ΔZ$) around 1.3, which is closed to the solar value. The mixing-length parameter converges to about 1.7, which is $\sim$ 10\% lower than the solar valu…
An increasingly popular method to determine stellar ages of red-giant stars for the purpose of Galactic archaeology is asteroseismic grid-based modelling (GBM). In asteroseismic GBM of red-giant stars with solar-like oscillations the large frequency separation ($Δν$) and the frequency of maximum oscillation power ($ν_{\rm max}$) are commonly used asteroseismic observables, in addition to the usual spectroscopic parameters effective temperature ($T_{\rm eff}$) and metallicity ([Fe/H]). The precision with which $Δν$ and $ν_{\rm max}$ can be determined largely depends on the length of the timeser…
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 aim to unravel the interior mixing profile of the pulsating eclipsing binary KIC9850387 by comparing its dynamical parameters and the parameters derived through a combination of evolutionary and asteroseismic modelling. We created a grid of stellar evolutionary models using the stellar evolutionary code \textsc{mesa} and performed an isochrone-cloud (isocloud) based evolutionary modelling of the system. We then generated a grid of pulsational models using the stellar pulsation code \textsc{gyre} based on the age constraints from the evolutionary modelling. Finally, we performed asteroseismi…
Context. Asteroseismology is an effcient tool not only for testing stellar structure and evolutionary theory but also constraining the parameters of stars for which solar-like oscillations are detected, presently. As an important southern asteroseismic target, Tau Ceti, is a metal-poor star. The main features of the oscillations and some frequencies of ? Ceti have been identified. Many scientists propose to comprehensively observe this star as part of the Stellar Observations Network Group. Aims. Our goal is to obtain the optimal model and reliable fundamental parameters for the metal-poor sta…
Photometric observations made by the NASA Kepler Mission have led to a dramatic increase in the number of main-sequence and subgiant stars with detected solar-like oscillations. We present an ensemble asteroseismic analysis of 76 solar-type stars. Using frequencies determined from the Kepler time-series photometry, we have measured three asteroseismic parameters that characterize the oscillations: the large frequency separation (Δν), the small frequency separation between modes of l=0 and l=2 (δν_02), and the dimensionless offset (ε). These measurements allow us to construct asteroseismic diag…
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 the results of modelling the subgiant star $β$ Hydri using the seismic observational constraints. We have computed several grids of stellar evolutionary tracks using Aarhus STellar Evolution Code (ASTEC, Christensen-Dalsgaard, 2008a), with and without helium diffusion and settling. For those models on each track that are located at the observationally determined position of $β$ Hydri in the HR diagram, we have calculated the oscillation frequencies using Aarhus adiabatic pulsation package (ADIPLS, Christensen-Dalsgaard, 2008b). Applying the near-surface corrections to the calculated…
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…
Asteroseismology is a powerful tool that can precisely characterize the mass, radius, and other properties of field stars. However, our inability to properly model the near-surface layers of stars creates a frequency-dependent frequency difference between the observed and the modeled frequencies, usually referred to as the "surface term". This surface term can add significant errors to the derived stellar properties unless removed properly. In this paper we simulate surface terms across a significant portion of the HR diagram, exploring four different masses ($M=0.8, 1.0, 1.2$, and $1.5$ M$_\o…
The goal of AIMS (Asteroseismic Inference on a Massive Scale) is to estimate stellar parameters and credible intervals/error bars in a Bayesian manner from a set of asteroseismic frequency data and so-called classical constraints. To achieve reliable parameter estimates and computational efficiency, it searches through a grid of pre-computed models using an MCMC algorithm -- interpolation within the grid of models is performed by first tessellating the grid using a Delaunay triangulation and then doing a linear barycentric interpolation on matching simplexes. Inputs for the modelling consist o…
We present the results of a spectroscopic multisite campaign for the beta Cephei star 12 (DD) Lacertae. Our study is based on more than thousand high-resolution high S/N spectra gathered with 8 different telescopes in a time span of 11 months. In addition we make use of numerous archival spectroscopic measurements. We confirm 10 independent frequencies recently discovered from photometry, as well as harmonics and combination frequencies. In particular, the SPB-like g-mode with frequency 0.3428 1/d reported before is detected in our spectroscopy. We identify the four main modes as (l1,m1) = (1,…
KIC 4150611: A quadruply eclipsing heptuple star system with a g-mode period-spacing pattern Asteroseismic modelling of the g-mode period-spacing pattern
Despite the fact that the initial helium abundance is an essential ingredient in modelling solar-type stars, its abundance in these stars remains a poorly constrained observational property. This is because the effective temperature in these stars is not high enough to allow helium ionization, not allowing any conclusions on its abundance when spectroscopic techniques are employed. To this end, stellar modellers resort to estimating the initial helium abundance via a semi-empirical helium-to-heavy element ratio, anchored to the the standard Big Bang nucleosynthesis value. Depending on the choi…
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…
Detailed understanding of stellar physics is essential towards a robust determination of stellar properties (e.g. radius, mass, and age). Among the vital input physics used in the modelling of solar-type stars which remain poorly constrained, is the initial helium abundance. To this end, when constructing stellar model grids, the initial helium abundance is estimated either (i) by using the semi-empirical helium-to-heavy element enrichment ratio, (${ΔY}/{ΔZ}$), anchored to the standard Big Bang Nucleosynthesis value or (ii) by setting the initial helium abundance as a free variable. Adopting 3…
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.
Models of solar-like oscillators yield acoustic modes at different frequencies than would be seen in actual stars possessing identical interior structure, due to modelling error near the surface. This asteroseismic "surface term" must be corrected when mode frequencies are used to infer stellar structure. Subgiants exhibit oscillations of mixed acoustic ($p$-mode) and gravity ($g$-mode) character, which defy description by the traditional $p$-mode asymptotic relation. Since nonparametric diagnostics of the surface term rely on this description, they cannot be applied to subgiants directly. In …
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 …
Asteroseismology can be used to constrain some properties of dark-matter (DM) particles (Casanellas & Lopes, 2013). In this work, we performed an asteroseismic modelling of the main-sequence solar-like pulsator KIC 2009505 (also known as Dushera) in order to test the existence of DM particles with the characteristics that explain the recent results found in some of the DM direct detection experiments. We found that the presence of a convective core in KIC 2009504 is incompatible with the existence of some particular models of DM particles.
An important goal of helio- and asteroseismology is to improve the modelling of stellar evolution. Here I provide a brief discussion of some of the uncertain issues in stellar modelling, of possible relevance to asteroseismic inferences.
Is a 1D perturbative method sufficient for asteroseismic modelling of $β$ Cephei pulsators? Implications for measurements of rotation and internal magnetic fields
Context: Recently, the CoRoT target HD 175272 (F5V), which shows a weak signal of solar-like oscillations, was modelled by a differential asteroseismic analysis (Ozel et al. 2013) relative to a seismically similar star, HD 181420 (F2V), for which there is a clear signature of solar-like oscillations. The results provided by Ozel et al. (2013) indicate the possibility of HD 175272 having subsolar mass, while being of the order of 1000 K hotter than the Sun. This seems unphysical -- standard stellar evolution theory generally does not predict solar-metallicity stars of subsolar mass to be hotter…
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…
We present an in-depth analysis of the bright subgiant HR 7322 (KIC 10005473) using Kepler short-cadence photometry, optical interferometry from CHARA, high-resolution spectra from SONG, and stellar modelling using GARSTEC grids and the Bayesian grid-fitting algorithm BASTA. HR 7322 is only the second subgiant with high-quality Kepler asteroseismology for which we also have interferometric data. We find a limb-darkened angular diameter of $0.443 \pm 0.007$ mas, which, combined with a distance derived using the parallax from Gaia DR2 and a bolometric flux, yields a linear radius of $2.00 \pm 0.…
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…
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 …
In the past few years, the CoRoT and Kepler missions have carried out what is now called the space photometry revolution. This revolution is still ongoing thanks to K2 and will be continued by the Tess and Plato2.0 missions. However, the photometry revolution must also be followed by progress in stellar modelling, in order to lead to more precise and accurate determinations of fundamental stellar parameters such as masses, radii and ages. In this context, the long-lasting problems related to mixing processes in stellar interior is the main obstacle to further improvements of stellar modelling.…
We test asteroseismic radii of Kepler main-sequence and subgiant stars by deriving their parallaxes which are compared with those of the first Gaia data release. We compute radii based on the asteroseismic scaling relations as well as by fitting observed oscillation frequencies to stellar models for a subset of the sample, and test the impact of using effective temperatures from either spectroscopy or the infrared flux method. An offset of 3%, showing no dependency on any stellar parameters, is found between seismic parallaxes derived from frequency modelling and those from Gaia. For parallaxe…
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 …
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…
Context. The Kepler space mission led to a large amount of high-precision time series of solar-like oscillators. Using a Bayesian analysis that combines asteroseismic techniques and additional ground-based observations, the mass, radius, luminosity, and distance of those stars can be estimated with good precision. This has given a new impetus to the research field of galactic archeology. Aims. The first data release of the Gaia space mission contains the TGAS catalog with parallax estimates for more than 2 million stars, including many of the Kepler targets. Our goal is to make a first proper …
Stellar magnetic fields are poorly understood but are known to be important for stellar evolution and exoplanet habitability. They drive stellar activity, which is the main observational constraint on theoretical models for magnetic field generation and evolution. Starspots are the main manifestation of the magnetic fields at the stellar surface. In this study we measure the variation of their latitude with time, called a butterfly diagram in the solar case, for the solar analogue HD 173701 (KIC 8006161). To that effect, we use Kepler data, to combine starspot rotation rates at different epoch…
Context: Detailed oscillation spectra comprising individual frequencies for numerous solar-type stars and red giants are or will become available. These data can lead to a precise characterisation of stars. Aims: Our goal is to test and compare different methods for obtaining stellar properties from oscillation frequencies and spectroscopic constraints, in order to evaluate their accuracy and the reliability of the error bars. Methods: In the context of the SpaceInn network, we carried out a hare-and-hounds exercise in which one group produced "observed" oscillation spectra for 10 artificial s…
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…
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…
Context: Four open clusters are present in the Kepler field of view and timeseries of nearly a year in length are now available. These timeseries allow us to derive asteroseismic global oscillation parameters of red-giant stars in the three open clusters NGC 6791, NGC 6819 and NGC 6811. From these parameters and effective temperatures, we derive mass, radii and luminosities for the clusters as well as field red giants. Aims: We study the influence of evolution and metallicity on the observed red-giant populations. Methods: The global oscillation parameters are derived using different published…
HD\,139614 is known to be a $\sim$14-Myr-old, possibly pre-main-sequence star in the Sco-Cen OB association in the Upper Centaurus-Lupus subgroup, with a slightly warped circumstellar disc containing ring structures hinting at one or more planets. The star's chemical abundance pattern is metal-deficient except for volatile elements, which places it in the $λ$ Boo class and suggests it has recently accreted gas-rich but dust-poor material. We identify seven dipole and four radial pulsation modes among its $δ$ Sct pulsations using the TESS light curve and an échelle diagram. Precision modelling …
The measured properties of stellar oscillations can provide powerful constraints on the internal structure and composition of stars. To begin this process, oscillation frequencies must be extracted from the observational data, typically time series of the star's brightness or radial velocity. In this paper, a probabilistic model is introduced for inferring the frequencies and amplitudes of stellar oscillation modes from data, assuming that there is some periodic character to the oscillations, but that they may not be exactly sinusoidal. Effectively we fit damped oscillations to the time series…
