arXiv subjects

M. Vrard

Publications and source records attributed to M. Vrard.

At least 19 recordsLinked to original sources

arXiv2026

Interferometric Survey of Stellar Parameters: Mass of the metallic A-type binary $\beta$ Aur

With the capabilities of the new visible CHARA/SPICA instrument and the multiple spectral band operation of CHARA, our goal is to resolve orbits of short-period binaries and develop a robust framework for combining interferometric, spectroscopic, and photometric observations into a single consistent model. For our target sample, we selected suitable binaries based on brightness, angular separation, and orbital properties based on the expected performance of the CHARA/SPICA instrument. As a case study, we analysed the bright eclipsing binary $\beta$ Aurigae, composed of two slightly evolved A1 stars. We combined new interferometric observations of $\beta$ Aur obtained with CHARA/SPICA, MIRC-X, and MYSTIC with archival MIRC data, radial velocities, and light curves. We first derived astrometric positions from interferometric observables and computed an orbital solution. Afterwards, we implemented a unified model, capable of tying interferometric modelling with the ellc code to simultaneously fit all observables using MCMC sampling. We performed a detailed analysis of the noise statistics of each data set and in the end we adopted a profile likelihood approach to account for underestimated noise and systematics. We derived a consistent orbital and physical solution for $\beta$ Aur through joint modelling. The inclusion of interferometric data tightly constrains the angular semi-major axis and inclination. Using profile likelihood to account for the different intrinsic levels of uncertainty of the fundamentally different observables, we derived the masses of the two stars, $M_1 = 2.359 \pm 0.005$ M$_S$ and $M_2 = 2.293 \pm 0.004$ M$_S$, their radii $R_1 = 2.752 \pm 0.002$ R$_S$ and $R_2 = 2.622 \pm 0.002$ R$_S$, and the distance to the binary, $d = 24.30\pm0.05$ pc.

astro-ph.SR↗

arXiv2026

CHARA/SPICA: The six-telescope visible combiner and near-infrared fringe tracker for the CHARA Array

The suite called Stellar Parameters and Images with a Cophased Array (SPICA) has two interferometric instruments installed at the focus of the CHARA Array located at Mount Wilson, CA. SPICA is made of SPICA-VIS, a fiber-fed six-beam visible spectrograph with three spectral resolutions, and SPICA-FT, a six-beam near-infrared fringe tracker for the fast stabilization of the fringes. SPICA is opening access to imaging in the visible domain with an unprecedented angular resolution down to 0.2 milliarcseconds. It has been designed around a large survey of fundamental parameters of stars over the Hertzsprung- Russell diagram, aiming at understanding the deviations from the standard empirical relations of stellar physics as a function of activity: limb darkening, multiplicity, rotation, winds, and environments. SPICA makes use of the advanced technologies in electron multiplying detectors in the visible and electron- avalanche photodiode arrays in the near-infrared. It benefits from the newly commissioned adaptive optics on the one-meter telescopes of the array. The modules of the visible instrument, SPICA-VIS, optimize the injection of light into single-mode fibers for spatial filtering before spectral dispersion in the image plane. The fringe tracker, SPICA-FT, performs group-delay and phase-delay tracking for six beams in the H band. SPICA-FT can use an all-in-one or ABCD encoding of the fringe signals. SPICA is operational on sky and is close to reaching the expected performance in low spectral resolution, in particular, for the Interferometric Survey of Stellar Parameters (ISSP). More work is still needed to achieve the ultimate performance in terms of sensitivity and to allow operations with higher spectral resolutions.

astro-ph.IM↗

arXiv2026

Extra modes in helium-core-burning stars probing an infra core cavity

Dipole mixed modes observed in the oscillation pattern of red giant stars probe the radiative regions in the stellar core. Oscillation spectra of helium-core-burning stars sometimes show extra peaks that remain unexplained by the dipole mixed-mode pattern expected from the coupling of a radiative cavity in the stellar core and a pressure cavity in the stellar envelope. We use the asymptotic expansion developed for a multi-cavity star in order to characterize these extra peaks. The analytical resonance condition of the multi-cavity gravito-acoustic modes, with two inner gravity cavities and an outer pressure cavity, helps us explain that the apparent extra peaks are dipole mixed modes that follow the 3-cavity oscillation pattern. The derivation of the two asymptotic period spacings associated with the two distinct regions in the radiative core provides an estimate of the full radiative cavity. Our results provide new constraints for analysing the overshoot or mixing in the core of helium-core-burning stars. An important structure discontinuity inside the radiative core may explain the larger than expected observed period spacings.

astro-ph.SR↗

arXiv2024

Red giants evolutionary status determination: the complete Kepler catalog

Evolved cool stars have three distinct evolutionary status: shell Hydrogen-burning (RGB), core Helium and shell Hydrogen burning (RC), and double shell burning (AGB). Asteroseismology can distinguish between the RC and the other status, but distinguishing RGB and AGB has been difficult seismically and spectroscopically. The precise boundaries of different status in the HR diagram have also been difficult to establish. In this article, we present a comprehensive catalog of asteroseismic evolutionary status, RGB and RC, for evolved red giants in the Kepler field. We carefully examine boundary cases to define the lower edge of the RC phase in radius and surface gravity. We also test different published asteroseisemic methods claiming to distinguish AGB and RGB stars against a sample where AGB candidates were selected using a spectrocopic identification method. We used six different seismic techniques to distinguish RC and RGB stars, and tested two proposed methods for distinguishing AGB and RGB stars. These status were compared with those inferred from spectroscopy. We present consensus evolutionary status for 18,784 stars out of the 30,337 red giants present in the Kepler data, including 11,516 stars with APOGEE spectra available. The agreement between seismic and spectroscopic classification is excellent for distinguishing RC stars, agreeing at the 94% level. Most disagreements can be traced to uncertainties in spectroscopic parameters, but some are caused by blends with background stars. We find a sharp lower boundary in surface gravity at log(g) = 2.99+/-0.01 for the RC and discuss the implications. We demonstrate that asteroseismic tools for distinguishing AGB and RGB stars are consistent with spectroscopic evolutionary status at near the RC but that the agreement between the different methods decreases rapidly as the star evolves.

astro-ph.SR↗

arXiv2023

Constraining stellar and orbital co-evolution through ensemble seismology of solar-like oscillators in binary systems -- A census of oscillating red-giants and main-sequence stars in Gaia DR3 binaries

Binary systems constitute a valuable astrophysics tool for testing our understanding of stellar structure and evolution. Systems containing a oscillating component are interesting as asteroseismology offers independent parameters for the oscillating component that aid the analysis. About 150 of such systems are known in the literature. To enlarge the sample of these benchmark objects, we crossmatch the Two-Body-Orbit Catalogue (TBO) of Gaia DR3, with catalogs of confirmed solar-like oscillators on the main-sequence and red-giant phase from NASA Kepler and TESS. We obtain 954 new binary system candidates hosting solar-like oscillators, of which 45 and 909 stars are on the main sequence and red-giant, resp., including 2 new red giants in eclipsing systems. 918 oscillators in potentially long-periodic systems are reported. We increase the sample size of known solar-like oscillators in binary systems by an order of magnitude. We present the seismic properties of the full sample and conclude that the grand majority of the orbital elements in the TBO is physically reasonable. 82% of all TBO binary candidates with multiple times with APOGEE are confirmed from radial-velocity measurement. However, we suggest that due to instrumental noise of the TESS satellite the seismically inferred masses and radii of stars with $ν_\textrm{max}$$\lesssim$30$μ$Hz could be significantly overestimated. For 146 giants the seismically inferred evolutionary state has been determined and shows clear differences in their distribution in the orbital parameters, which are accounted the accumulative effect of the equilibrium tide acting in these evolved binary systems. For other 146 systems hosting oscillating stars values for the orbital inclination were found in the TBO. From testing the TBO on the SB9 catalogue, we obtain a completeness factor of 1/3.

astro-ph.SR↗

arXiv2023

Solar-like oscillations in $γ$ Cephei A as seen through SONG and TESS

Fundamental stellar parameters such as mass and radius are some of the most important building blocks in astronomy, both when it comes to understanding the star itself and when deriving the properties of any exoplanet(s) they may host. Asteroseismology of solar-like oscillations allows us to determine these parameters with high precision. We investigate the solar-like oscillations of the red-giant-branch star $γ$ Cep A, which harbours a giant planet on a wide orbit. We did this by utilising both ground-based radial velocities from the SONG network and space-borne photometry from the NASA TESS mission. From the radial velocities and photometric observations, we created a combined power spectrum, which we used in an asteroseismic analysis to extract individual frequencies. We clearly identify several radial and quadrupole modes as well as multiple mixed, dipole modes. We used these frequencies along with spectroscopic and astrometric constraints to model the star, and we find a mass of $1.27^{+0.05}_{-0.07}$ M$_\odot$, a radius of $4.74^{+0.07}_{-0.08}$ R$_\odot$, and an age of $5.7^{+0.8}_{-0.9}$ Gyr. We then used the mass of $γ$ Cep A and our SONG radial velocities to derive masses for $γ$ Cep B and $γ$ Cep Ab of $0.328^{+0.009}_{-0.012}$ M$_\odot$ and $6.6^{+2.3}_{-2.8}$ M$_{\rm Jup}$, respectively.

astro-ph.SR↗

arXiv2022

KIC 7955301: a hierarchical triple system with eclipse timing variations and an oscillating red giant

KIC 7955301 is a hierarchical triple system with eclipse timing and depth variations discovered by the Kepler mission. It is composed of a non-eclipsing primary star at the bottom of the red giant branch on a 209-day orbit with a K/G-type main-sequence inner eclipsing binary, orbiting in 15.3 days. This system was noted for the large amplitude of its eclipse timing variations (4 hours), and the clear solar-like oscillations of the red-giant component, including p-modes of degree up to l=3 and mixed l=1 modes. The system is a single-lined spectroscopic triple. We perform a dynamical model by combining the Kepler photometric data, eclipse timing variations, and radial-velocity data obtained at Apache Point (ARCES) and Haute Provence (SOPHIE) observatories. The dynamical mass of the red-giant is determined with a 2% precision at 1.30 (+0.03,-0.02) solar mass. We perform asteroseismic modeling based on the global seismic parameters and on the individual frequencies. Both methods lead to a mass of the red giant that matches the dynamical mass within the uncertainties. Asteroseismology also reveals the rotation rate of the core (15 days), the envelope (150 days), and the inclination (75 deg) of the red giant. Three different approaches lead to an age between 3.3 and 5.8 Gyr, which highlights the difficulty of determining stellar ages despite the exceptional wealth of available information. On short timescales, the inner binary exhibits eclipses with varying depths during a 7.3-year long interval, and no eclipses during the consecutive 11.9 years. This is why Kepler could detect its eclipses, TESS will not, and the future ESA PLATO mission should. Over the long term, the system owes its evolution to the evolution of its individual components. It could end its current smooth evolution by merging by the end of the red giant or the asymptotic giant branch of the primary star.

astro-ph.SR↗

arXiv2020

On using dipolar modes to constrain the helium glitch in red-giant stars

The space-borne missions CoRoT and Kepler have revealed numerous mixed modes in red-giant stars. These modes carry a wealth of information about red-giant cores, but are of limited use when constraining rapid structural variations in their envelopes. This limitation can be circumvented if we have access to the frequencies of the pure acoustic dipolar modes in red giants, i.e. the dipole modes that would exist in the absence of coupling between gravity and acoustic waves. We present a pilot study aimed at evaluating the implications of using these pure acoustic mode frequencies in seismic studies of the helium structural variation in red giants. The study is based on artificial seismic data for a red-giant-branch stellar model, bracketing seven acoustic dipole radial orders around vmax. The pure acoustic dipole-mode frequencies are derived from a fit to the mixed-mode period spacings and then used to compute the pure acoustic dipole-mode second differences. The pure acoustic dipole-mode second differences inferred through this procedure follow the same oscillatory function as the radial modes second differences. The additional constraints brought by the dipolar modes allow us to adopt a more complete description of the glitch signature when performing the fit to the second differences. The amplitude of the glitch retrieved from this fit is 15% smaller than that from the fit based on the radial modes alone. Also, we find that thanks to the additional constraints, a bias in the inferred glitch location, found when adopting the simpler description of the glitch, is avoided.

astro-ph.SR↗

arXiv2020

Tess asteroseismology of the known planet host star $λ^2$ Fornacis

The Transiting Exoplanet Survey Satellite (TESS) is observing bright known planet-host stars across almost the entire sky. These stars have been subject to extensive ground-based observations, providing a large number of radial velocity (RV) measurements. In this work we use the new TESS photometric observations to characterize the star $λ^2$ Fornacis, and following this to update the parameters of the orbiting planet $λ^2$ For b. We measure the p-mode oscillation frequencies in $λ^2$ For, and in combination with non-seismic parameters estimate the stellar fundamental properties using stellar models. Using the revised stellar properties and a time series of archival RV data from the UCLES, HIRES and HARPS instruments spanning almost 20 years, we refit the orbit of $λ^2$ For b and search the RV residuals for remaining variability. We find that $λ^2$ For has a mass of $1.16\pm0.03$M$_\odot$ and a radius of $1.63\pm0.04$R$_\odot$, with an age of $6.3\pm0.9$Gyr. This and the updated RV measurements suggest a mass of $λ^2$ For b of $16.8^{+1.2}_{-1.3}$M$_\oplus$, which is $\sim5$M$_\oplus$ less than literature estimates. We also detect a periodicity at 33 days in the RV measurements, which is likely due to the rotation of the host star. While previous literature estimates of the properties of $λ^2$ are ambiguous, the asteroseismic measurements place the star firmly at the early stage of its subgiant evolutionary phase. Typically only short time series of photometric data are available from TESS, but by using asteroseismology it is still possible to provide tight constraints on the properties of bright stars that until now have only been observed from the ground. This prompts a reexamination of archival RV data from the past few decades to update the characteristics of the planet hosting systems observed by TESS for which asteroseismology is possible.

astro-ph.SR↗

arXiv2019

Analytical modelling of period spacings across the HR diagram

The characterisation of stellar cores may be accomplished through the modelling of asteroseismic data from stars exhibiting either gravity-mode or mixed-mode pulsations, potentially shedding light on the physical processes responsible for the production, mixing, and segregation of chemical elements. In this work we validate against model data an analytical expression for the period spacing that will facilitate the inference of the properties of stellar cores, including the detection and characterisation of buoyancy glitches (strong chemical gradients). This asymptotically-based analytical expression is tested both in models with and without buoyancy glitches. It does not assume that glitches are small and, consequently, predicts non-sinusoidal glitch-induced period-spacing variations, as often seen in model and real data. We show that the glitch position and width inferred from the fitting of the analytical expression to model data consisting of pure gravity modes are in close agreement (typically better than 7$\%$ relative difference) with the properties measured directly from the stellar models. In the case of fitting mixed-mode model data, the same expression is shown to reproduce well the numerical results, when the glitch properties are known a priori. In addition, the fits performed to mixed-mode model data reveal a frequency dependence of the coupling coefficient, $q$, for a moderate-luminosity red-giant-branch model star. Finally, we find that fitting the analytical expression to the mixed-mode period spacings may provide a way to infer the frequencies of the pure acoustic dipole modes that would exist if no coupling took place between acoustic and gravity waves.

astro-ph.SR↗

arXiv2018

Amplitude and lifetime of radial modes in red giant star spectra observed by Kepler

Context: the space-borne missions CoRoT and Kepler have provided photometric observations of unprecedented quality. The study of solar-like oscillations observed in red giant stars by these satellites allows a better understanding of the different physical processes occurring in their interiors. In particular, the study of the mode excitation and damping is a promising way to improve our understanding of stellar physics that has, so far, been performed only on a limited number of targets. Aims: the recent asteroseismic characterization of the evolutionary status for a large number of red giants allows us to study the physical processes acting in the interior of red giants and how they are modify during stellar evolution. In this work, we aim to obtain information on the excitation and damping of pressure modes through the measurement of the stars' pressure mode widths and amplitudes and to analyze how they are modified with stellar evolution. The objective is to bring observational constraints on the modeling of the physical processes behind mode excitation and damping. Methods: we fit the frequency spectra of red giants with well defined evolutionary status using Lorentzians functions to derive the pressure mode widths and amplitudes. To strengthen our conclusions, we used two different fitting techniques. Results: pressure mode widths and amplitudes were determined for more than 5000 red giants. With a stellar sample two orders of magnitude larger than previous results, we confirmed that the mode width depends on stellar evolution and varies with stellar effective temperature. In addition, we discovered that the mode width depends on stellar mass. We also confirmed observationally the influence of the stellar metallicity on the mode amplitudes, as predicted by models.

astro-ph.SR↗

arXiv2017

Kepler red-clump stars in the field and in open clusters: constraints on core mixing

Convective mixing in Helium-core-burning (HeCB) stars is one of the outstanding issues in stellar modelling. The precise asteroseismic measurements of gravity-modes period spacing ($ΔΠ_1$) has opened the door to detailed studies of the near-core structure of such stars, which had not been possible before. Here we provide stringent tests of various core-mixing scenarios against the largely unbiased population of red-clump stars belonging to the old open clusters monitored by Kepler, and by coupling the updated precise inference on $ΔΠ_1$ in thousands field stars with spectroscopic constraints. We find that models with moderate overshooting successfully reproduce the range observed of $ΔΠ_1$ in clusters. In particular we show that there is no evidence for the need to extend the size of the adiabatically stratified core, at least at the beginning of the HeCB phase. This conclusion is based primarily on ensemble studies of $ΔΠ_1$ as a function of mass and metallicity. While $ΔΠ_1$ shows no appreciable dependence on the mass, we have found a clear dependence of $ΔΠ_1$ on metallicity, which is also supported by predictions from models.

astro-ph.GA↗

arXiv2016

Period spacings in red giants; III. Coupling factors of mixed modes

The power of asteroseismology relies on the capability of global oscillations to infer the stellar structure. For evolved stars, we benefit from unique information directly carried out by mixed modes that probe their radiative cores. This third article of the series devoted to mixed modes in red giants focuses on their coupling factors that remained largely unexploited up to now. With the measurement of the coupling factors, we intend to give physical constraints on the regions surrounding the radiative core and the hydrogen-burning shell of subgiants and red giants. A new method for measuring the coupling factor of mixed modes is set up. It is derived from the method recently implemented for measuring period spacings. It runs in an automated way so that it can be applied to a large sample of stars. Coupling factors of mixed modes were measured for thousands of red giants. They show specific variation with mass and evolutionary stage. Weak coupling is observed for the most evolved stars on the red giant branch only; large coupling factors are measured at the transition between subgiants and red giants, as well as in the red clump. The measurement of coupling factors in dipole mixed modes provides a new insight into the inner interior structure of evolved stars. While the large frequency separation and the asymptotic period spacings probe the envelope and the core, respectively, the coupling factor is directly sensitive to the intermediate region in between and helps determining its extent. Observationally, the determination of the coupling factor is a prior to precise fits of the mixed-mode pattern, and can now be used to address further properties of the mixed-mode pattern, as the signature of the buoyancy glitches and the core rotation.

astro-ph.SR↗

arXiv2016

Dipole modes with depressed amplitudes in red giants are mixed modes

Seismic observations have shown that a number of evolved stars exhibit low-amplitude dipole modes, which are referred to as depressed modes. Recently, these low amplitudes have been attributed to the presence of a strong magnetic field in the stellar core of those stars. We intend to study the properties of depressed modes in evolved stars, which is a necessary condition before concluding on the physical nature of the mechanism responsible for the reduction of the dipole mode amplitudes. We perform a thorough characterization of the global seismic parameters of depressed dipole modes and show that these modes have a mixed character. The observation of stars showing dipole mixed modes that are depressed is especially useful for deriving model-independent conclusions on the dipole mode damping. Observations prove that depressed dipole modes in red giants are not pure pressure modes but mixed modes. This result invalidates the hypothesis that the depressed dipole modes result from the suppression of the oscillation in the radiative core of the stars. Observations also show that, except for the visibility, the seismic properties of the stars with depressed modes are equivalent to those of normal stars. The mixed nature of the depressed modes in red giants and their unperturbed global seismic parameters carry strong constraints on the physical mechanism responsible for the damping of the oscillation in the core. This mechanism is able to damp the oscillation in the core but cannot fully suppress it. Moreover, it cannot modify the radiative cavity probed by the gravity component of the mixed modes. The recent mechanism involving high magnetic field proposed for explaining depressed modes is not compliant with the observations and cannot be used to infer the strength and the prevalence of high magnetic fields in red giants.

astro-ph.SR↗

arXiv2016

Period spacings in red giants II. Automated measurement

The space missions CoRoT and Kepler have provided photometric data of unprecedented quality for asteroseismology. A very rich oscillation pattern has been discovered for red giants, including mixed modes that are used to decipher the red giants interiors. They carry information on the radiative core of red giant stars and bring strong constraints on stellar evolution. Since more than 15,000 red giant light curves have been observed by Kepler, we have developed a simple and efficient method for automatically characterizing the mixed-mode pattern and measuring the asymptotic period spacing. With the asymptotic expansion of the mixed modes, we have revealed the regularity of the gravity-mode pattern. The stretched periods were used to study the evenly space periods with a Fourier analysis and to measure the gravity period spacing, even when rotation severely complicates the oscillation spectra. We automatically measured gravity period spacing for more than 6,100 Kepler red giants. The results confirm and extend previous measurements made by semi-automated methods. We also unveil the mass and metallicity dependence of the relation between the frequency spacings and the period spacings for stars on the red giant branch. The delivery of thousands of period spacings combined with all other seismic and non-seismic information provides a new basis for detailed ensemble asteroseismology.

astro-ph.SR↗

arXiv2015

Period spacings in red giants I. Disentangling rotation and revealing core structure discontinuities

Asteroseismology allows us to probe the physical conditions inside the core of red giant stars. This relies on the properties of the global oscillations with a mixed character that are highly sensitive to the physical properties of the core. However, overlapping rotational splittings and mixed-mode spacings result in complex structures in the mixed-mode pattern, which severely complicates its identification and the measurement of the asymptotic period spacing. This work aims at disentangling the rotational splittings from the mixed-mode spacings, in order to open the way to a fully automated analysis of large data sets. An analytical development of the mixed-mode asymptotic expansion is used to derive the period spacing between two consecutive mixed modes. The échelle diagrams constructed with the appropriately stretched periods are used to exhibit the structure of the gravity modes and of the rotational splittings. We propose a new view on the mixed-mode oscillation pattern based on corrected periods, called stretched periods, that mimic the evenly spaced gravity-mode pattern. This provides a direct understanding of all oscillation components, even in the case of rapid rotation. The measurement of the asymptotic period spacing and the signature of the structural glitches on mixed modes are then made easy. This work opens the possibility to derive all seismic global parameters in an automated way, including the identification of the different rotational multiplets and the measurement of the rotational splitting, even when this splitting is significantly larger than the period spacing. Revealing buoyancy glitches provides a detailed view on the radiative core.

astro-ph.SR↗

arXiv2015

Helium signature in red giant oscillation patterns observed by Kepler

The space-borne missions CoRoT and Kepler have provided a large amount of precise photometric data. Among the stars observed, red giants show a rich oscillation pattern that allows their precise characterization. Long-duration observations allow for investigating the fine structure of this oscillation pattern. A common pattern of oscillation frequency was observed in red giant stars, which corresponds to the second-order development of the asymptotic theory. This pattern, called the universal red giant oscillation pattern, describes the frequencies of stellar acoustic modes. We aim to investigate the deviations observed from this universal pattern, thereby characterizing them in terms of the location of the second ionization zone of helium. We also show how this seismic signature depends on stellar evolution. We measured the frequencies of radial modes with a maximum likelihood estimator method, then we identified a modulation corresponding to the departure from the universal oscillation pattern. We identify the modulation component of the radial mode frequency spacings in more than five hundred red giants. The variation in the modulation that we observe at different evolutionary states brings new constraints on the interior models for these stars. We also derive an updated form of the universal pattern that accounts for the modulation and provides highly precise radial frequencies.

astro-ph.SR↗

arXiv2014

Mixed modes in red giants: a window on stellar evolution

The detection of oscillations with a mixed character in subgiants and red giants allows us to probe the physical conditions in their cores. With these mixed modes, we aim at determining seismic markers of stellar evolution. Kepler asteroseismic data were selected to map various evolutionary stages and stellar masses. Seismic evolutionary tracks were then drawn with the combination of the frequency and period spacings. We measured the asymptotic period spacing for more than 1170 stars at various evolutionary stages. This allows us to monitor stellar evolution from the main sequence to the asymptotic giant branch and draw seismic evolutionary tracks. We present clear quantified asteroseismic definitions that characterize the change in the evolutionary stages, in particular the transition from the subgiant stage to the early red giant branch, and the end of the horizontal branch.The seismic information is so precise that clear conclusions can be drawn independently of evolution models. The quantitative seismic information can now be used for stellar modeling, especially for studying the energy transport in the helium-burning core or for specifying the inner properties of stars entering the red or asymptotic giant branches. Modeling will also allow us to study stars that are identified to be in the helium-subflash stage, high-mass stars either arriving or quitting the secondary clump, or stars that could be in the blue-loop stage.

astro-ph.SR↗