Global Oscillation Parameters Research Articles

The Bayesian Asteroseismology Data Modeling Pipeline and Its Application to K2 Data

Abstract We present the Bayesian Asteroseismology data Modeling (BAM) pipeline, an automated asteroseismology pipeline that returns global oscillation parameters and granulation parameters from the analysis of photometric time series. BAM also determines whether a star is likely to be a solar-like oscillator. We have designed BAM to specially process K2 light curves, which suffer from unique noise signatures that can confuse asteroseismic analysis, though it may be used on any photometric time series—including those from Kepler and TESS. We demonstrate that the BAM oscillation parameters are consistent within ∼1.53% (random) ± 0.2% (systematic) and 1.51% (random) ± 0.6% (systematic) for and with benchmark results for typical K2 red giant stars in the K2 Galactic Archaeology Program’s (GAP) Campaign 1 sample. Application of BAM to 13,016 K2 Campaign 1 targets not in the GAP sample yields 104 red giant solar-like oscillators. Based on the number of serendipitous giants we find, we estimate an upper limit on the average purity in dwarf selection among C1 proposals of ≈99%, which could be lower when considering incompleteness in BAM detection efficiency and proper-motion cuts specific to C1 Guest Observer proposals.

Asteroseismology of the Hyades red giant and planet host ϵ Tauri

Context. Asteroseismic analysis of solar-like stars allows us to determine physical parameters such as stellar mass, with a higher precision compared to most other methods. Even in a well-studied cluster such as the Hyades, the masses of the red giant stars are not well known, and previous mass estimates are based on model calculations (isochrones). The four known red giants in the Hyades are assumed to be clump (core-helium-burning) stars based on their positions in colour-magnitude diagrams, however asteroseismology offers an opportunity to test this assumption. Aims. Using asteroseismic techniques combined with other methods, we aim to derive physical parameters and the evolutionary stage for the planet hosting star ϵ Tau, which is one of the four red giants located in the Hyades. Methods. We analysed time-series data from both ground and space to perform the asteroseismic analysis. By combining high signal-to-noise radial-velocity data from the ground-based SONG network with continuous space-based data from the revised Kepler mission K2, we derive and characterize 27 individual oscillation modes for ϵ Tau, along with global oscillation parameters such as the large frequency separation Δν and the ratio between the amplitude of the oscillations measured in radial velocity and intensity as a function of frequency. The latter has been measured previously for only two stars, the Sun and Procyon. Combining the seismic analysis with interferometric and spectroscopic measurements, we derive physical parameters for ϵ Tau, and discuss its evolutionary status. Results. Along with other physical parameters, we derive an asteroseismic mass for ϵ Tau of M = 2.458 ± 0.073 M⊙, which is slightly lower than previous estimates, and which leads to a revised minimum mass of the planetary companion. Noting that the SONG and K2 data are non-simultaneous, we estimate the amplitude ratio between intensity and radial velocity to be 42.2 ± 2.3 ppm m−1 s, which is higher than expected from scaling relations.

Non-linear seismic scaling relations

Context. In recent years the global seismic scaling relations for the frequency of maximum power, νmax ∝ g / √Teff, and for the large frequency separation, Δν ∝ √ρ¯, have drawn attention in various fields of astrophysics. This is because these relations can be used to estimate parameters, such as the mass and radius of stars that show solar-like oscillations. With the exquisite photometry of Kepler, the uncertainties in the seismic observables are small enough to estimate masses and radii with a precision of only a few per cent. Even though this seems to work quite well for main-sequence stars, there is empirical evidence, mainly from studies of eclipsing binary systems, that the seismic scaling relations systematically overestimate the mass and radius of red giants by about 15% and 5%, respectively. Various model-based corrections of the Δν-scaling reduce the problem but do not solve it. Aims. Our goal is to define revised seismic scaling relations that account for the known systematic mass and radius discrepancies in a completely model-independent way. Methods. We use probabilistic methods to analyse the seismic data and to derive non-linear scaling relations based on a sample of six red giant branch (RGB) stars that are members of eclipsing binary systems and about 60 red giants on the RGB as well as in the core-helium burning red clump (RC) in the two open clusters NGC 6791 and NGC 6819. Results. We re-examine the global oscillation parameters of the giants in the binary systems in order to determine their seismic fundamental parameters and we find them to agree with the dynamic parameters from the literature if we adopt non-linear scalings. We note that a curvature and glitch corrected Δνcor should be preferred over a local or average value of Δν. We then compare the observed seismic parameters of the cluster giants to those scaled from independent measurements and find the same non-linear behaviour as for the eclipsing binaries. Our final proposed scaling relations are based on both samples and cover a broad range of evolutionary stages from RGB to RC stars: g / √Teff = (νmax / νmax,⊙)1.0075±0.0021 and √ρ¯ = (Δνcor / Δνcor,⊙)[η − (0.0085 ± 0.0025) log2(Δνcor / Δνcor,⊙)]−1, where g, Teff, and ρ¯ are in solar units, νmax,⊙ = 3140 ± 5 μHz and Δνcor,⊙ = 135.08 ± 0.02 μHz, and η is equal to one in the case of RGB stars and 1.04 ± 0.01 for RC stars. Conclusions. A direct consequence of these new scaling relations is that the average mass of stars on the ascending giant branch reduces to 1.10 ± 0.03 M⊙ in NGC 6791 and 1.45 ± 0.06 M⊙ in NGC 6819, allowing us to revise the clusters’ distance modulus to 13.11 ± 0.03 and 11.91 ± 0.03 mag, respectively. We also find strong evidence that both clusters are significantly older than concluded from previous seismic investigations.

Convective-core Overshoot and Suppression of Oscillations: Constraints from Red Giants in NGC 6811

Abstract Using data from the NASA spacecraft Kepler, we study solar-like oscillations in red giant stars in the open cluster NGC 6811. We determine oscillation frequencies, frequency separations, period spacings of mixed modes, and mode visibilities for eight cluster giants. The oscillation parameters show that these stars are helium-core-burning red giants. The eight stars form two groups with very different oscillation power spectra; the four stars with the lowest Δν values display rich sets of mixed l = 1 modes, while this is not the case for the four stars with higher Δν. For the four stars with lowest Δν, we determine the asymptotic period spacing of the mixed modes, ΔP, which together with the masses we derive for all eight stars suggest that they belong to the so-called secondary clump. Based on the global oscillation parameters, we present initial theoretical stellar modeling that indicates that we can constrain convective-core overshoot on the main sequence and in the helium-burning phase for these ∼2 M ⊙ stars. Finally, our results indicate less mode suppression than predicted by recent theories for magnetic suppression of certain oscillation modes in red giants.

CALIBRATION OF LAMOST STELLAR SURFACE GRAVITIES USING THE KEPLER ASTEROSEISMIC DATA

ABSTRACT Asteroseismology is a powerful tool to precisely determine the evolutionary status and fundamental properties of stars. With the unprecedented precision and nearly continuous photometric data acquired by the NASA Kepler mission, parameters of more than 104 stars have been determined nearly consistently. However, most studies still use photometric effective temperatures (T eff) and metallicities ([Fe/H]) as inputs, which are not sufficiently accurate as suggested by previous studies. We adopted the spectroscopic T eff and [Fe/H] values based on the Large sky Area Multi-Object fiber Spectroscopic Telescope (LAMOST) low-resolution spectra (R ≃ 1800), and combined them with the global oscillation parameters to derive the physical parameters of a large sample of stars. Clear trends were found between and spectroscopic T eff as well as log g, which may result in an overestimation of up to 0.5 dex for the log g values of giants in the LAMOST catalog. We established empirical calibration relations for the log g values of dwarfs and giants. These results can be used for determining the precise distances to these stars based on their spectroscopic parameters.

ASTEROSEISMIC STUDY ON CLUSTER DISTANCE MODULI FOR RED GIANT BRANCH STARS IN NGC 6791 AND NGC 6819

Stellar distance is an important basic parameter in stellar astrophysics. Stars in a cluster are thought to be formed coevally from the same interstellar cloud of gas and dust. They are therefore expected to have common properties. These common properties strengthen our ability to constrain theoretical models and/or to determine fundamental parameters, such as stellar mass, metal fraction, and distance when tested against an ensemble of cluster stars. Here we derive a new relation based on solar-like oscillations, photometric observations, and the theory of stellar structure and evolution of red giant branch stars to determine cluster distance moduli through the global oscillation parameters $\Delta\nu$ and $\nu_{\rm max}$, and photometric data \textit{V}. The values of $\Delta\nu$ and $\nu_{\rm max}$ are derived from \textit{kepler} observations. At the same time, it is used to interpret the trends between \textit{V} and $\Delta\nu$. From the analyses of this newly derived relation and observational data of NGC 6791 and NGC 6819 we devise a method in which all stars in a cluster are regarded as one entity to determine the cluster distance modulus. This approach fully reflects the characteristic of member stars in a cluster as a natural sample. From this method we derive true distance moduli of $13.09\pm0.10$ mag for NGC 6791 and $11.88\pm0.14$ mag for NGC 6819. Additionally, we find that the distance modulus only slightly depends on the metallicity [Fe/H] in the new relation. A change of 0.1 dex in [Fe/H] will lead to a change of 0.06 mag in the distance modulus.

NEW ASTEROSEISMIC SCALING RELATIONS BASED ON THE HAYASHI TRACK RELATION APPLIED TO RED GIANT BRANCH STARS IN NGC 6791 AND NGC 6819

Stellar mass $M$, radius $R$, and gravity $g$ are important basic parameters in stellar physics. Accurate values for these parameters can be obtained from the gravitational interaction between stars in multiple systems or from asteroseismology. Stars in a cluster are thought to be formed coevally from the same interstellar cloud of gas and dust. The cluster members are therefore expected to have some properties in common. These common properties strengthen our ability to constrain stellar models and asteroseismically derived $M$, $R$ and $g$ when tested against an ensemble of cluster stars. Here we derive new scaling relations based on a relation for stars on the Hayashi track ($\sqrt{T_{\rm eff}} \sim g^pR^q$) to determine the masses and metallicities of red giant branch stars in open clusters NGC 6791 and NGC 6819 from the global oscillation parameters $\Delta\nu$ (the large frequency separation) and $\nu_{\rm max}$ (frequency of maximum oscillation power). The $\Delta\nu$ and $\nu_{\rm max}$ values are derived from \kepler\ observations. From the analysis of these new relations we derive: (1) direct observational evidence that the masses of red giant branch stars in a cluster are the same within their uncertainties, (2) new methods to derive $M$ and $z$ of the cluster in a self consistent way from $\Delta\nu$ and $\nu_{\rm max}$, with lower intrinsic uncertainties, (3) the mass dependence in the $\Delta\nu$ - $\nu_{\rm max}$ relation for red giant branch stars.

Period-luminosity relations in evolved red giants explained by solar-like oscillations

Solar-like oscillations in red giants have been investigated with CoRoT and Kepler, while pulsations in more evolved M giants have been studied with ground-based microlensing surveys. After 3.1 years of observation with Kepler, it is now possible to make a link between these different observations of semi-regular variables. We aim to identify period-luminosity sequences in evolved red giants identified as semi-regular variables. Then, we investigate the consequences of the comparison of ground-based and space-borne observations. We have first measured global oscillation parameters of evolved red giants observed with Kepler with the envelope autocorrelation function method. We then used an extended form of the universal red giant oscillation pattern, extrapolated to very low frequency, to fully identify their oscillations. From the link between red giant oscillations observed by Kepler and period-luminosity sequences, we have identified these relations in evolved red giants as radial and non-radial solar-like oscillations. We were able to expand scaling relations at very low frequency. This helped us to identify the different sequences of period-luminosity relations, and allowed us to propose a calibration of the K magnitude with the observed frequency large separation. Interpreting period-luminosity relations in red giants in terms of solar-like oscillations allows us to investigate, with a firm physical basis, the time series obtained from ground-based microlensing surveys. This can be done with an analytical expression that describes the low-frequency oscillation spectra. The different behavior of oscillations at low frequency, with frequency separations scaling only approximately with the square root of the mean stellar density, can be used to address precisely the physics of the semi-regular variables.

Asymptotic and measured large frequency separations

With the space-borne missions CoRoT and Kepler, a large amount of asteroseismic data is now available. So-called global oscillation parameters are inferred to characterize the large sets of stars, to perform ensemble asteroseismology, and to derive scaling relations. The mean large separation is such a key parameter. It is therefore crucial to measure it with the highest accuracy. As the conditions of measurement of the large separation do not coincide with its theoretical definition, we revisit the asymptotic expressions used for analysing the observed oscillation spectra. Then, we examine the consequence of the difference between the observed and asymptotic values of the mean large separation. The analysis is focused on radial modes. We use series of radial-mode frequencies to compare the asymptotic and observational values of the large separation. We propose a simple formulation to correct the observed value of the large separation and then derive its asymptotic counterpart. We prove that, apart from glitches due to stellar structure discontinuities, the asymptotic expansion is valid from main-sequence stars to red giants. Our model shows that the asymptotic offset is close to 1/4, as in the theoretical development. High-quality solar-like oscillation spectra derived from precise photometric measurements are definitely better described with the second-order asymptotic expansion. The second-order term is responsible for the curvature observed in the \'echelle diagrams used for analysing the oscillation spectra and this curvature is responsible for the difference between the observed and asymptotic values of the large separation. Taking it into account yields a revision of the scaling relations providing more accurate asteroseismic estimates of the stellar mass and radius.

Red giant oscillations: Stellar models and mode frequency calculations

AbstractWe present preliminary results on modelling KIC 7693833, the so far most metal‐poor red giant star observed by Kepler. From time series spanning several months, global oscillation parameters and individual frequencies were obtained and compared to theoretical calculations. Evolution models are calculated taking into account spectroscopic and asteroseismic constraints. The oscillation frequencies of the models were computed and compared to the Kepler data. In the range of mass computed, there is no preferred model, giving an uncertainty of about 30 K in Teff, 0.02 dex in log g, 0.7R⊙ in radius, and of about 2.5 Gyrs in age (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Solar-like oscillations in red giants observed withKepler: influence of increased timespan on global oscillation parameters

The length of the asteroseismic timeseries obtained from the Kepler satellite analysed here span 19 months. Kepler provides the longest continuous timeseries currently available, which calls for a study of the influence of the increased timespan on the accuracy and precision of the obtained results. We find that in general a minimum of the order of 400 day long timeseries are necessary to obtain reliable results for the global oscillation parameters in more than 95% of the stars, but this does depend on <dnu>. In a statistical sense the quoted uncertainties seem to provide a reasonable indication of the precision of the obtained results in short (50-day) runs, they do however seem to be overestimated for results of longer runs. Furthermore, the different definitions of the global parameters used in the different methods have non-negligible effects on the obtained values. Additionally, we show that there is a correlation between nu_max and the flux variance. We conclude that longer timeseries improve the likelihood to detect oscillations with automated codes (from ~60% in 50 day runs to > 95% in 400 day runs with a slight method dependence) and the precision of the obtained global oscillation parameters. The trends suggest that the improvement will continue for even longer timeseries than the 600 days considered here, with a reduction in the median absolute deviation of more than a factor of 10 for an increase in timespan from 50 to 2000 days (the currently foreseen length of the mission). This work shows that global parameters determined with high precision - thus from long datasets - using different definitions can be used to identify the evolutionary state of the stars. (abstract truncated)

Asteroseismic inferences on red giants in open clusters NGC 6791, NGC 6819, and NGC 6811 usingKepler

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 methods and the effective temperatures are derived from 2MASS colours. The observational results are compared with BaSTI evolution models. Results: We find that the mass has significant influence on the asteroseismic quantities delta_nu vs. nu_max relation, while the influence of metallicity is negligible, under the assumption that the metallicity does not affect the excitation / damping of the oscillations. The positions of the stars in the H-R diagram depend on both mass and metallicity. Furthermore, the stellar masses derived for the field stars are bracketed by those of the cluster stars. Conclusions: Both the mass and metallicity contribute to the observed difference in locations in the H-R diagram of the old metal-rich cluster NGC 6791 and the middle-aged solar-metallicity cluster NGC 6819. For the young cluster NGC 6811, the explanation of the position of the stars in the H-R diagram challenges the assumption of solar metallicity, and this open cluster might have significantly lower metallicity [Fe/H] in the range -0.3 to -0.7 dex. Also, nearly all the observed field stars seem to be older than NGC 6811 and younger than NGC 6791.

Solar-like oscillations in red giants observed withKepler: comparison of global oscillation parameters from different methods

The large number of stars for which uninterrupted high-precision photometric timeseries data are being collected with \textit{Kepler} and CoRoT initiated the development of automated methods to analyse the stochastically excited oscillations in main-sequence, subgiant and red-giant stars. Aims: We investigate the differences in results for global oscillation parameters of G and K red-giant stars due to different methods and definitions. We also investigate uncertainties originating from the stochastic nature of the oscillations. Methods: For this investigation we use Kepler data obtained during the first four months of operation. These data have been analysed by different groups using already published methods and the results are compared. We also performed simulations to investigate the uncertainty on the resulting parameters due to different realizations of the stochastic signal. Results: We obtain results for the frequency of maximum oscillation power (nu_max) and the mean large separation (<delta nu>) from different methods for over one thousand red-giant stars. The results for these parameters agree within a few percent and seem therefore robust to the different analysis methods and definitions used here. The uncertainties for nu_max and <delta nu> due to differences in realization noise are not negligible and should be taken into account when using these results for stellar modelling.

Asteroseismology of red giants from the first four months ofKeplerdata: Fundamental stellar parameters

Clear power excess in a frequency range typical for solar-type oscillations in red giants has been detected in more than 1000 stars, which have been observed during the first 138 days of the science operation of the NASA Kepler satellite. This sample includes stars in a wide mass and radius range with spectral types G and K, extending in luminosity from the bottom of the giant branch up to high-luminous red giants. The high-precision asteroseismic observations with Kepler provide a perfect source for testing stellar structure and evolutionary models, as well as investigating the stellar population in our Galaxy. We fit a global model to the observed frequency spectra, which allows us to accurately estimate the granulation background signal and the global oscillation parameters, such as the frequency of maximum oscillation power. We find regular patterns of radial and non-radial oscillation modes and use a new technique to automatically identify the mode degree and the characteristic frequency separations between consecutive modes of the same spherical degree. In most cases, we can also measure the small separation. The seismic parameters are used to estimate stellar masses and radii and to place the stars in an H-R diagram by using an extensive grid of stellar models that covers a wide parameter range. Using Bayesian techniques throughout our analysis allows us to determine reliable uncertainties for all parameters. We provide accurate seismic parameters and their uncertainties for a large sample of red giants and determine their asteroseismic fundamental parameters. We investigate the influence of the stars' metallicities on their positions in the H-R diagram. We study the red-giant populations in the red clump and bump and compare them to a synthetic population and find a mass and metallicity gradient in the red clump and clear evidence of a secondary-clump population.

Automated extraction of oscillation parameters for Kepler observations of solar-type stars

The recent launch of the Kepler space telescope brings the opportunity to study oscillations systematically in large numbers of solar-like stars. In the framework of the asteroFLAG project, we have developed an automated pipeline to estimate global oscillation parameters, such as the frequency of maximum power (νmax) and the large frequency spacing (�ν), for a large number of time series. We present an effective method based on the autocorrelation function to find excess power and use a scaling relation to estimate granulation timescales as initial conditions for background modelling. We derive reliable uncertainties for νmax and �ν through extensive simulations. We have tested the pipeline on about 2000 simulated Kepler stars with magnitudes of V ∼7–12 and were able to correctly determine νmax and �ν for about half of the sample. For about 20%, the returned large frequency spacing is accurate enough to determine stellar radii to a 1% precision. We conclude that the methods presented here are a promising approach to process the large amount of data expected from Kepler.