Mean Large Separation Research Articles

Study with WhoSGlAd of the acoustic depth of the helium glitch across the seismic HR diagram and its impact on the inferred helium abundance

ABSTRACTThe acoustic glitches’ signature present in solar-like stars holds invaluable information. Indeed, it is caused by a sharp variation in the sound speed, therefore carrying localized information. One such glitch is the helium glitch caused by the hydrogen and first and second partial helium ionization region, allowing us to constrain the surface helium abundance. However, the function adjusted to the glitch signature depends non-linearly on the acoustic depth at which it occurs, He. Retrieving the faint glitch signature and estimating τHe are difficult but crucial tasks to accurately measure the glitch parameters and, ultimately, accurately infer the helium abundance. In this paper, we aim at providing a way to estimate τHe using precise seismic indicators, independent of stellar modelling. Consequently, we aim at improving the WhoSGlAd (Whole Spectrum and Glitches Adjustment) method by automatically providing a model-independent measure of the glitch’s parameters. We compute the evolution of THe, a dimensionless form of the acoustic depth, along a grid of models and adjust an empirical linear relation between THe and the mean large separation and frequency ratio as defined in WhoSGlAd. We further optimize over the value of this estimate to ensure the stability and accuracy of the approach. The proposed approach provides an excellent estimate of the acoustic depth and allows us to swiftly retrieve the glitch signature of observed spectra. We demonstrate that the we can accurately model the helium abundance of four Kepler targets by comparing model (both versions of WhoSGlAd) and literature values.

Asteroseismology of 16,000 Kepler Red Giants: Global Oscillation Parameters, Masses, and Radii

Abstract The Kepler mission has provided exquisite data to perform an ensemble asteroseismic analysis on evolved stars. In this work we systematically characterize solar-like oscillations and granulation for 16,094 oscillating red giants, using end-of-mission long-cadence data. We produced a homogeneous catalog of the frequency of maximum power (typical uncertainty ), the mean large frequency separation ( ), oscillation amplitude ( ), granulation power ( ), power excess width ( ), seismically derived stellar mass ( ), radius ( ), and thus surface gravity ( dex). Thanks to the large red giant sample, we confirm that red-giant-branch (RGB) and helium-core-burning (HeB) stars collectively differ in the distribution of oscillation amplitude, granulation power, and width of power excess, which is mainly due to the mass difference. The distribution of oscillation amplitudes shows an extremely sharp upper edge at fixed , which might hold clues for understanding the excitation and damping mechanisms of the oscillation modes. We find that both oscillation amplitude and granulation power depend on metallicity, causing a spread of 15% in oscillation amplitudes and a spread of 25% in granulation power from [Fe/H] = −0.7 to 0.5 dex. Our asteroseismic stellar properties can be used as reliable distance indicators and age proxies for mapping and dating galactic stellar populations observed by Kepler. They will also provide an excellent opportunity to test asteroseismology using Gaia parallaxes, and lift degeneracies in deriving atmospheric parameters in large spectroscopic surveys such as APOGEE and LAMOST.

Seismic diagnostics of solar-like oscillating stars

High precision and long-lasting Kepler data enabled us to estimate stellar properties with asteroseismology as an accurate tool. We performed asteroseismic analysis on six solar-like stars observed by the Kepler mission: KIC 6064910, KIC 6766513, KIC 7107778, KIC 10079226, KIC 10147635 and KIC 12069127. The extraction of seismic information includes two parts. First, we obtained two global asteroseismic parameters, mean large separation and frequency of maximum power , with autocorrelation function and collapsed autocorrelation function. Second, we extracted individual oscillation modes νnl with low-l degree using a least-squares fit. Stellar grid models were built with Yale Rotating Stellar Evolution Code (YREC) to analyze stellar properties. They covered the range of with a step of 0.02 and dex with a step of 0.1 dex. We used a Bayesian approach to estimate stellar fundamental parameters of the six stars, under the constraints of asteroseismic parameters (, ) and non-asteroseismic parameters (, ). We discover that the six targets include five sub-giant stars with and one main-sequence star with , and with ages in the range of .

An analysis of the solar-like oscillations in the red giant star KIC 5701829 observed withKepler

AbstractThe preliminary results of an analysis of the red giant star KIC 5701829 observed for 29 days in short-cadence mode with theKeplersatellite are reported. The oscillation spectrum of this star is characterized by the presence of a well-defined solar-like oscillation pattern due to acoustic modes. The characterization of the power spectrum has been performed following three basics steps commonly used in the analysis of solar-like oscillations: fitting and correcting for the background, estimating the frequency of maximum power (νmax) and the large separation (Δν), and extracting individual frequencies. We have found that the frequency of maximum oscillation power, νmax, and the mean large frequency separation, Δν, are around, 143 and 12 μHz, respectively. The global asteroseismic parameters along with atmospheric parameters from the literature allow us to infer about evolutionary status of the star.

Detection of solar-like oscillations in the bright red giant starsγPiscium andθ1 Tauri from a 190-day high-precision spectroscopic multi-site campaign

Red giants are evolved stars which exhibit solar-like oscillations. Although a multitude of stars have been observed with space telescopes, only a handful of red-giant stars were targets of spectroscopic asteroseismic observing projects. We search for solar-like oscillations in the two bright red-giant stars $\gamma$ Psc and $\theta^1$ Tau from time series of ground-based spectroscopy and determine the frequency of the excess of oscillation power $\nu_{max}$ and the mean large frequency separation $\Delta\nu$ for both stars. The radial velocities of $\gamma$ Psc and $\theta^1$ Tau were monitored for 120 and 190 days, respectively. Nearly 9000 spectra were obtained. To reach the accurate radial velocities, we used simultaneous thorium-argon and iodine-cell calibration of our optical spectra. In addition to the spectroscopy, we acquired VLTI observations of $\gamma$ Psc for an independent estimate of the radius. Also 22 days of observations of $\theta^1$ Tau with the MOST-satellite were analysed. The frequency analysis of the radial velocity data of $\gamma$ Psc revealed an excess of oscillation power around 32 $\mu$Hz and a large frequency separation of 4.1$\pm$0.1$\mu$Hz. $\theta^1$ Tau exhibits oscillation power around 90 $\mu$Hz, with a large frequency separation of 6.9$\pm$0.2$\mu$Hz. Scaling relations indicate that $\gamma$ Psc is a star of about $\sim$1 M$_\odot$ and $\sim$10 R$_\odot$. $\theta^1$ Tau appears to be a massive star of about $\sim$2.7 M$_\odot$ and $\sim$11 R$_\odot$. The radial velocities of both stars were found to be modulated on time scales much longer than the oscillation periods. While the mass of $\theta^1$ Tau is in agreement with results from dynamical parallaxes, we find a lower mass for $\gamma$ Psc than what is given in the literature. The long periodic variability agrees with the expected time scales of rotational modulation.

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.

Probing the core structure and evolution of red giants using gravity-dominated mixed modes observed withKepler

We report for the first time a parametric fit to the pattern of the \ell = 1 mixed modes in red giants, which is a powerful tool to identify gravity-dominated mixed modes. With these modes, which share the characteristics of pressure and gravity modes, we are able to probe directly the helium core and the surrounding shell where hydrogen is burning. We propose two ways for describing the so-called mode bumping that affects the frequencies of the mixed modes. Firstly, a phenomenological approach is used to describe the main features of the mode bumping. Alternatively, a quasi-asymptotic mixed-mode relation provides a powerful link between seismic observations and the stellar interior structure. We used period \'echelle diagrams to emphasize the detection of the gravity-dominated mixed modes. The asymptotic relation for mixed modes is confirmed. It allows us to measure the gravity-mode period spacings in more than two hundred red giant stars. The identification of the gravity-dominated mixed modes allows us to complete the identification of all major peaks in a red giant oscillation spectrum, with significant consequences for the true identification of \ell = 3 modes, of \ell = 2 mixed modes, for the mode widths and amplitudes, and for the \ell = 1 rotational splittings. The accurate measurement of the gravity-mode period spacing provides an effective probe of the inner, g-mode cavity. The derived value of the coupling coefficient between the cavities is different for red giant branch and clump stars. This provides a probe of the hydrogen-shell burning region that surrounds the helium core. Core contraction as red giants ascend the red giant branch can be explored using the variation of the gravity-mode spacing as a function of the mean large separation.

Frequency dependence of the large frequency separation of solar-like oscillators: influence of the helium second-ionization zone

ABSTRACT The large frequency separation (Δν) between modes of the same degree and consecutive orders in a star is approximately proportional to the square root of its mean density. To determine Δν as accurately as possible, a mean large frequency separation (〈Δν〉) computed over several orders is often used. It is, however, known that Δν varies with frequency in a second-order effect. From observations, it has been shown that this frequency dependence is more important for main-sequence stars than it is for red giant stars. Here we use yrec models to verify and explain this observational result. We find that for stars with R ≳ 8 R⊙, the effect of the helium second-ionization zone (He ii zone) is relatively small. For these stars, the deep location of the He ii zone induces a frequency modulation covering only a few Δν, while the amplitude of the modulation is low due to the relatively weak and extended He ii layer, causing a shallow wide depression in the first adiabatic exponent (Γ1). For less evolved stars, the He ii zone is located closer to the surface, and it is more confined, i.e. a deep narrow depression in Γ1. This causes frequency modulations with relatively high amplitudes covering up to about 20Δν, inducing a relatively large frequency modulation. Additionally, we find that for less evolved stars, the He ii zone is stronger and more localized for more massive stars and for stars with low metallicities further increasing the amplitude of the frequency modulation.

MODELINGKEPLEROBSERVATIONS OF SOLAR-LIKE OSCILLATIONS IN THE RED GIANT STAR HD 186355

We have analysed oscillations of the red giant star HD 186355 observed by the NASA Kepler satellite. The data consist of the first five quarters of science operations of Kepler, which cover about 13 months. The high-precision time-series data allow us to accurately extract the oscillation frequencies from the power spectrum. We find the frequency of the maximum oscillation power, {\nu}_max, and the mean large frequency separation, {\Delta}{\nu}, are around 106 and 9.4 {\mu}Hz respectively. A regular pattern of radial and non-radial oscillation modes is identified by stacking the power spectra in an echelle diagram. We use the scaling relations of {\Delta}{\nu} and {\nu}_max to estimate the preliminary asteroseismic mass, which is confirmed with the modelling result (M = 1.45 \pm 0.05 M_sun) using the Yale Rotating stellar Evolution Code (YREC7). In addition, we constrain the effective temperature, luminosity and radius from comparisons between observational constraints and models. A number of mixed l = 1 modes are also detected and taken into account in our model comparisons. We find a mean observational period spacing for these mixed modes of about 58 s, suggesting that this red giant branch star is in the shell hydrogen-burning phase.

Quantitative estimates of the constraints on solar-like models imposed by observables

Context. Seismic parameters such as the large Δ0 and small δ02 frequency separations are now being measured in a very large number of stars and begin to be used to test the physics of stellar models. Aims. We estimate the influence of different observed quantities (oscillation frequencies, interferometry, etc.) and the impact of their accuracy in constraining stellar model parameters. Methods. To relate the errors in observed quantities to the precision of the theoretical model parameters, we analyse the behaviour of the χ 2 fitting function around its minimum using the singular value decomposition (SVD) formalism. A new indicator called “weighting” quantifies the relative importance of observational constraints on the determination of each physical parameter individually. These tools are applied to a grid of evolutionary sequences for solar-like stellar models with varying age and mass, and to a real case: HD 49933 – a typical case for which seismic observations are available from space using CoRoT. Results. The mass M is always the best determined parameter. The new indicator “weighting” allows us to rank the importance of the different constraints: the mean large separation Δ0, the radius R/R� , the mean small separation δ02, the luminosity L/L� ,t he effective temperature Teff. If the metallicity and age parameters are known, for example in an open cluster, using either individual or mean frequency separations yields the same uncertainties for masses less than 1.1 M� . For HD 49933 the combination of M and Y0: M 2 Y0 is well determined because of their correlation. However, they are poorly constrained individually. The frequency difference δ01 ,i f known with an error of about 0.3%, can determine the size of the convective core overshooting with about 3% accuracy.

Global asteroseismic properties of solar-like oscillations observed by Kepler: a comparison of complementary analysis methods

We present the asteroseismic analysis of 1948 F-, G- and K-type main-sequence and subgiant stars observed by the National Aeronautics and Space Administration Kepler mission. We detect and characterize solar-like oscillations in 642 of these stars. This represents the largest cohort of main-sequence and subgiant solar-like oscillators observed to date. The photometric observations are analysed using the methods developed by nine independent research teams. The results are combined to validate the determined global asteroseismic parameters and calculate the relative precision by which the parameters can be obtained. We correlate the relative number of detected solar-like oscillators with stellar parameters from the Kepler Input Catalogue and find a deficiency for stars with effective temperatures in the range 5300 ≲Teff≲ 5700 K and a drop-off in detected oscillations in stars approaching the red edge of the classical instability strip. We compare the power-law relationships between the frequency of peak power, νmax, the mean large frequency separation, Δν, and the maximum mode amplitude, Amax, and show that there are significant method-dependent differences in the results obtained. This illustrates the need for multiple complementary analysis methods to be used to assess the robustness and reproducibility of results derived from global asteroseismic parameters.

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.

The solar-like CoRoT target HD 170987: spectroscopic and seismic observations

The CoRoT mission is in its third year of observation and the data from the second long run in the galactic centre direction are being analysed. The solar-like oscillating stars that have been observed up to now have given some interesting results, specially concerning the amplitudes that are lower than predicted. We present here the results from the analysis of the star HD 170987.The goal of this research work is to characterise the global parameters of HD 170987. We look for global seismic parameters such as the mean large separation, maximum amplitude of the modes, and surface rotation because the signal-to-noise ratio in the observations do not allow us to measure individual modes. We also want to retrieve the stellar parameters of the star and its chemical composition.We have studied the chemical composition of the star using ground-based observations performed with the NARVAL spectrograph. We have used several methods to calculate the global parameters from the acoustic oscillations based on CoRoT data. The light curve of the star has been interpolated using inpainting algorithms to reduce the effect of data gaps. We find power excess related to p modes in the range [400 - 1200]muHz with a mean large separation of 55.2+-0.8muHz with a probability above 95% that increases to 55.9 +-0.2muHz in a higher frequency range [500 - 1250] muHz and a rejection level of 1%. A hint of the variation of this quantity with frequency is also found. The rotation period of the star is estimated to be around 4.3 days with an inclination axis of i=50 deg +20/-13. We measure a bolometric amplitude per radial mode in a range [2.4 - 2.9] ppm around 1000 muHz. Finally, using a grid of models, we estimate the stellar mass, M=1.43+-0.05 Msun, the radius, R=1.96+-0.046 Rsun, and the age ~2.4 Gyr.

Red-giant seismic properties analyzed with CoRoT

The CoRoT 5-month long observation runs give us the opportunity to analyze a large variety of red-giant stars and to derive fundamental stellar parameters from their asteroseismic properties. We perform an analysis of more than 4\,600 CoRoT light curves to extract as much information as possible. We take into account the characteristics of the star sample and of the method in order to provide asteroseismic results as unbiased as possible. We also study and compare the properties of red giants of two opposite regions of the Galaxy. We analyze the time series with the envelope autocorrelation function in order to extract precise asteroseismic parameters with reliable error bars. We examine first the mean large frequency separation of solar-like oscillations and the frequency of maximum seismic amplitude, then the parameters of the excess power envelope. With the additional information of the effective temperature, we derive the stellar mass and radius. We have identified more than 1\,800 red giants among the 4\,600 light curves and have obtained accurate distributions of the stellar parameters for about 930 targets. We were able to reliably measure the mass and radius of several hundred red giants. We have derived precise information on the stellar population distribution and on the red clump. Comparison between the stars observed in two different fields shows that the stellar asteroseismic properties are globally similar, but with different characteristics for red-clump stars. This study shows the efficiency of statistical asteroseismology: validating scaling relations allows us to infer fundamental stellar parameters, to derive precise information on the red-giant evolution and interior structure and to analyze and compare stellar populations from different fields.

On detecting the large separation in the autocorrelation of stellar oscillation times series

The observations carried out by the space missions CoRoT and Kepler provide a large set of asteroseismic data. Their analysis requires an efficient procedure first to determine if the star is reliably showing solar-like oscillations, second to measure the so-called large separation, third to estimate the asteroseismic information that can be retrieved from the Fourier spectrum. We develop in this paper a procedure, based on the autocorrelation of the seismic Fourier spectrum. We have searched for criteria able to predict the output that one can expect from the analysis by autocorrelation of a seismic time series. First, the autocorrelation is properly scaled for taking into account the contribution of white noise. Then, we use the null hypothesis H0 test to assess the reliability of the autocorrelation analysis. Calculations based on solar and CoRoT times series are performed in order to quantify the performance as a function of the amplitude of the autocorrelation signal. We propose an automated determination of the large separation, whose reliability is quantified by the H0 test. We apply this method to analyze a large set of red giants observed by CoRoT. We estimate the expected performance for photometric time series of the Kepler mission. Finally, we demonstrate that the method makes it possible to distinguish l=0 from l=1 modes. The envelope autocorrelation function has proven to be very powerful for the determination of the large separation in noisy asteroseismic data, since it enables us to quantify the precision of the performance of different measurements: mean large separation, variation of the large separation with frequency, small separation and degree identification.

The CoRoT target HD 175726: an active star with weak solar-like oscillations

Context. The CoRoT short runs give us the opportunity to observe a large variety of late-type stars through their solar-like oscillations. We report observations of the star HD175726 that lasted for 27 days during the first short run of the mission. The time series reveals a high-activity signal and the power spectrum presents an excess due to solar-like oscillations with a low signal-to-noise ratio. Aims. Our aim is to identify the most efficient tools to extract as much information as possible from the power density spectrum. Methods. The most productive method appears to be the autocorrelation of the time series, calculated as the spectrum of the filtered spectrum. This method is efficient, very rapid computationally, and will be useful for the analysis of other targets, observed with CoRoT or with forthcoming missions such as Kepler and Plato. Results. The mean large separation has been measured to be 97.2+-0.5 microHz, slightly below the expected value determined from solar scaling laws.We also show strong evidence for variation of the large separation with frequency. The bolometric mode amplitude is only 1.7+-0.25 ppm for radial modes, which is 1.7 times less than expected. Due to the low signal-to-noise ratio, mode identification is not possible for the available data set of HD175726. Conclusions. This study shows the possibility of extracting a seismic signal despite a signal-to-noise ratio of only 0.37. The observation of such a target shows the efficiency of the CoRoT data, and the potential benefit of longer observing runs.

Core modes as a seismic probe of mixing beyond the convective core

Inhalt (u.a.): M. BREGER: Delta Scuti stars: Observational aspects; M.S. Cunha: Theory of rapidly oscillating Ap stars; M. SACHKOV et al.: Vertical structure of pulsations in roAp stars; G. HOUDEK: Theoretical asteroseismology of solar-like oscillations; B.L. POPIELSKI: Core modes as a seismic probe of mixing beyond the convective core; M. GODART: Temperature gradients in the core overshooting region; W.A. DZIEMBOWSKI – J. DASZYŃSKA-DASZKIEWICZ – A.A. PAMYATNYKH: Interpretation of the Be star HD 163868 oscillation spectrum based on the MOST observations; D. KILKENNY: Pulsating Hot Subdwarfs – An Observational Review; M.H. MONTGOMERY: Mapping Convection using Pulsating White Dwarf Stars; M. ROTH: The Network Activities in HELAS; I. KUDZEJ et al.: A New Slovak Observatory 500 km from Vienna; W.W. WEISS: Microsatellites; G. KOPACKI – S. FRANDSEN: RR Lyrae stars in M4

The diameter and evolutionary state of Procyon A

We report the angular diameter measurement obtained with the VINCI/VLTI instrument on the nearby star Procyon A (alpha CMi A, F5IV-V), at a relative precision of +/- 0.9%. We obtain a uniform disk angular diameter in the K band of UD = 5.376 +/- 0.047 mas and a limb darkened value of LD = 5.448 +/- 0.053 mas. Together with the Hipparcos parallax, this gives a linear diameter of 2.048 +/- 0.025 D_sun. We use this result in combination with spectroscopic, photometric and asteroseismic constraints to model this star with the CESAM code. One set of modeling parameters that reproduces the observations within their error bars are an age of 2314 Myr, an initial helium mass fraction Y_i = 0.301 and an initial mass ratio of heavy elements to hydrogen Z/X_i = 0.0314. We also computed the adiabatic oscillation spectrum of our model of Procyon A, giving a mean large frequency separation of Delta nu_0 = 54.7 microHz. This value is in agreement with the seismic observations by Martic et al. (1999, 2001). The interferometric diameter and the asteroseismic large frequency spacing together suggest a mass closer to 1.4 M_sun than to 1.5 M_sun. We conclude that Procyon is currently ending its life on the main sequence, as its luminosity class indicates.