By considering stellar models with the same interior structure but different outer layers we demonstrate that the ratio of the small to large separations of acoustic oscillations in solar-like stars ...is essentially independent of the structure of the outer layers, and is determined solely by the interior structure. Defining the scaled Eulerian pressure perturbation $\psi_\ell(\omega,t) = r p' /(\rho c)^{1/2}$ we define the internal phase shift $\delta_\ell(\omega,t)$ through the relation $\omega\psi/({\rm d}\psi/{\rm d}t)=\tan(\omega t -\pi\ell/2 + \delta_\ell)$. The $\delta_\ell$ are almost independent of acoustic radius $t=\int {\rm d}r/c$ outside the stellar core and can be determined as a continuous functions of ω from partial wave solutions for the interior – that is solutions of the oscillation equations for any ω that satisfy the Laplace boundary condition at a sufficiently large acoustic radius tf outside the stellar core. If the ω are eigenfrequencies then they satisfy the Eigenfrequency Equation $\omega T=(n+\ell/2) \pi+\alpha(\omega)-\delta_\ell(\omega)$ where $\alpha(\omega)$ is the $\ell$ independent surface phase shift (Roxburgh & Vorontsov 2000). Using this result we show that the ratio of small to large separations is determined to high accuracy solely by the internal phase shifts $\delta_\ell(\omega)$ and hence by the interior structure alone. The error in this result is estimated and shown to be smaller than that associated with the errors in the determination of the frequencies (≈0.1–0.3 μHz) from the upcoming space missions MOST, COROT and Eddington.
With four years of nearly continuous photometry from Kepler, we are finally in a good position to apply asteroseismology to ... Doradus stars. In particular, several analyses have demonstrated the ...possibility to detect non-uniform period spacings, which have been predicted to be directly related to rotation. In this paper, we define a new seismic diagnostic for rotation in ... Doradus stars which are too rapidly rotating to present rotational splittings. Based on the non-uniformity of their period spacings, we define the observable S as the slope of the period spacing when plotted as a function of period. We provide a one-to-one relation between this observable S and the internal rotation, which applies widely in the instability strip of ... Doradus stars. We apply the diagnostic to a handful of stars observed by Kepler. Thanks to g modes in ... Doradus stars, we are now able to determine the internal rotation of stars on the lower main sequence, which is still not possible for Sun-like stars. (ProQuest: ... denotes formulae/symbols omitted.)
Context. The first asteroseismology results from CoRoT are presented, on a star showing Sun-like oscillations. We have analyzed a 60 day lightcurve of high-quality photometric data collected by CoRoT ...on the F5 V star HD 49933. The data reveal a rich spectrum of overtones of low-degree p modes. Aims. Our aim was to extract robust estimates of the key parameters of the p modes observed in the power spectrum of the lightcurve. Methods. Estimation of the mode parameters was performed using maximum likelihood estimation of the power spectrum. A global fitting strategy was adopted whereby 15 mode orders of the mode spectrum (45 modes) were fitted simultaneously. Results. The parameter estimates that we list include mode frequencies, peak linewidths, mode amplitudes, and a mean rotational frequency splitting. We find that the average large frequency (overtone) spacing derived from the fitted mode frequencies is 85.9 ± 0.15 μHz. The frequency of maximum amplitude of the radial modes is at 1760 μHz, where the observed rms mode amplitude is 3.75 ± 0.23 ppm. The mean rotational splitting of the non-radial modes appears to be in the range ≈2.7 μHz to ≈3.4 μHz. The angle of inclination offered by the star, as determined by fits to the amplitude ratios of the modes, appears to be in the range ≈50 degrees to ≈62 degrees.
We present a detailed spectroscopic study of 93 solar-type stars that are targets of the NASA/Kepler mission and provide detailed chemical composition of each target. We find that the overall ...metallicity is well represented by Fe lines. Relative abundances of light elements (CNO) and α elements are generally higher for low-metallicity stars. Our spectroscopic analysis benefits from the accurately measured surface gravity from the asteroseismic analysis of the Kepler light curves. The accuracy on the log g parameter is better than 0.03 dex and is held fixed in the analysis. We compare our T
eff determination with a recent colour calibration of V
T−K
S TYCHO V magnitude minus Two Micron All Sky Survey (2MASS) K
S magnitude and find very good agreement and a scatter of only 80 K, showing that for other nearby Kepler targets, this index can be used. The asteroseismic log g values agree very well with the classical determination using Fe i-Fe ii balance, although we find a small systematic offset of 0.08 dex (asteroseismic log g values are lower). The abundance patterns of metals, α elements and the light elements (CNO) show that a simple scaling by Fe/H is adequate to represent the metallicity of the stars, except for the stars with metallicity below −0.3, where α-enhancement becomes important. However, this is only important for a very small fraction of the Kepler sample. We therefore recommend that a simple scaling with Fe/H be employed in the asteroseismic analyses of large ensembles of solar-type stars.
ABSTRACT
Asteroseismology is a powerful tool to infer fundamental stellar properties. The use of these asteroseismic-inferred properties in a growing number of astrophysical contexts makes it vital ...to understand their accuracy. Consequently, we performed a hare-and-hounds exercise where the hares simulated data for six artificial main-sequence stars and the hounds inferred their properties based on different inference procedures. To mimic a pipeline such as that planned for the PLATO mission, all hounds used the same model grid. Some stars were simulated using the physics adopted in the grid, others a different one. The maximum relative differences found (in absolute value) between the inferred and true values of the mass, radius, and age were 4.32, 1.33, and 11.25 per cent, respectively. The largest systematic differences in radius and age were found for a star simulated assuming gravitational settling, not accounted for in the model grid, with biases of −0.88 per cent (radius) and 8.66 per cent (age). For the mass, the most significant bias (−3.16 per cent) was found for a star with a helium enrichment ratio outside the grid range. Moreover, an ∼7 per cent dispersion in age was found when adopting different prescriptions for the surface corrections or shifting the classical observations by ±1σ. The choice of the relative weight given to the classical and seismic constraints also impacted significantly the accuracy and precision of the results. Interestingly, only a few frequencies were required to achieve accurate results on the mass and radius. For the age the same was true when at least one l = 2 mode was considered.
Aims. This paper investigates the diagnostic potential of narrow, frequency-windowed autocorrelation as a tool for probing the properties of solar-like oscillating stars when the determination of ...individual frequencies is impossible or is subject to large uncertainties, and when mode identification is difficult. Methods. I use theoretical analysis including phase-shifts, modelling, and data analysis. Results. Narrow-windowed autocorrelation of a time series can reveal the variation with frequency of the large separations $\Delta(\nu)$ and the half large separations $\Delta_{01}, \Delta_{10}$, thus helping with mode identification. This technique is applied to the CoRoT p-mode oscillators HD 49933, HD 175726, HD 181420, and HD 181906. Theoretical analysis and modelling are presented to illustrate the technique.
In previous papers we showed that the ratios of the small to large separations of acoustic oscillations in solar-like stars are approximately independent of the structure of the outer layers, and are ...therefore diagnostics of the interior structure alone. Here we present similar results for a range stellar models of mass $0.8, 1.0, 1.2, 1.5, 2, 10~ M_\odot$, all of which show this same property.
Context. The star HD 49385 is the first G-type solar-like pulsator observed in the seismology field of the space telescope CoRoT. The satellite collected 137 days of high-precision photometric data ...on this star, confirming that it presents solar-like oscillations. HD 49385 was also observed in spectroscopy with the NARVAL spectrograph in January 2009. Aims. Our goal is to characterize HD 49385 using both spectroscopic and seismic data. Methods. The fundamental stellar parameters of HD 49385 are derived with the semi-automatic software VWA, and the projected rotational velocity is estimated by fitting synthetic profiles to isolated lines in the observed spectrum. A maximum likelihood estimation is used to determine the parameters of the observed p modes. We perform a global fit, in which modes are fitted simultaneously over nine radial orders, with degrees ranging from $\ell$ = 0 to $\ell$ = 3 (36 individual modes). Results. Precise estimates of the atmospheric parameters (Teff, M/H, log g) and of the ν sin i of HD 49385 are obtained. The seismic analysis of the star leads to a clear identification of the modes for degrees $\ell$ = 0,1,2. Around the maximum of the signal (ν $\simeq$ 1013 μHz), some peaks are found significant and compatible with the expected characteristics of $\ell$ = 3 modes. Our fit yields robust estimates of the frequencies, linewidths and amplitudes of the modes. We find amplitudes of ~5.6 ± 0.8 ppm for radial modes at the maximum of the signal. The lifetimes of the modes range from one day (at high frequency) to a bit more than two days (at low frequency). Significant peaks are found outside the identified ridges and are fitted. They are attributed to mixed modes.
Aims: We investigate the diagnostic potential of l = 0,1 p-modes and the origin of the periodicity in their small separations. Methods: We used theoretical analysis, phase-shifts, modelling. and data ...analysis. Results: The periodicity in the small separations between modes of l = 0, 1 is determined by the acoustic radius of the base of the outer convective envelope. The mean variation is determined primarily by the structure of the inner core. The separations are related to the inner phase shifts differences delta_1-delta0 which we show can be determined directly from the frequencies. The modulation period is shifted slightly by the frequency dependence of the phase shifts and the amplitudes. We present results using data from the BiSON, IRIS, and GOLF experiments, and a solar model, all of which give a modulation period of ~359±5 muHz corresponding to an acoustic radius ~1422±20 s.
Context. Solar-like oscillations have now been observed in several stars, thanks to ground-based spectroscopic observations and space-borne photometry. CoRoT, which has been in orbit since December ...2006, has observed the star HD49933 twice. The oscillation spectrum of this star has proven difficult to interpret. Aims. Thanks to a new timeseries provided by CoRoT, we aim to provide a robust description of the oscillations in HD49933, i.e., to identify the degrees of the observed modes, and to measure mode frequencies, widths, amplitudes and the average rotational splitting. Methods. Several methods were used to model the Fourier spectrum: Maximum Likelihood Estimators and Bayesian analysis using Markov Chain Monte-Carlo techniques. Results. The different methods yield consistent result, and allow us to make a robust identification of the modes and to extract precise mode parameters. Only the rotational splitting remains difficult to estimate precisely, but is clearly relatively large (several μHz in size).
PDF
