Context. Asteroseismology allows us to probe stellar interiors. In the case of red giant stars, conditions in the stellar interior are such as to allow for the existence of mixed modes, consisting in ...a coupling between gravity waves in the radiative interior and pressure waves in the convective envelope. Mixed modes can thus be used to probe the physical conditions in red giant cores. However, we still need to identify the physical mechanisms that transport angular momentum inside red giants, leading to the slow-down observed for red giant core rotation. Thus large-scale measurements of red giant core rotation are of prime importance to obtain tighter constraints on the efficiency of the internal angular momentum transport, and to study how this efficiency changes with stellar parameters. Aims. This work aims at identifying the components of the rotational multiplets for dipole mixed modes in a large number of red giant oscillation spectra observed by Kepler. Such identification provides us with a direct measurement of the red giant mean core rotation. Methods. We compute stretched spectra that mimic the regular pattern of pure dipole gravity modes. Mixed modes with the same azimuthal order are expected to be almost equally spaced in stretched period, with a spacing equal to the pure dipole gravity mode period spacing. The departure from this regular pattern allows us to disentangle the various rotational components and therefore to determine the mean core rotation rates of red giants. Results. We automatically identify the rotational multiplet components of 1183 stars on the red giant branch with a success rate of 69% with respect to our initial sample. As no information on the internal rotation can be deduced for stars seen pole-on, we obtain mean core rotation measurements for 875 red giant branch stars. This large sample includes stars with a mass as large as 2.5 M⊙, allowing us to test the dependence of the core slow-down rate on the stellar mass. Conclusions. Disentangling rotational splittings from mixed modes is now possible in an automated way for stars on the red giant branch, even for the most complicated cases, where the rotational splittings exceed half the mixed-mode spacing. This work on a large sample allows us to refine previous measurements of the evolution of the mean core rotation on the red giant branch. Rather than a slight slow-down, our results suggest rotation is constant along the red giant branch, with values independent of the mass.
Period spacings in red giants Vrard, M; Mosser, B; Samadi, R
Astronomy and astrophysics (Berlin),
4/2016, Volume:
588
Journal Article
Peer reviewed
Context. 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. Aims. Since more than 15000 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. Methods. 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. Results. We automatically measured gravity period spacing for more than 6100 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. Conclusions. The delivery of thousands of period spacings combined with all other seismic and non-seismic information provides a new basis for detailed ensemble asteroseismology.
Context. The space mission Kepler provides us with long and uninterrupted photometric time series of red giants. We are now able to probe the rotational behaviour in their deep interiors using the ...observations of mixed modes. Aims. We aim to measure the rotational splittings in red giants and to derive scaling relations for rotation related to seismic and fundamental stellar parameters. Methods. We have developed a dedicated method for automated measurements of the rotational splittings in a large number of red giants. Ensemble asteroseismology, namely the examination of a large number of red giants at different stages of their evolution, allows us to derive global information on stellar evolution. Results. We have measured rotational splittings in a sample of about 300 red giants. We have also shown that these splittings are dominated by the core rotation. Under the assumption that a linear analysis can provide the rotational splitting, we observe a small increase of the core rotation of stars ascending the red giant branch. Alternatively, an important slow down is observed for red-clump stars compared to the red giant branch. We also show that, at fixed stellar radius, the specific angular momentum increases with increasing stellar mass. Conclusions. Ensemble asteroseismology indicates what has been indirectly suspected for a while: our interpretation of the observed rotational splittings leads to the conclusion that the mean core rotation significantly slows down during the red giant phase. The slow-down occurs in the last stages of the red giant branch. This spinning down explains, for instance, the long rotation periods measured in white dwarfs.
Context. With the space-borne missions CoRoT and Kepler, a large amount of asteroseismic data is now available and has led to a variety of work. So-called global oscillation parameters are inferred ...to characterize the large sets of stars, perform ensemble asteroseismology, and derive scaling relations. The mean large separation is such a key parameter, easily deduced from the radial-frequency differences in the observed oscillation spectrum and closely related to the mean stellar density. It is therefore crucial to measure it with the highest accuracy in order to obtain the most precise asteroseismic indices. Aims. As the conditions of measurement of the large separation do not coincide with its theoretical definition, we revisit the asymptotic expressions used for analyzing the observed oscillation spectra. Then, we examine the consequence of the difference between the observed and asymptotic values of the mean large separation. Methods. The analysis is focused on radial modes. We use series of radial-mode frequencies in published analyses of stars with solar-like oscillations to compare the asymptotic and observational values of the large separation. This comparison relies on the proper use of the second-order asymptotic expansion. Results. We propose a simple formulation to correct the observed value of the large separation and then derive its asymptotic counterpart. The measurement of the curvature of the radial ridges in the échelle diagram provides the correcting factor. 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, for low-mass, main-sequence stars, subgiants and red giants. Conclusions. 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 échelle diagrams used for analyzing 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, which provides more accurate asteroseismic estimates of the stellar mass and radius. After correction of the bias (6% for the stellar radius and 3% for the mass), the performance of the calibrated relation is about 4% and 8% for estimating, respectively, the stellar radius and the stellar mass for masses less than 1.3 M⊙; the accuracy is twice as bad for higher mass stars and red giants.
Context. CoRoT and Kepler observations of red giant stars revealed very rich spectra of non-radial solar-like oscillations. Of particular interest was the detection of mixed modes that exhibit ...significant amplitude, both in the core and at the surface of the stars. It opens the possibility of probing the internal structure from their innermost layers up to their surface throughout their evolution on the red giant branch, as well as on the red clump. Aims. Our objective is primarily to provide physical insight into the mechanism responsible for mixed-mode amplitudes and lifetimes. Subsequently, we aim at understanding the evolution and structure of red-giant spectra along with their evolution. The study of energetic aspects of these oscillations is also important for predicting the mode parameters in the power spectrum. Methods. Non-adiabatic computations, including a time-dependent treatment of convection, are performed and provide the lifetimes of radial and non-radial mixed modes. We then combine these mode lifetimes and inertias with a stochastic excitation model that gives us their heights in the power spectra. Results. For stars representative of CoRoT and Kepler observations, we show under which circumstances mixed modes have heights comparable to radial ones. We stress the importance of the radiative damping in determining the height of mixed modes. Finally, we derive an estimate for the height ratio between a g-type and a p-type mode. This can thus be used as a first estimate of the detectability of mixed modes.
The CoRoT and Kepler space-borne missions have provided us with a wealth of high-quality observational data that allows for seismic inferences of stellar interiors. This requires the computation of ...precise and accurate theoretical frequencies, but imperfect modeling of the uppermost stellar layers introduces systematic errors. To overcome this problem, an empirical correction has been introduced by Kjeldsen et al. and is now commonly used for seismic inferences. Our aim is to constrain the surface-effect corrections across the Hertzsprung-Russell (HR) diagram using a set of 3D hydrodynamical simulations. We used a grid of these simulations computed with the COsup 5 BOLD code to model the outer layers of solar-like stars. Upper layers of the corresponding 1D standard models were then replaced by the layers obtained from the horizontally averaged 3D models. Surface-effect corrections vary significantly across the HR diagram. Therefore, empirical relations like those by Kjeldsen et al. must not be calibrated on the Sun but should instead be constrained using realistic physical modeling as provided by 3D hydrodynamical simulations.
Asteroseismology based on observations from the space-borne missions CoRoT and Kepler provides a powerful means of testing the modeling of transport processes in stars. Rotational splittings are ...currently measured for a large number of red giant stars and can provide stringent constraints on the rotation profiles. The aim of this paper is to obtain a theoretical framework for understanding the properties of the observed rotational splittings of red giant stars with slowly rotating cores. This allows us to establish appropriate seismic diagnostics for the rotation of these evolved stars. Rotational splittings were computed for stochastically excited dipolar modes by adopting a first-order perturbative approach for two 1.3 M sub(bigodot) benchmark models that assume slowly rotating cores. For red giant stars with slowly rotating cores, we show that the variation in the rotational splittings of l = 1 modes with frequency depends only on the large frequency separation, the g-mode period spacing, and the ratio of the average envelope to core rotation rates (R). This led us to propose a way to infer directly R from the observations. This method is validated using the Kepler red giant star KIC 5356201. Finally, we provide theoretical support for using a Lorentzian profile to measure the observed splittings for red giant stars.
Context. The CoRoT and Kepler space-borne missions have provided us with a wealth of high-quality observational data that allows for seismic inferences of stellar interiors. This requires the ...computation of precise and accurate theoretical frequencies, but imperfect modeling of the uppermost stellar layers introduces systematic errors. To overcome this problem, an empirical correction has been introduced by Kjeldsen et al. (2008, ApJ, 683, L175) and is now commonly used for seismic inferences. Nevertheless, we still lack a physical justification allowing for the quantification of the surface-effect corrections. Aims. Our aim is to constrain the surface-effect corrections across the Hertzsprung-Russell (HR) diagram using a set of 3D hydrodynamical simulations. Methods. We used a grid of these simulations computed with the CO5BOLD code to model the outer layers of solar-like stars. Upper layers of the corresponding 1D standard models were then replaced by the layers obtained from the horizontally averaged 3D models. The frequency differences between these patched models and the 1D standard models were then calculated using the adiabatic approximation and allowed us to constrain the Kjeldsen et al. power law, as well as a Lorentzian formulation. Results. We find that the surface effects on modal frequencies depend significantly on both the effective temperature and the surface gravity. We further provide the variation in the parameters related to the surface-effect corrections using their power law as well as a Lorentzian formulation. Scaling relations between these parameters and the elevation (related to the Mach number) is also provided. The Lorentzian formulation is shown to be more robust for the whole frequency spectrum, while the power law is not suitable for the frequency shifts in the frequency range above νmax. Finally, we show that, owing to turbulent pressure, the elevation of the uppermost layers modifies the location of the hydrogen ionization zone and consequently introduces glitches in the surface effects for models with high (low) effective temperature (surface gravity). Conclusions. Surface-effect corrections vary significantly across the HR diagram. Therefore, empirical relations like those by Kjeldsen et al. must not be calibrated on the Sun but should instead be constrained using realistic physical modeling as provided by 3D hydrodynamical simulations.
Context. There are now more than 22 months of long-cadence data available for thousands of red giants observed with the Kepler space mission. Consequently, we are able to clearly resolve fine details ...in their oscillation spectra and see many components of the mixed modes that probe the stellar core. Aims. We report for the first time a parametric fit to the pattern of the ℓ = 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. Methods. 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 échelle diagrams to emphasize the detection of the gravity-dominated mixed modes. Results. 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 ℓ = 3 modes, of ℓ = 2 mixed modes, for the mode widths and amplitudes, and for the ℓ = 1 rotational splittings. Conclusions. 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.
Context. Asteroseismology is a unique tool that can be used to study the interior of stars and hence deliver unique information for the studiy of stellar physics, stellar evolution, and Galactic ...archaeology. Aims. We aim to develop a simple model of the information content of asteroseismology and to characterize the ability and precision with which fundamental properties of stars can be estimated for different space missions. Methods. We defined and calibrated metrics of the seismic performance. The metrics, expressed by a seismic index ℰ defined by simple scaling relations, are calculated for an ensemble of stars. We studied the relations between the properties of mission observations, fundamental stellar properties, and the performance index. We also defined thresholds for asteroseismic detection and measurement of different stellar properties. Results. We find two regimes of asteroseismic performance: the first where the signal strength is dominated by stellar properties and not by observational noise; and the second where observational properties dominate. Typically, for evolved stars, stellar properties provide the dominant terms in estimating the information content, while main sequence stars fall in the regime where the observational properties, especially stellar magnitude, dominate. We estimate scaling relations to predict ℰ with an intrinsic scatter of around 21%. Incidentally, the metrics allow us to distinguish stars burning either hydrogen or helium. Conclusions. Our predictions will help identify the nature of the cohort of existing and future asteroseismic observations. In addition, the predicted performance for PLATO will help define optimal observing strategies for defined scientific goals.
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