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Register a new userProbing the core structure and evolution of red giants using gravity-dominated mixed modes observed with Kepler
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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.
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When the core hydrogen is exhausted during stellar evolution, the central region of a star contracts and the outer envelope expands and cools, giving rise to a red giant, in which convection occupies a large fraction of the star. Conservation of angular momentum requires that the cores of these stars rotate faster than their envelopes, and indirect evidence supports this. Information about the angular momentum distribution is inaccessible to direct observations, but it can be extracted from the effect of rotation on oscillation modes that probe the stellar interior. Here, we report the detection of non-rigid rotation in the interiors of red-giant stars by exploiting the rotational frequency splitting of recently detected mixed modes. We demonstrate an increasing rotation rate from the surface of the star to the stellar core. Comparing with theoretical stellar models, we conclude that the core must rotate at least ten times faster than the surface. This observational result confirms the theoretical prediction of a steep gradient in the rotation profile towards the deep stellar interior.
Dipole mixed pulsation modes of consecutive radial order have been detected for thousands of low-mass red-giant stars with the NASA space telescope Kepler. Such modes have the potential to reveal information on the physics of the deep stellar interior. Different methods have been proposed to derive an observed value for the gravity-mode period spacing, the most prominent one relying on a relation derived from asymptotic pulsation theory applied to the gravity-mode character of the mixed modes. Our aim is to compare results based on this asymptotic relation with those derived from an empirical approach for three pulsating red-giant stars. We developed a data-driven method to perform frequency extraction and mode identification. Next, we used the identified dipole mixed modes to determine the gravity-mode period spacing by means of an empirical method and by means of the asymptotic relation. In our methodology, we consider the phase offset, $epsilon_{mathrm{g}}$, of the asymptotic relation as a free parameter. Using the frequencies of the identified dipole mixed modes for each star in the sample, we derived a value for the gravity-mode period spacing using the two different methods. These differ by less than 5%. The average precision we achieved for the period spacing derived from the asymptotic relation is better than 1%, while that of our data-driven approach is 3%. Good agreement is found between values for the period spacing derived from the asymptotic relation and from the empirical method. Full abstract in PDF file.
Turbulent motions in the convective envelope of red giants excite a rich spectrum of solar-like oscillation modes. Observations by CoRoT and Kepler have shown that the mode amplitudes increase dramatically as the stars ascend the red giant branch, i.e., as the frequency of maximum power, $ u_mathrm{max}$, decreases. Most studies nonetheless assume that the modes are well described by the linearized fluid equations. We investigate to what extent the linear approximation is justified as a function of stellar mass $M$ and $ u_mathrm{max}$, focusing on dipole mixed modes with frequency near $ u_mathrm{max}$. A useful measure of a modes nonlinearity is the product of its radial wavenumber and its radial displacement, $k_r xi_r$ (i.e., its shear). We show that $k_r xi_r propto u_mathrm{max}^{-9/2}$, implying that the nonlinearity of mixed modes increases significantly as a star evolves. The modes are weakly nonlinear ($k_r xi_r > 10^{-3}$) for $ u_mathrm{max} lesssim 150 , mumathrm{Hz}$ and strongly nonlinear ($k_r xi_r > 1$) for $ u_mathrm{max} lesssim 30 , mumathrm{Hz}$, with only a mild dependence on $M$ over the range we consider ($1.0 - 2.0 M_odot$). A weakly nonlinear mixed mode can excite secondary waves in the stellar core through the parametric instability, resulting in enhanced, but partial, damping of the mode. By contrast, a strongly nonlinear mode breaks as it propagates through the core and is fully damped there. Evaluating the impact of nonlinear effects on observables such as mode amplitudes and linewidths requires large mode network simulations. We plan to carry out such calculations in the future and investigate whether nonlinear damping can explain why some red giants exhibit dipole modes with unusually small amplitudes, known as depressed modes.
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.
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.
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