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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.
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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.
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.
The power of asteroseismology relies on the capability of global oscillations to infer the stellar structure. For evolved stars, we benefit from unique information directly carried out by mixed modes that probe their radiative cores. This third article of the series devoted to mixed modes in red giants focuses on their coupling factors that remained largely unexploited up to now. With the measurement of the coupling factors, we intend to give physical constraints on the regions surrounding the radiative core and the hydrogen-burning shell of subgiants and red giants. A new method for measuring the coupling factor of mixed modes is set up. It is derived from the method recently implemented for measuring period spacings. It runs in an automated way so that it can be applied to a large sample of stars. Coupling factors of mixed modes were measured for thousands of red giants. They show specific variation with mass and evolutionary stage. Weak coupling is observed for the most evolved stars on the red giant branch only; large coupling factors are measured at the transition between subgiants and red giants, as well as in the red clump. The measurement of coupling factors in dipole mixed modes provides a new insight into the inner interior structure of evolved stars. While the large frequency separation and the asymptotic period spacings probe the envelope and the core, respectively, the coupling factor is directly sensitive to the intermediate region in between and helps determining its extent. Observationally, the determination of the coupling factor is a prior to precise fits of the mixed-mode pattern, and can now be used to address further properties of the mixed-mode pattern, as the signature of the buoyancy glitches and the core rotation.
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W. A. Dziembowski (Warsaw University Observatory
, Copernicusn Astronomical Center
, Warsaw
2012
Lots of information on solar-like oscillations in red giants has been obtained thanks to observations with CoRoT and Kepler space telescopes. Data on dipolar modes appear most interesting. We study properties of dipolar oscillations in luminous red giants to explain mechanism of mode trapping in the convective envelope and to assess what may be learned from the new data. Equations for adiabatic oscillations are solved by numerical integration down to the bottom of convective envelope, where the boundary condition is applied. The condition is based on asymptotic decomposition of the fourth order system into components describing a running wave and a uniform shift of radiative core. If the luminosity of a red giant is sufficiently high, for instance at M = 2 Msun greater than about 100 Lsun, the dipolar modes become effectively trapped in the acoustic cavity, which covers the outer part of convective envelope. Energy loss caused by gravity wave emission at the envelope base is a secondary or negligible source of damping. Frequencies are insensitive to structure of the deep interior.
The detection of mixed modes in subgiants and red giants by the CoRoT and emph{Kepler} space-borne missions allows us to investigate the internal structure of evolved low-mass stars. In particular, the measurement of the mean core rotation rate as a function of the evolution places stringent constraints on the physical mechanisms responsible for the angular momentum redistribution in stars. It showed that the current stellar evolution codes including the modelling of rotation fail to reproduce the observations. An additional physical process that efficiently extracts angular momentum from the core is thus necessary. Our aim is to assess the ability of mixed modes to do this. To this end, we developed a formalism that provides a modelling of the wave fluxes in both the mean angular momentum and the mean energy equations in a companion paper. In this article, mode amplitudes are modelled based on recent asteroseismic observations, and a quantitative estimate of the angular momentum transfer is obtained. This is performed for a benchmark model of 1.3 $M_{odot}$ at three evolutionary stages, representative of the evolved pulsating stars observed by CoRoT and Kepler. We show that mixed modes extract angular momentum from the innermost regions of subgiants and red giants. However, this transport of angular momentum from the core is unlikely to counterbalance the effect of the core contraction in subgiants and early red giants. In contrast, for more evolved red giants, mixed modes are found efficient enough to balance and exceed the effect of the core contraction, in particular in the hydrogen-burning shell. Our results thus indicate that mixed modes are a promising candidate to explain the observed spin-down of the core of evolved red giants, but that an other mechanism is to be invoked for subgiants and early red giants.
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