M. J. Goupil

Gravity modes as a way to distinguish between hydrogen- and helium-burning red giant stars

Red giants are evolved stars that have exhausted the supply of hydrogen in their cores and instead burn hydrogen in a surrounding shell. Once a red giant is sufficiently evolved, the helium in the core also undergoes fusion. Outstanding issues in our understanding of red giants include uncertainties in the amount of mass lost at the surface before helium ignition and the amount of internal mixing from rotation and other processes. Progress is hampered by our inability to distinguish between red giants burning helium in the core and those still only burning hydrogen in a shell. Asteroseismology offers a way forward, being a powerful tool for probing the internal structures of stars using their natural oscillation frequencies. Here we report observations of gravity-mode period spacings in red giants that permit a distinction between evolutionary stages to be made. We use high-precision photometry obtained by the Kepler spacecraft over more than a year to measure oscillations in several hundred red giants. We find many stars whose dipole modes show sequences with approximately regular period spacings. These stars fall into two clear groups, allowing us to distinguish unambiguously between hydrogen-shell-burning stars (period spacing mostly ∼50 seconds) and those that are also burning helium (period spacing ∼100 to 300 seconds).

SEISMIC EVIDENCE FOR A RAPIDLY ROTATING CORE IN A LOWER-GIANT-BRANCH STAR OBSERVED WITH KEPLER

Rotation is expected to have an important influence on the structure and the evolution of stars. However, the mechanisms of angular momentum transport in stars remain theoretically uncertain and very complex to take into account in stellar models. To achieve a better understanding of these processes, we desperately need observational constraints on the internal rotation of stars, which until very recently was restricted to the Sun. In this paper, we report the detection of mixed modes—i.e., modes that behave both as g modes in the core and as p modes in the envelope—in the spectrum of the early red giant KIC 7341231, which was observed during one year with the Kepler spacecraft. By performing an analysis of the oscillation spectrum of the star, we show that its non-radial modes are clearly split by stellar rotation and we are able to determine precisely the rotational splittings of 18 modes. We then find a stellar model that reproduces very well the observed atmospheric and seismic properties of the star. We use this model to perform inversions of the internal rotation profile of the star, which enables us to show that the core of the star is rotating at least five times faster than the envelope. This will shed new light on the processes of transport of angular momentum in stars. In particular, this result can be used to place constraints on the angular momentum coupling between the core and the envelope of early red giants, which could help us discriminate between the theories that have been proposed over the last few decades.

Spin down of the core rotation in red giants

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.

CoRoT measures solar-like oscillations and granulation in stars hotter than the Sun.

Oscillations of the Sun have been used to understand its interior structure. The extension of similar studies to more distant stars has raised many difficulties despite the strong efforts of the international community over the past decades. The CoRoT (Convection Rotation and Planetary Transits) satellite, launched in December 2006, has now measured oscillations and the stellar granulation signature in three main sequence stars that are noticeably hotter than the sun. The oscillation amplitudes are about 1.5 times as large as those in the Sun; the stellar granulation is up to three times as high. The stellar amplitudes are about 25% below the theoretic values, providing a measurement of the nonadiabaticity of the process ruling the oscillations in the outer layers of the stars.

Solar-like Oscillations in Low-luminosity Red Giants: First Results from Kepler

We have measured solar-like oscillations in red giants using time-series photometry from the first 34 days of science operations of the Kepler Mission. The light curves, obtained with 30 minute sampling, reveal clear oscillations in a large sample of G and K giants, extending in luminosity from the red clump down to the bottom of the giant branch. We confirm a strong correlation between the large separation of the oscillations (Δν) and the frequency of maximum power (νmax). We focus on a sample of 50 low-luminosity stars (νmax > 100 μHz, L <~ 30 L sun) having high signal-to-noise ratios and showing the unambiguous signature of solar-like oscillations. These are H-shell-burning stars, whose oscillations should be valuable for testing models of stellar evolution and for constraining the star formation rate in the local disk. We use a new technique to compare stars on a single echelle diagram by scaling their frequencies and find well-defined ridges corresponding to radial and non-radial oscillations, including clear evidence for modes with angular degree l = 3. Measuring the small separation between l = 0 and l = 2 allows us to plot the so-called C-D diagram of δν02 versus Δν. The small separation δν01 of l = 1 from the midpoint of adjacent l = 0 modes is negative, contrary to the Sun and solar-type stars. The ridge for l = 1 is notably broadened, which we attribute to mixed modes, confirming theoretical predictions for low-luminosity giants. Overall, the results demonstrate the tremendous potential of Kepler data for asteroseismology of red giants.

The underlying physical meaning of the νmax νc relation

Asteroseismology of stars that exhibit solar-like oscillations are enjoying a growing interest with the wealth of observational results obtained with the CoRoT and Kepler missions. In this framework, scaling laws between asteroseismic quantities and stellar parameters are becoming essential tools to study a rich variety of stars. However, the physical underlying mechanisms of those scaling laws are still poorly known. Our objective is to provide a theoretical basis for the scaling between the frequency of the maximum in the power spectrum (νmax) of solar-like oscillations and the cut-off frequency (νc). Using the SoHO GOLF observations together with theoretical considerations, we first confirm that the maximum of the height in oscillation power spectrum is determined by the so-called plateau of the damping rates. The physical origin of the plateau can be traced to the destabilizing effect of the Lagrangian perturbation of entropy in the upper-most layers, which becomes important when the modal period and the local thermal relaxation time-scale are comparable. Based on this analysis, we then find a linear relation between νmax and νc, with a coefficient that depends on the ratio of the Mach number of the exciting turbulence to the third power to the mixing-length parameter.

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

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 � = 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 echelle 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 � = 3 modes, of � = 2 mixed modes, for the mode widths and amplitudes, and for the � = 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.

Seismic constraints on the radial dependence of the internal rotation profiles of six Kepler subgiants and young red giants

Context. We still do not understand which physical mechanisms are responsible for the transport of angular momentum inside stars. The recent detection of mixed modes that contain the clear signature of rotation in the spectra of Kepler subgiants and red giants gives us the opportunity to make progress on this question.Aims. Our aim is to probe the radial dependence of the rotation profiles for a sample of Kepler targets. For this purpose, subgiants and early red giants are particularly interesting targets because their rotational splittings are more sensitive to the rotation outside the deeper core than is the case for their more evolved counterparts.Methods. We first extracted the rotational splittings and frequencies of the modes for six young Kepler red giants. We then performed a seismic modeling of these stars using the evolutionary codes Cesam2k and astec. By using the observed splittings and the rotational kernels of the optimal models, we inverted the internal rotation profiles of the six stars.Results. We obtain estimates of the core rotation rates for these stars, and upper limits to the rotation in their convective envelope. We show that the rotation contrast between the core and the envelope increases during the subgiant branch. Our results also suggest that the core of subgiants spins up with time, while their envelope spins down. For two of the stars, we show that a discontinuous rotation profile with a deep discontinuity reproduces the observed splittings significantly better than a smooth rotation profile. Interestingly, the depths that are found to be most probable for the discontinuities roughly coincide with the location of the H-burning shell, which separates the layers that contract from those that expand.Conclusions. We characterized the differential rotation pattern of six young giants with a range of metallicities, and with both radiative and convective cores on the main sequence. This will bring observational constraints to the scenarios of angular momentum transport in stars. Moreover, if the existence of sharp gradients in the rotation profiles of young red giants is confirmed, it is expected to help in distinguishing between the physical processes that could transport angular momentum in the subgiant and red giant branches.

Mixed modes in red-giant stars observed with CoRoT

Context. The CoRoT mission has provided thousands of red-giant light curves. The analysis of their solar-like oscillations allows us to characterize their stellar properties. Aims. Up to now, the global seismic parameters of the pressure modes have been unable to distinguish red-clump giants from members of the red-giant branch. As recently done with Kepler red giants, we intend to analyze and use the so-called mixed modes to determine the evolutionary status of the red giants observed with CoRoT. We also aim at deriving different seismic characteristics depending on evolution. Methods. The complete identification of the pressure eigenmodes provided by the red-giant universal oscillation pattern allows us to aim at the mixed modes surrounding the l = 1 expected eigenfrequencies. A dedicated method based on the envelope autocorrelation function is proposed to analyze their period separation. Results. We have identified the mixed-mode signature separation thanks to their pattern that is compatible with the asymptotic law of gravity modes. We have shown that, independent of any modeling, the g-mode spacings help to distinguish the evolutionary status of a red-giant star. We then report the different seismic and fundamental properties of the stars, depending on their evolutionary status. In particular, we show that high-mass stars of the secondary clump present very specific seismic properties. We emphasize that stars belonging to the clump were affected by significant mass loss. We also note significant population and/or evolution differences in the different fields observed by CoRoT.

Characterization of the power excess of solar-like oscillations in red giants with Kepler

Context. The space mission Kepler provides us with long and uninterrupted photometric time series of red giants. This allows us to examine their seismic global properties and to compare these with theoretical predictions. Aims. We aim to describe the oscillation power excess observed in red giant oscillation spectra with global seismic parameters, and to investigate empirical scaling relations governing these parameters. From these scalings relations, we derive new physical properties of red giant oscillations. Methods. Various different methods were compared in order to validate the processes and to derive reliable output values. For consistency, a single method was then used to determine scaling relations for the relevant global asteroseismic parameters: mean mode height, mean height of the background signal superimposed on the oscillation power excess, width of the power excess, bolometric amplitude of the radial modes and visibility of non-radial modes. A method for deriving oscillation amplitudes is proposed, which relies on the complete identification of the red giant oscillation spectrum. Results. The comparison of the different methods has shown the important role of the way the background is modelled. The convergence reached by the collaborative work enables us to derive significant results concerning the oscillation power excess. We obtain several scaling relations, and identify the influence of the stellar mass and the evolutionary status. The effect of helium burning on the red giant interior structure is confirmed: it yields a strong mass-radius relation for clump stars. We find that none of the amplitude scaling relations motivated by physical considerations predict the observed mode amplitudes of red giant stars. In parallel, the degree-dependent mode visibility exhibits important variations. Both effects seem related to the significant influence of the high mode mass of non-radial mixed modes. A family of red giants with very weak dipole modes is identified, and its properties are analyzed. Conclusions. The clear correlation between the power densities of the background signal and of the stellar oscillation induces important consequences to be considered for deriving a reliable theoretical relation of the mode amplitude. As a by-product of this work, we have verified that red giant asteroseismology delivers new insights for stellar and Galactic physics, given the evidence for mass loss at the tip of the red giant branch.